gsl-1.0.8/0000755000175000017500000000000011201031723010101 5ustar shshgsl-1.0.8/DESCRIPTION0000644000175000017500000000065411201030403011606 0ustar shshName: GSL Version: 1.0.8 Date: 2009-05-03 Author: Teemu Ikonen Maintainer: Teemu Ikonen Title: GNU Scientific Library. Description: Octave bindings to the GNU Scientific Library Depends: octave (>= 2.9.7) Autoload: yes BuildRequires: gsl-devel License: GPL version 2 or later Url: http://octave.sf.net # Version 1.0.5 -> Version 1.0.6 Ray Rogers rrogers@@plaidheron.com gsl-1.0.8/inst/0000755000175000017500000000000011201031723011056 5ustar shshgsl-1.0.8/inst/test_sf.c0000644000175000017500000046013711201030403012676 0ustar shsh/* specfunc/test_sf.c * * Copyright (C) 2007 Brian Gough * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2004 Gerard Jungman * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 3 of the License, or (at * your option) any later version. * * This program is distributed in the hope that it will be useful, but * WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */ /* Author: G. Jungman */ #include #include #include #include #include #include #include #include #include #include "test_sf.h" double test_sf_frac_diff(double x1, double x2) { if(x1 == 0.0 && x2 == 0.0) { return 0.0; } else if (x1 == 0.0) { return fabs(x2); } else if(x1 <= DBL_MAX && x2 <= DBL_MAX && (x1 + x2 != 0.0)) { return fabs((x1-x2)/(x1+x2)); } else { return 1.0; } } /* Check a result against a given value and tolerance. */ int test_sf_check_result(char * message_buff, gsl_sf_result r, double val, double tol) { int s = 0; double f = 0, d = 0; if (gsl_isnan(r.val) || gsl_isnan(val)) { s = (gsl_isnan(r.val) != gsl_isnan(val)) ? TEST_SF_INCONS : s; } else if (gsl_isinf(r.val) || gsl_isinf(val)) { s = (gsl_isinf(r.val) != gsl_isinf(val)) ? TEST_SF_INCONS : s; } else { f = test_sf_frac_diff(val, r.val); d = fabs(val - r.val); if(d > 2.0 * TEST_SIGMA * r.err) s |= TEST_SF_INCONS; if(r.err < 0.0) s |= TEST_SF_ERRNEG; if(gsl_isinf(r.err)) s |= TEST_SF_ERRBAD; #if TEST_EXCESSIVE_ERROR if(d > 0 && r.err > 1e4 * fabs(val)*tol) s |= TEST_SF_ERRBIG; #endif if(f > TEST_FACTOR * tol) s |= TEST_SF_TOLBAD; } if(s != 0) { char buff[2048]; sprintf(buff, " expected: %20.16e\n", val); strcat(message_buff, buff); sprintf(buff, " obtained: %20.16e +/- %.16e (rel=%g)\n", r.val, r.err, r.err/(fabs(r.val) + r.err)); strcat(message_buff, buff); sprintf(buff, " fracdiff: %20.16e\n", f); strcat(message_buff, buff); sprintf(buff, " tolerance: %20.16e\n", tol); strcat(message_buff, buff); } if(s & TEST_SF_INCONS) { strcat(message_buff, " value/expected not consistent within reported error\n"); } if(s & TEST_SF_ERRNEG) { strcat(message_buff, " reported error negative\n"); } if(s & TEST_SF_ERRBAD) { strcat(message_buff, " reported error is bad\n"); } if(s & TEST_SF_ERRBIG) { strcat(message_buff, " reported error is much too big\n"); } if(s & TEST_SF_TOLBAD) { strcat(message_buff, " value not within tolerance of expected value\n"); } return s; } /* Check a result against a given value and tolerance. */ int test_sf_check_e10(char * message_buff, int e10, int e10_in) { int s = 0; if (e10 != e10_in) { s = TEST_SF_EXPBAD; } if(s != 0) { char buff[2048]; sprintf(buff, " expected exponent: 10^%d\n", e10_in); strcat(message_buff, buff); sprintf(buff, " obtained exponent: 10^%d", e10); strcat(message_buff, buff); } if(s & TEST_SF_EXPBAD) { strcat(message_buff, " exponent is incorrect\n"); } return s; } int test_sf_check_val(char * message_buff, double rval, double val, double tol) { int s = 0; double f = test_sf_frac_diff(val, rval); if(f > TEST_FACTOR * tol) s |= TEST_SF_TOLBAD; if(s != 0) { char buff[2048]; sprintf(buff, " expected: %20.16e\n", val); strcat(message_buff, buff); sprintf(buff, " obtained: %20.16e\n", rval); strcat(message_buff, buff); sprintf(buff, " fracdiff: %20.16e\n", f); strcat(message_buff, buff); } if(s & TEST_SF_TOLBAD) { strcat(message_buff, " value not within tolerance of expected value\n"); } return s; } /* Relax the condition on the agreement and on the usefulness * of the error estimate. */ int test_sf_check_result_relax(char * message_buff, gsl_sf_result r, double val, double tol) { int s = 0; double f = test_sf_frac_diff(val, r.val); if(f > GSL_MAX_DBL(TEST_SNGL, TEST_FACTOR * tol)) s |= TEST_SF_INCONS; if(r.err < 0.0) s |= TEST_SF_ERRNEG; if(gsl_isinf(r.err)) s |= TEST_SF_ERRBAD; if(f > TEST_FACTOR * tol) s |= TEST_SF_TOLBAD; if(s != 0) { char buff[2048]; sprintf(buff, " expected: %20.16e\n", val); strcat(message_buff, buff); sprintf(buff, " obtained: %20.16e +/- %.16e (rel=%g)\n", r.val, r.err, r.err/(fabs(r.val) + r.err)); strcat(message_buff, buff); sprintf(buff, " fracdiff: %20.16e\n", f); strcat(message_buff, buff); } if(s & TEST_SF_INCONS) { strcat(message_buff, " value/expected not consistent MAX(tol,SINGLE_PREC)\n"); } if(s & TEST_SF_ERRNEG) { strcat(message_buff, " reported error negative\n"); } if(s & TEST_SF_ERRBAD) { strcat(message_buff, " reported error is bad\n"); } if(s & TEST_SF_TOLBAD) { strcat(message_buff, " value not within tolerance of expected value\n"); } return s; } /* Check a return value. */ int test_sf_check_return(char * message_buff, int val_return, int expected_return) { if(val_return != expected_return) { char buff[256]; sprintf(buff, " unexpected return code: %d\n", val_return); strcat(message_buff, buff); return TEST_SF_RETBAD; } else { return 0; } } int test_sf (gsl_sf_result r, double val_in, double tol, int status, int expect_return, const char * desc) { char message_buff[4096]; int local_s = 0; message_buff[0] = '\0'; local_s |= test_sf_check_result(message_buff, r, val_in, tol); local_s |= test_sf_check_return(message_buff, status, expect_return); gsl_test(local_s, desc); if(local_s != 0) { /* printf(" %s %d\n", __FILE__, __LINE__); */ printf("%s", message_buff); printf(" %22.18e %22.18e\n", r.val, r.err); } return local_s; } int test_sf_e10 (gsl_sf_result_e10 re, double val_in, int e10_in, double tol, int status, int expect_return, const char * desc) { char message_buff[4096]; int local_s = 0; gsl_sf_result r; r.val = re.val; r.err = re.err; message_buff[0] = '\0'; local_s |= test_sf_check_result(message_buff, r, val_in, tol); local_s |= test_sf_check_e10(message_buff, re.e10, e10_in); local_s |= test_sf_check_return(message_buff, status, expect_return); gsl_test(local_s, desc); if(local_s != 0) { /* printf(" %s %d\n", __FILE__, __LINE__); */ printf("%s", message_buff); printf(" %22.18e %22.18e 10^%d\n", re.val, re.err, re.e10); } return local_s; } int test_sf_val (double val, double val_in, double tol, const char * desc) { char message_buff[4096]; int local_s = 0; message_buff[0] = '\0'; local_s |= test_sf_check_val(message_buff, val, val_in, tol); gsl_test(local_s, desc); if(local_s != 0) { /* printf(" %s %d\n", __FILE__, __LINE__); */ printf("%s", message_buff); printf(" %22.18e\n", val); } return local_s; } int test_sf_rlx (gsl_sf_result r, double val_in, double tol, int status, int expect_return, const char * desc) { char message_buff[4096]; int local_s = 0; message_buff[0] = '\0'; local_s |= test_sf_check_result_relax(message_buff, r, val_in, tol); local_s |= test_sf_check_return(message_buff, status, expect_return); gsl_test(local_s, desc); if(local_s != 0) { /* printf(" %s %d\n", __FILE__, __LINE__); */ printf("%s", message_buff); printf(" %22.18e %22.18e\n", r.val, r.err); } return local_s; } int test_sf_2 (gsl_sf_result r1, double val1, double tol1, gsl_sf_result r2, double val2, double tol2, int status, int expect_return, const char * desc) { char message_buff[4096]; int local_s = 0; message_buff[0] = '\0'; local_s |= test_sf_check_result(message_buff, r1, val1, tol1); local_s |= test_sf_check_result(message_buff, r2, val2, tol2); local_s |= test_sf_check_return(message_buff, status, expect_return); gsl_test(local_s, desc); if(local_s != 0) { /* printf(" %s %d\n", __FILE__, __LINE__); */ printf("%s", message_buff); printf(" %22.18e %22.18e\n", r1.val, r1.err); printf(" %22.18e %22.18e\n", r2.val, r2.err); } return local_s; } int test_sf_sgn (gsl_sf_result r, double sgn, double val_in, double tol, double expect_sgn, int status, int expect_return, const char * desc) { char message_buff[4096]; gsl_sf_result local_r; int local_s = 0; message_buff[0] = '\0'; local_r.val = sgn; local_r.err = 0.0; local_s |= test_sf_check_result(message_buff, r, val_in, tol); local_s |= test_sf_check_result(message_buff, local_r, expect_sgn, 0.0); local_s |= test_sf_check_return(message_buff, status, expect_return); gsl_test(local_s, desc); if(local_s != 0) { /* printf(" %s %d\n", __FILE__, __LINE__); */ printf("%s", message_buff); printf(" %22.18e %22.18e\n", r.val, r.err); } return local_s; } int test_clausen(void) { gsl_sf_result r; int s = 0; TEST_SF(s, gsl_sf_clausen_e, (M_PI/20.0, &r), 0.4478882448133546, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_clausen_e, (M_PI/6.0, &r), 0.8643791310538927, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_clausen_e, (M_PI/3.0, &r), 1.0149416064096535, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_clausen_e, ( 2.0*M_PI + M_PI/3.0, &r), 1.0149416064096535, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_clausen_e, (100.0*M_PI + M_PI/3.0, &r), 1.0149416064096535, TEST_TOL0, GSL_SUCCESS); return s; } int test_coupling(void) { gsl_sf_result r; int s = 0; /* Test 3j */ TEST_SF(s, gsl_sf_coupling_3j_e, (0, 1, 1, 0, 1, -1, &r), sqrt(1.0/2.0), TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_3j_e, (1, 1, 2, 1, -1, 0, &r), sqrt(1.0/6.0), TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_3j_e, (2, 4, 6, 0, 2, -2, &r), sqrt(8.0/105.0), TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_3j_e, (4, 4, 8, 0, 0, 0, &r), sqrt(2.0/35.0), TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_3j_e, (4, 4, 8, 2, -2, 0, &r), 2.0/3.0*sqrt(2.0/35.0), TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_3j_e, (4, 4, 8, 4, -4, 0, &r), 1.0/(3.0*sqrt(70.0)), TEST_TOL2, GSL_SUCCESS); /* Test 3j error checking */ TEST_SF(s, gsl_sf_coupling_3j_e, (-1, 1, 2, 1, -1, 0, &r), GSL_NAN, GSL_NAN, GSL_EDOM); TEST_SF(s, gsl_sf_coupling_3j_e, (1, -1, 2, 1, -1, 0, &r), GSL_NAN, GSL_NAN, GSL_EDOM); TEST_SF(s, gsl_sf_coupling_3j_e, (1, 1, -2, 1, -1, 0, &r), GSL_NAN, GSL_NAN, GSL_EDOM); /* Test |m_i|<=j_i */ TEST_SF(s, gsl_sf_coupling_3j_e, (1, 1, 2, 2, -1, 0, &r), 0, 0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_3j_e, (1, 1, 2, 1, -2, 0, &r), 0, 0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_3j_e, (1, 1, 2, 1, -1, 3, &r), 0, 0, GSL_SUCCESS); /* Test triangle condition j1 + j2 >= j, j >= j2 - j1, j>= j1 - j2 */ TEST_SF(s, gsl_sf_coupling_3j_e, (1, 1, 3, 1, -1, 0, &r), 0, 0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_3j_e, (1, 4, 2, 1, -1, 0, &r), 0, 0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_3j_e, (4, 1, 2, 1, -1, 0, &r), 0, 0, GSL_SUCCESS); /* Test 6j */ TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, 2, 2, 2, &r), 1.0/6.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_6j_e, (4, 4, 2, 4, 4, 4, &r), -1.0/10.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_6j_e, (4, 4, 2, 4, 4, 2, &r), 1.0/6.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_6j_e, (4, 4, 2, 2, 2, 2, &r), -0.5/sqrt(5.0), TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_6j_e, (4, 4, 4, 2, 2, 2, &r), sqrt(7.0/3.0)/10.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_6j_e, (6, 6, 6, 4, 4, 4, &r), -sqrt(3.0/5.0)/14.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_6j_e, (6, 6, 6, 4, 4, 2, &r), -sqrt(3.0/5.0)/7.0, TEST_TOL0, GSL_SUCCESS); /* Test 6j error checking */ TEST_SF(s, gsl_sf_coupling_6j_e, (-2, 2, 4, 2, 2, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM); TEST_SF(s, gsl_sf_coupling_6j_e, (2, -2, 4, 2, 2, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM); TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, -4, 2, 2, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM); TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, -2, 2, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM); TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, 2, -2, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM); TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, 2, 2, -2, &r), GSL_NAN, GSL_NAN, GSL_EDOM); /* Test 6j triangle conditions */ TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, 2, 2, 7, &r), 0, 0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, 2, 7, 2, &r), 0, 0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, 7, 2, 2, &r), 0, 0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 7, 2, 2, 2, &r), 0, 0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_6j_e, (2, 7, 4, 2, 2, 2, &r), 0, 0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_6j_e, (7, 2, 4, 2, 2, 2, &r), 0, 0, GSL_SUCCESS); /* Test 9j */ TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 2, 1, 1, 2, &r), -sqrt(1.0/6.0)/10.0, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_9j_e, (8, 4, 10, 7, 3, 8, 1, 1, 2, &r), sqrt(7.0/3.0)/60.0, TEST_TOL2, GSL_SUCCESS); /* Test 9j error checking */ TEST_SF(s, gsl_sf_coupling_9j_e, (-4, 2, 4, 3, 3, 2, 1, 1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM); TEST_SF(s, gsl_sf_coupling_9j_e, (4, -2, 4, 3, 3, 2, 1, 1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM); TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, -4, 3, 3, 2, 1, 1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM); TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, -3, 3, 2, 1, 1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM); TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, -3, 2, 1, 1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM); TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, -2, 1, 1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM); TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 2, -1, 1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM); TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 2, 1, -1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM); TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 2, 1, 1, -2, &r), GSL_NAN, GSL_NAN, GSL_EDOM); TEST_SF(s, gsl_sf_coupling_9j_e, (10, 2, 4, 3, 3, 2, 1, 1, 2, &r), 0, 0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_9j_e, (4, 10, 4, 3, 3, 2, 1, 1, 2, &r), 0, 0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 10, 3, 3, 2, 1, 1, 2, &r), 0, 0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 10, 3, 2, 1, 1, 2, &r), 0, 0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 10, 2, 1, 1, 2, &r), 0, 0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 10, 1, 1, 2, &r), 0, 0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 2, 10, 1, 2, &r), 0, 0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 2, 1, 10, 2, &r), 0, 0, GSL_SUCCESS); TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 2, 1, 1, 10, &r), 0, 0, GSL_SUCCESS); return s; } int test_dawson(void) { gsl_sf_result r; int s = 0; TEST_SF(s, gsl_sf_dawson_e, (1.0e-15, &r), 1.0e-15, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_dawson_e, (0.5, &r), 0.4244363835020222959, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_dawson_e, (2.0, &r), 0.30134038892379196603, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_dawson_e, (1000.0, &r), 0.0005000002500003750009, TEST_TOL0, GSL_SUCCESS); return s; } int test_debye(void) { gsl_sf_result r; int s = 0; TEST_SF(s, gsl_sf_debye_1_e, (0.1, &r), 0.975277750004723276, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_debye_1_e, (1.0, &r), 0.777504634112248239, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_debye_1_e, (10.0, &r), 0.164443465679946027, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_debye_2_e, (0.1, &r), 0.967083287045302664, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_debye_2_e, (1.0, &r), 0.70787847562782924, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_debye_2_e, (10.0, &r), 0.0479714980201218708, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_debye_3_e, (0.1, &r), 0.962999940487211048, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_debye_3_e, (1.0, &r), 0.674415564077814667, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_debye_3_e, (10.0, &r), 0.0192957656903454886, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_debye_4_e, (0.1, &r), 0.960555486124335944, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_debye_4_e, (1.0, &r), 0.654874068886737049, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_debye_4_e, (10.0, &r), 0.00967367556027115896, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_debye_5_e, (0.1, &r), 0.95892849428310568745, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_debye_5_e, (1.0, &r), 0.6421002580217790246, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_debye_5_e, (10.0, &r), 0.005701535852992908538, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_debye_6_e, (0.1, &r), 0.95776777382605465878, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_debye_6_e, (1.0, &r), 0.63311142583495107588, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_debye_6_e, (10.0, &r), 3.7938493294615955279e-3, TEST_TOL0, GSL_SUCCESS); return s; } int test_elementary(void) { gsl_sf_result r; double x = 0.2*DBL_MAX; int s = 0; TEST_SF(s, gsl_sf_multiply_e, (-3.0,2.0, &r), -6.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_multiply_e, (x, 1.0/x, &r), 1.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_multiply_e, (x, 0.2, &r), 0.04*DBL_MAX, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_multiply_e, (x, 4.0, &r), 0.8*DBL_MAX, TEST_TOL1, GSL_SUCCESS); s += ( gsl_sf_multiply_e(DBL_MAX, 1.1, &r) != GSL_EOVRFLW); s += ( gsl_sf_multiply_e(DBL_MIN, DBL_MIN, &r) != GSL_EUNDRFLW); s += ( gsl_sf_multiply_e(DBL_MIN, -DBL_MIN, &r) != GSL_EUNDRFLW); return s; } int test_ellint(void) { gsl_sf_result r; gsl_mode_t mode = GSL_MODE_DEFAULT; int s = 0; TEST_SF(s, gsl_sf_ellint_Kcomp_e, ( 0.99, mode, &r), 3.3566005233611923760, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_Kcomp_e, ( 0.50, mode, &r), 1.6857503548125960429, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_Kcomp_e, (0.010, mode, &r), 1.5708355989121522360, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_Ecomp_e, (0.99, mode, &r), 1.0284758090288040010, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_Ecomp_e, (0.50, mode, &r), 1.4674622093394271555, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_Ecomp_e, (0.01, mode, &r), 1.5707570561503852873, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_Pcomp_e, (0.99, 0.1, mode, &r), 3.13792612351836506315593, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_Pcomp_e, (0.50, 0.1, mode, &r), 1.60455249360848890075108, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_Pcomp_e, (0.01, 0.1, mode, &r), 1.49773208536003801277453, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_Dcomp_e, (0.99, mode, &r), 2.375395076351788975665323192, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_Dcomp_e, (0.50, mode, &r), 0.8731525818926755496456335628, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_Dcomp_e, (0.01, mode, &r), 0.7854276176694868932799393751, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (M_PI/3.0, 0.99, mode, &r), 1.3065333392738766762, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (M_PI/3.0, 0.50, mode, &r), 1.0895506700518854093, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (M_PI/3.0, 0.01, mode, &r), 1.0472129063770918952, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (M_PI/3.0, 0.99, mode, &r), 0.8704819220377943536, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (M_PI/3.0, 0.50, mode, &r), 1.0075555551444720293, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (M_PI/3.0, 0.01, mode, &r), 1.0471821963889481104, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (M_PI/3.0, 0.99, 0.5, mode, &r), 1.1288726598764099882, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (M_PI/3.0, 0.50, 0.5, mode, &r), 0.9570574331323584890, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (M_PI/3.0, 0.01, 0.5, mode, &r), 0.9228868127118118465, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_RF_e, (5.0e-11, 1.0e-10, 1.0, mode, &r), 12.36441982979439, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_RF_e, (1.0, 2.0, 3.0, mode, &r), 0.7269459354689082, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_RD_e, (5.0e-11, 1.0e-10, 1.0, mode, &r), 34.0932594919337362, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_RD_e, (1.0, 2.0, 3.0, mode, &r), 0.2904602810289906, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_RC_e, (1.0, 2.0, mode, &r), 0.7853981633974482, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_RJ_e, (2.0, 3.0, 4.0, 5.0, mode, &r), 0.1429757966715675, TEST_TOL0, GSL_SUCCESS); /* E, argument phi > pi/2 */ TEST_SF(s, gsl_sf_ellint_E_e, (M_PI/2.0, 0.99, mode, &r), 1.02847580902880400098389, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (M_PI/2.0, 0.50, mode, &r), 1.46746220933942715545980, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (M_PI/2.0, 0.01, mode, &r), 1.57075705615038528733708, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (2*M_PI/3.0, 0.99, mode, &r), 1.18646969601981364833972, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (2*M_PI/3.0, 0.50, mode, &r), 1.92736886353438228163734, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (2*M_PI/3.0, 0.01, mode, &r), 2.09433191591182246425715, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (M_PI, 0.99, mode, &r), 2.05695161805760800196777, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (M_PI, 0.50, mode, &r), 2.93492441867885431091959, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (M_PI, 0.01, mode, &r), 3.14151411230077057467416, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (4*M_PI/3, 0.99, mode, &r), 2.92743354009540235559582, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (4*M_PI/3, 0.50, mode, &r), 3.94247997382332634020184, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (4*M_PI/3, 0.01, mode, &r), 4.18869630868971868509117, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (3*M_PI/2.0, 0.99, mode, &r), 3.08542742708641200295166, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (3*M_PI/2.0, 0.50, mode, &r), 4.40238662801828146637939, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (3*M_PI/2.0, 0.01, mode, &r), 4.71227116845115586201123, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (5*M_PI/3, 0.99, mode, &r), 3.24342131407742165030750, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (5*M_PI/3, 0.50, mode, &r), 4.86229328221323659255693, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (5*M_PI/3, 0.01, mode, &r), 5.23584602821259303893130, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (2*M_PI, 0.99, mode, &r), 4.11390323611521600393555, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (2*M_PI, 0.50, mode, &r), 5.86984883735770862183918, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (2*M_PI, 0.01, mode, &r), 6.28302822460154114934831, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (7*M_PI/3.0, 0.99, mode, &r), 4.98438515815301035756360, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (7*M_PI/3.0, 0.50, mode, &r), 6.87740439250218065112143, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (7*M_PI/3.0, 0.01, mode, &r), 7.33021042099048925976532, TEST_TOL0, GSL_SUCCESS); /* Test some negative arguments, phi < 0 */ TEST_SF(s, gsl_sf_ellint_E_e, (-M_PI/2.0, 0.99, mode, &r), -1.02847580902880400098389, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-M_PI/2.0, 0.50, mode, &r), -1.46746220933942715545980, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-M_PI/2.0, 0.01, mode, &r), -1.57075705615038528733708, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-2*M_PI/3.0, 0.99, mode, &r), -1.18646969601981364833972, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-2*M_PI/3.0, 0.50, mode, &r), -1.92736886353438228163734, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-2*M_PI/3.0, 0.01, mode, &r), -2.09433191591182246425715, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-M_PI, 0.99, mode, &r), -2.05695161805760800196777, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-M_PI, 0.50, mode, &r), -2.93492441867885431091959, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-M_PI, 0.01, mode, &r), -3.14151411230077057467416, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-4*M_PI/3, 0.99, mode, &r), -2.92743354009540235559582, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-4*M_PI/3, 0.50, mode, &r), -3.94247997382332634020184, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-4*M_PI/3, 0.01, mode, &r), -4.18869630868971868509117, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-3*M_PI/2.0, 0.99, mode, &r), -3.08542742708641200295166, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-3*M_PI/2.0, 0.50, mode, &r), -4.40238662801828146637939, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-3*M_PI/2.0, 0.01, mode, &r), -4.71227116845115586201123, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-5*M_PI/3, 0.99, mode, &r), -3.24342131407742165030750, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-5*M_PI/3, 0.50, mode, &r), -4.86229328221323659255693, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-5*M_PI/3, 0.01, mode, &r), -5.23584602821259303893130, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-2*M_PI, 0.99, mode, &r), -4.11390323611521600393555, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-2*M_PI, 0.50, mode, &r), -5.86984883735770862183918, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-2*M_PI, 0.01, mode, &r), -6.28302822460154114934831, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-7*M_PI/3.0, 0.99, mode, &r), -4.98438515815301035756360, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-7*M_PI/3.0, 0.50, mode, &r), -6.87740439250218065112143, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_E_e, (-7*M_PI/3.0, 0.01, mode, &r), -7.33021042099048925976532, TEST_TOL0, GSL_SUCCESS); /* F, argument phi > pi/2 */ TEST_SF(s, gsl_sf_ellint_F_e, (M_PI/2.0, 0.99, mode, &r), 3.35660052336119237603347, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (M_PI/2.0, 0.50, mode, &r), 1.68575035481259604287120, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (M_PI/2.0, 0.01, mode, &r), 1.57083559891215223602641, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (2*M_PI/3.0, 0.99, mode, &r), 5.40666770744850807588478, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (2*M_PI/3.0, 0.50, mode, &r), 2.28195003957330667648585, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (2*M_PI/3.0, 0.01, mode, &r), 2.09445829144721257687207, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (M_PI, 0.99, mode, &r), 6.71320104672238475206694, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (M_PI, 0.50, mode, &r), 3.37150070962519208574241, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (M_PI, 0.01, mode, &r), 3.14167119782430447205281, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (4*M_PI/3, 0.99, mode, &r), 8.01973438599626142824910, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (4*M_PI/3, 0.50, mode, &r), 4.46105137967707749499897, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (4*M_PI/3, 0.01, mode, &r), 4.18888410420139636723356, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (3*M_PI/2.0, 0.99, mode, &r), 10.0698015700835771281004, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (3*M_PI/2.0, 0.50, mode, &r), 5.05725106443778812861361, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (3*M_PI/2.0, 0.01, mode, &r), 4.71250679673645670807922, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (5*M_PI/3, 0.99, mode, &r), 12.1198687541708928279517, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (5*M_PI/3, 0.50, mode, &r), 5.65345074919849876222825, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (5*M_PI/3, 0.01, mode, &r), 5.23612948927151704892488, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (2*M_PI, 0.99, mode, &r), 13.4264020934447695041339, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (2*M_PI, 0.50, mode, &r), 6.74300141925038417148481, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (2*M_PI, 0.01, mode, &r), 6.28334239564860894410562, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (7*M_PI/3.0, 0.99, mode, &r), 14.7329354327186461803160, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (7*M_PI/3.0, 0.50, mode, &r), 7.83255208930226958074138, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (7*M_PI/3.0, 0.01, mode, &r), 7.33055530202570083928637, TEST_TOL0, GSL_SUCCESS); /* F, negative argument phi < 0 */ TEST_SF(s, gsl_sf_ellint_F_e, (-M_PI/2.0, 0.99, mode, &r), -3.35660052336119237603347, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-M_PI/2.0, 0.50, mode, &r), -1.68575035481259604287120, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-M_PI/2.0, 0.01, mode, &r), -1.57083559891215223602641, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-2*M_PI/3.0, 0.99, mode, &r), -5.40666770744850807588478, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-2*M_PI/3.0, 0.50, mode, &r), -2.28195003957330667648585, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-2*M_PI/3.0, 0.01, mode, &r), -2.09445829144721257687207, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-M_PI, 0.99, mode, &r), -6.71320104672238475206694, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-M_PI, 0.50, mode, &r), -3.37150070962519208574241, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-M_PI, 0.01, mode, &r), -3.14167119782430447205281, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-4*M_PI/3, 0.99, mode, &r), -8.01973438599626142824910, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-4*M_PI/3, 0.50, mode, &r), -4.46105137967707749499897, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-4*M_PI/3, 0.01, mode, &r), -4.18888410420139636723356, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-3*M_PI/2.0, 0.99, mode, &r), -10.0698015700835771281004, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-3*M_PI/2.0, 0.50, mode, &r), -5.05725106443778812861361, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-3*M_PI/2.0, 0.01, mode, &r), -4.71250679673645670807922, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-5*M_PI/3, 0.99, mode, &r), -12.1198687541708928279517, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-5*M_PI/3, 0.50, mode, &r), -5.65345074919849876222825, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-5*M_PI/3, 0.01, mode, &r), -5.23612948927151704892488, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-2*M_PI, 0.99, mode, &r), -13.4264020934447695041339, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-2*M_PI, 0.50, mode, &r), -6.74300141925038417148481, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-2*M_PI, 0.01, mode, &r), -6.28334239564860894410562, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-7*M_PI/3.0, 0.99, mode, &r), -14.7329354327186461803160, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-7*M_PI/3.0, 0.50, mode, &r), -7.83255208930226958074138, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_F_e, (-7*M_PI/3.0, 0.01, mode, &r), -7.33055530202570083928637, TEST_TOL0, GSL_SUCCESS); /* P, argument phi > pi/2 */ TEST_SF(s, gsl_sf_ellint_P_e, (M_PI/2.0, 0.99, -0.1, mode, &r), 3.61678162163246646783050, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (M_PI/2.0, 0.50, -0.1, mode, &r), 1.78030349465454812629168, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (M_PI/2.0, 0.01, -0.1, mode, &r), 1.65580719756898353270922, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (2*M_PI/3.0, 0.99, -0.1, mode, &r), 5.88008918207571119911983, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (2*M_PI/3.0, 0.50, -0.1, mode, &r), 2.43655207300356008717867, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (2*M_PI/3.0, 0.01, -0.1, mode, &r), 2.23211110528200554950903, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (M_PI, 0.99, -0.1, mode, &r), 7.23356324326493293566099, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (M_PI, 0.50, -0.1, mode, &r), 3.56060698930909625258336, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (M_PI, 0.01, -0.1, mode, &r), 3.31161439513796706541844, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (4*M_PI/3, 0.99, -0.1, mode, &r), 8.58703730445415467220216, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (4*M_PI/3, 0.50, -0.1, mode, &r), 4.68466190561463241798805, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (4*M_PI/3, 0.01, -0.1, mode, &r), 4.39111768499392858132786, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (3*M_PI/2.0, 0.99, -0.1, mode, &r), 10.8503448648973994034915, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (3*M_PI/2.0, 0.50, -0.1, mode, &r), 5.34091048396364437887504, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (3*M_PI/2.0, 0.01, -0.1, mode, &r), 4.96742159270695059812767, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (5*M_PI/3, 0.99, -0.1, mode, &r), 13.1136524253406441347808, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (5*M_PI/3, 0.50, -0.1, mode, &r), 5.99715906231265633976204, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (5*M_PI/3, 0.01, -0.1, mode, &r), 5.54372550041997261492747, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (2*M_PI, 0.99, -0.1, mode, &r), 14.4671264865298658713220, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (2*M_PI, 0.50, -0.1, mode, &r), 7.12121397861819250516672, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (2*M_PI, 0.01, -0.1, mode, &r), 6.62322879027593413083689, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (7*M_PI/3.0, 0.99, -0.1, mode, &r), 15.8206005477190876078631, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (7*M_PI/3.0, 0.50, -0.1, mode, &r), 8.24526889492372867057141, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (7*M_PI/3.0, 0.01, -0.1, mode, &r), 7.70273208013189564674630, TEST_TOL0, GSL_SUCCESS); /* P, negative argument phi < 0 */ TEST_SF(s, gsl_sf_ellint_P_e, (-M_PI/2.0, 0.99, -0.1, mode, &r), -3.61678162163246646783050, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-M_PI/2.0, 0.50, -0.1, mode, &r), -1.78030349465454812629168, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-M_PI/2.0, 0.01, -0.1, mode, &r), -1.65580719756898353270922, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-2*M_PI/3.0, 0.99, -0.1, mode, &r), -5.88008918207571119911983, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-2*M_PI/3.0, 0.50, -0.1, mode, &r), -2.43655207300356008717867, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-2*M_PI/3.0, 0.01, -0.1, mode, &r), -2.23211110528200554950903, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-M_PI, 0.99, -0.1, mode, &r), -7.23356324326493293566099, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-M_PI, 0.50, -0.1, mode, &r), -3.56060698930909625258336, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-M_PI, 0.01, -0.1, mode, &r), -3.31161439513796706541844, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-4*M_PI/3, 0.99, -0.1, mode, &r), -8.58703730445415467220216, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-4*M_PI/3, 0.50, -0.1, mode, &r), -4.68466190561463241798805, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-4*M_PI/3, 0.01, -0.1, mode, &r), -4.39111768499392858132786, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-3*M_PI/2.0, 0.99, -0.1, mode, &r), -10.8503448648973994034915, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-3*M_PI/2.0, 0.50, -0.1, mode, &r), -5.34091048396364437887504, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-3*M_PI/2.0, 0.01, -0.1, mode, &r), -4.96742159270695059812767, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-5*M_PI/3, 0.99, -0.1, mode, &r), -13.1136524253406441347808, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-5*M_PI/3, 0.50, -0.1, mode, &r), -5.99715906231265633976204, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-5*M_PI/3, 0.01, -0.1, mode, &r), -5.54372550041997261492747, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-2*M_PI, 0.99, -0.1, mode, &r), -14.4671264865298658713220, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-2*M_PI, 0.50, -0.1, mode, &r), -7.12121397861819250516672, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-2*M_PI, 0.01, -0.1, mode, &r), -6.62322879027593413083689, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-7*M_PI/3.0, 0.99, -0.1, mode, &r), -15.8206005477190876078631, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-7*M_PI/3.0, 0.50, -0.1, mode, &r), -8.24526889492372867057141, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_P_e, (-7*M_PI/3.0, 0.01, -0.1, mode, &r), -7.70273208013189564674630, TEST_TOL0, GSL_SUCCESS); /* D, argument phi > pi/2 */ TEST_SF(s, gsl_sf_ellint_D_e, (M_PI/2.0, 0.99, 0, mode, &r), 2.375395076351788975665323192, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (M_PI/2.0, 0.50, 0, mode, &r), 0.8731525818926755496456335628, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (M_PI/2.0, 0.01, 0, mode, &r), 0.7854276176694868932799393751, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (2*M_PI/3.0, 0.99, 0, mode, &r), 4.305885125424644860264320635, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (2*M_PI/3.0, 0.50, 0, mode, &r), 1.418324704155697579394036402, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (2*M_PI/3.0, 0.01, 0, mode, &r), 1.263755353901126149206022061, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (M_PI, 0.99, 0, mode, &r), 4.750790152703577951330646444, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (M_PI, 0.50, 0, mode, &r), 1.746305163785351099291267125, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (M_PI, 0.01, 0, mode, &r), 1.570855235338973786559878750, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (4*M_PI/3, 0.99, 0, mode, &r), 5.195695179982511042396972113, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (4*M_PI/3, 0.50, 0, mode, &r), 2.074285623415004619188497818, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (4*M_PI/3, 0.01, 0, mode, &r), 1.877955116776821423913735408, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (3*M_PI/2.0, 0.99, 0, mode, &r), 7.126185229055366926995969476, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (3*M_PI/2.0, 0.50, 0, mode, &r), 2.619457745678026648936900687, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (3*M_PI/2.0, 0.01, 0, mode, &r), 2.356282853008460679839818125, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (5*M_PI/3, 0.99, 0, mode, &r), 9.056675278128222811594967044, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (5*M_PI/3, 0.50, 0, mode, &r), 3.164629867941048678685303509, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (5*M_PI/3, 0.01, 0, mode, &r), 2.834610589240099935765900794, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (2*M_PI, 0.99, 0, mode, &r), 9.501580305407155902661292832, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (2*M_PI, 0.50, 0, mode, &r), 3.492610327570702198582534249, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (2*M_PI, 0.01, 0, mode, &r), 3.141710470677947573119757500, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (7*M_PI/3.0, 0.99, 0, mode, &r), 9.946485332686088993727618315, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (7*M_PI/3.0, 0.50, 0, mode, &r), 3.820590787200355718479764901, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (7*M_PI/3.0, 0.01, 0, mode, &r), 3.448810352115795210473614120, TEST_TOL0, GSL_SUCCESS); /* P, negative argument phi < 0 */ TEST_SF(s, gsl_sf_ellint_D_e, (-M_PI/2.0, 0.99, 0, mode, &r), -2.375395076351788975665323192, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-M_PI/2.0, 0.50, 0, mode, &r), -0.8731525818926755496456335628, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-M_PI/2.0, 0.01, 0, mode, &r), -0.7854276176694868932799393751, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-2*M_PI/3.0, 0.99, 0, mode, &r), -4.305885125424644860264320635, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-2*M_PI/3.0, 0.50, 0, mode, &r), -1.418324704155697579394036402, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-2*M_PI/3.0, 0.01, 0, mode, &r), -1.263755353901126149206022061, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-M_PI, 0.99, 0, mode, &r), -4.750790152703577951330646444, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-M_PI, 0.50, 0, mode, &r), -1.746305163785351099291267125, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-M_PI, 0.01, 0, mode, &r), -1.570855235338973786559878750, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-4*M_PI/3, 0.99, 0, mode, &r), -5.195695179982511042396972113, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-4*M_PI/3, 0.50, 0, mode, &r), -2.074285623415004619188497818, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-4*M_PI/3, 0.01, 0, mode, &r), -1.877955116776821423913735408, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-3*M_PI/2.0, 0.99, 0, mode, &r), -7.126185229055366926995969476, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-3*M_PI/2.0, 0.50, 0, mode, &r), -2.619457745678026648936900687, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-3*M_PI/2.0, 0.01, 0, mode, &r), -2.356282853008460679839818125, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-5*M_PI/3, 0.99, 0, mode, &r), -9.056675278128222811594967044, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-5*M_PI/3, 0.50, 0, mode, &r), -3.164629867941048678685303509, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-5*M_PI/3, 0.01, 0, mode, &r), -2.834610589240099935765900794, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-2*M_PI, 0.99, 0, mode, &r), -9.501580305407155902661292832, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-2*M_PI, 0.50, 0, mode, &r), -3.492610327570702198582534249, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-2*M_PI, 0.01, 0, mode, &r), -3.141710470677947573119757500, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-7*M_PI/3.0, 0.99, 0, mode, &r), -9.946485332686088993727618315, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-7*M_PI/3.0, 0.50, 0, mode, &r), -3.820590787200355718479764901, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_ellint_D_e, (-7*M_PI/3.0, 0.01, 0, mode, &r), -3.448810352115795210473614120, TEST_TOL0, GSL_SUCCESS); return s; } int test_erf(void) { gsl_sf_result r; int s = 0; TEST_SF(s, gsl_sf_erfc_e, (-10.0, &r), 2.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_erfc_e, (-5.0000002, &r), 1.9999999999984625433, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_erfc_e, (-5.0, &r), 1.9999999999984625402, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_erfc_e, (-1.0, &r), 1.8427007929497148693, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_erfc_e, (-0.5, &r), 1.5204998778130465377, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_erfc_e, (1.0, &r), 0.15729920705028513066, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_erfc_e, (3.0, &r), 0.000022090496998585441373, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_erfc_e, (7.0, &r), 4.183825607779414399e-23, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_erfc_e, (10.0, &r), 2.0884875837625447570e-45, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_erfc_e, (-1.0, &r), log(1.842700792949714869), TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_erfc_e, (-0.1, &r), 0.106576400586522485015, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_erfc_e, (-1e-10, &r), 1.1283791670318505967e-10, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_erfc_e, (0.0, &r), log(1.0), TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_erfc_e, (1e-10, &r), -1.128379167159174551e-10, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_erfc_e, (0.001, &r), -0.0011290158896213548027, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_erfc_e, (0.1, &r), -0.119304973737395598329, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_erfc_e, (1.0, &r), log(0.15729920705028513066), TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_erfc_e, (10.0, &r), log(2.0884875837625447570e-45), TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_erf_e, (-10.0, &r), -1.0000000000000000000, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_erf_e, (0.5, &r), 0.5204998778130465377, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_erf_e, (1.0, &r), 0.8427007929497148693, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_erf_e, (10.0, &r), 1.0000000000000000000, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_erf_Z_e, (1.0, &r), 0.24197072451914334980, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_erf_Q_e, (10.0, &r), 7.619853024160526066e-24, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hazard_e, (-20.0, &r), 5.5209483621597631896e-88, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hazard_e, (-10.0, &r), 7.6945986267064193463e-23, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hazard_e, (-1.0, &r), 0.28759997093917836123, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hazard_e, ( 0.0, &r), 0.79788456080286535588, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hazard_e, ( 1.0, &r), 1.5251352761609812091, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hazard_e, (10.0, &r), 10.098093233962511963, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hazard_e, (20.0, &r), 20.049753068527850542, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hazard_e, (30.0, &r), 30.033259667433677037, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hazard_e, (50.0, &r), 50.019984031905639809, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hazard_e, (80.0, &r), 80.012496096798234468, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hazard_e, (150.0, &r), 150.00666607420571802, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hazard_e, (300.0, &r), 300.00333325926337415, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hazard_e, (900.0, &r), 900.00111110836764382, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hazard_e, (1001.0, &r), 1001.0009989990049990, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hazard_e, (2000.0, &r), 2000.0004999997500003, TEST_TOL0, GSL_SUCCESS); return s; } int test_exp(void) { gsl_sf_result r; gsl_sf_result_e10 re; double x; int sa; int s = 0; TEST_SF(s, gsl_sf_exp_e, (-10.0, &r), exp(-10.0), TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exp_e, ( 10.0, &r), exp( 10.0), TEST_TOL0, GSL_SUCCESS); sa = 0; sa += gsl_sf_exp_e10_e(1.0, &re); sa += ( test_sf_frac_diff(re.val, M_E ) > TEST_TOL0 ); sa += ( re.err > TEST_TOL1 ); sa += ( re.e10 != 0 ); gsl_test(sa, " gsl_sf_exp_e10_e(1.0, &re)"); sa = 0; sa += gsl_sf_exp_e10_e(2000.0, &re); sa += ( test_sf_frac_diff(re.val, 3.88118019428363725 ) > TEST_TOL3 ); sa += ( re.err > TEST_TOL5 ); sa += ( re.e10 != 868 ); gsl_test(sa, " gsl_sf_exp_e10_e(2000.0, &re)"); TEST_SF(s, gsl_sf_exp_err_e, (-10.0, TEST_TOL1, &r), exp(-10.0), TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_exp_err_e, ( 10.0, TEST_TOL1, &r), exp( 10.0), TEST_TOL1, GSL_SUCCESS); sa = 0; sa += gsl_sf_exp_err_e10_e(1.0, TEST_SQRT_TOL0, &re); sa += ( test_sf_frac_diff(re.val, M_E ) > TEST_TOL1 ); sa += ( re.err > 32.0 * TEST_SQRT_TOL0 ); sa += ( re.e10 != 0 ); gsl_test(sa, " gsl_sf_exp_err_e10_e(1.0, TEST_SQRT_TOL0, &re)"); sa = 0; sa += gsl_sf_exp_err_e10_e(2000.0, 1.0e-10, &re); sa += ( test_sf_frac_diff(re.val, 3.88118019428363725 ) > TEST_TOL3 ); sa += ( re.err > 1.0e-07 ); sa += ( re.e10 != 868 ); gsl_test(sa, " gsl_sf_exp_err_e10_e(2000.0, 1.0e-10, &re)"); x = 0.8*GSL_LOG_DBL_MAX; TEST_SF(s, gsl_sf_exp_mult_e, (-10.0, 1.0e-06, &r), 1.0e-06*exp(-10.0), TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exp_mult_e, (-10.0, 2.0, &r), 2.0*exp(-10.0), TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exp_mult_e, (-10.0, -2.0, &r), -2.0*exp(-10.0), TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exp_mult_e, ( 10.0, 1.0e-06, &r), 1.0e-06*exp( 10.0), TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exp_mult_e, ( 10.0, -2.0, &r), -2.0*exp( 10.0), TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exp_mult_e, (x, 1.00001, &r), 1.00001*exp(x), TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_exp_mult_e, (x, 1.000001, &r), 1.000001*exp(x), TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_exp_mult_e, (x, 1.000000001, &r), 1.000000001*exp(x), TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_exp_mult_e, (x, 100.0, &r), 100.0*exp(x), TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_exp_mult_e, (x, 1.0e+20, &r), 1.0e+20*exp(x), TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_exp_mult_e, (x, exp(-x)*exp(M_LN2), &r), 2.0, TEST_TOL4, GSL_SUCCESS ); TEST_SF(s, gsl_sf_exp_mult_err_e, (-10.0, TEST_SQRT_TOL0, 2.0, TEST_SQRT_TOL0, &r), 2.0*exp(-10.0), TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exp_mult_err_e, (x, TEST_SQRT_TOL0*x, exp(-x)*exp(M_LN2), TEST_SQRT_TOL0*exp(-x)*exp(M_LN2), &r), 2.0, TEST_SQRT_TOL0, GSL_SUCCESS ); sa = 0; sa += gsl_sf_exp_mult_e10_e(1.0, 1.0, &re); sa += ( test_sf_frac_diff(re.val, M_E ) > TEST_TOL0 ); sa += ( re.err > TEST_TOL2 ); sa += ( re.e10 != 0 ); gsl_test(sa, "gsl_sf_exp_mult_e10_e(1.0, 1.0, &re)"); TEST_SF_E10(s, gsl_sf_exp_mult_e10_e, (1.0, 1.0, &re), M_E, 0, TEST_TOL0, GSL_SUCCESS); sa = 0; sa += gsl_sf_exp_mult_e10_e(1000.0, 1.0e+200, &re); sa += ( test_sf_frac_diff(re.val, 1.970071114017046993888879352) > TEST_TOL3 ); sa += ( re.err > 1.0e-11 ); sa += ( re.e10 != 634 ); gsl_test(sa, "gsl_sf_exp_mult_e10_e(1000.0, 1.0e+200, &re)"); TEST_SF_E10(s, gsl_sf_exp_mult_e10_e, (1000.0, 1.0e+200, &re), 1.970071114017046993888879352, 634, TEST_TOL3, GSL_SUCCESS); sa = 0; sa += gsl_sf_exp_mult_err_e10_e(1.0, TEST_TOL0, 1.0, TEST_TOL0, &re); sa += ( test_sf_frac_diff(re.val, M_E ) > TEST_TOL0 ); sa += ( re.err > TEST_TOL2 ); sa += ( re.e10 != 0 ); gsl_test(sa, "gsl_sf_exp_mult_err_e10_e(1.0, TEST_TOL0, 1.0, TEST_TOL0, &re)"); TEST_SF_E10(s, gsl_sf_exp_mult_err_e10_e, (1.0, TEST_TOL0, 1.0, TEST_TOL0, &re), M_E, 0, TEST_TOL0, GSL_SUCCESS); sa = 0; sa += gsl_sf_exp_mult_err_e10_e(1000.0, 1.0e-12, 1.0e+200, 1.0e+190, &re); sa += ( test_sf_frac_diff(re.val, 1.9700711140165661 ) > TEST_TOL3 ); sa += ( re.err > 1.0e-09 ); sa += ( re.e10 != 634 ); gsl_test(sa, "gsl_sf_exp_mult_err_e10_e(1.0e-12, 1.0e+200, &re)"); TEST_SF_E10(s, gsl_sf_exp_mult_err_e10_e, (1000.0, 1.0e-12, 1.0e+200, 1.0e+190, &re), 1.9700711140165661,634, TEST_TOL3, GSL_SUCCESS); /* Test cases from Szymon Jaroszewicz */ TEST_SF_E10(s, gsl_sf_exp_mult_e10_e, (10000.0, 1.0, &re), 8.806818225662921587261496007, 4342, TEST_TOL5, GSL_SUCCESS); TEST_SF_E10(s, gsl_sf_exp_mult_e10_e, (100.0, 1.0, &re), 2.688117141816135448412625551e43, 0, TEST_TOL1, GSL_SUCCESS); TEST_SF_E10(s, gsl_sf_exp_e10_e, (100.0, &re), 2.688117141816135448412625551e43, 0, TEST_TOL1, GSL_SUCCESS); TEST_SF_E10(s, gsl_sf_exp_e10_e, (1000.0, &re), 1.970071114017046993888879352, 434, TEST_TOL1, GSL_SUCCESS); TEST_SF_E10(s, gsl_sf_exp_e10_e, (-100.0, &re), 3.720075976020835962959695803e-44, 0, TEST_TOL1, GSL_SUCCESS); TEST_SF_E10(s, gsl_sf_exp_e10_e, (-1000.0, &re), 5.075958897549456765291809479, -435, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expm1_e, (-10.0, &r), exp(-10.0)-1.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expm1_e, (-0.001, &r), -0.00099950016662500845, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expm1_e, (-1.0e-8, &r), -1.0e-08 + 0.5e-16, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expm1_e, ( 1.0e-8, &r), 1.0e-08 + 0.5e-16, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expm1_e, ( 0.001, &r), 0.0010005001667083417, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expm1_e, ( 10.0, &r), exp(10.0)-1.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_e, (-10.0, &r), 0.0999954600070237515, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_e, (-0.001, &r), 0.9995001666250084, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_e, (-1.0e-8, &r), 1.0 - 0.5e-08, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_e, ( 1.0e-8, &r), 1.0 + 0.5e-08, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_e, ( 0.001, &r), 1.0005001667083417, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_e, ( 10.0, &r), 2202.5465794806716517, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_2_e, (-10.0, &r), 0.18000090799859524970, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_2_e, (-0.001, &r), 0.9996667499833361107, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_2_e, (-1.0e-8, &r), 0.9999999966666666750, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_2_e, ( 1.0e-8, &r), 1.0000000033333333417, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_2_e, ( 0.001, &r), 1.0003334166833361115, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_2_e, ( 10.0, &r), 440.3093158961343303, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (3, -1000.0, &r), 0.00299400600000000000, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (3, -100.0, &r), 0.02940600000000000000, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (3, -10.0, &r), 0.24599972760042142509, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (3, -3.0, &r), 0.5444917625849191238, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (3, -0.001, &r), 0.9997500499916678570, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (3, -1.0e-8, &r), 0.9999999975000000050, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (3, 1.0e-8, &r), 1.0000000025000000050, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (3, 0.001, &r), 1.0002500500083345240, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (3, 3.0, &r), 2.5745637607083706091, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (3, 3.1, &r), 2.6772417068460206247, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (3, 10.0, &r), 131.79279476884029910, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (3, 100.0, &r), 1.6128702850896812690e+38, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (50, -1000.0, &r), 0.04766231609253975959, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (50, -100.0, &r), 0.3348247572345889317, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (50, -10.0, &r), 0.8356287051853286482, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (50, -3.0, &r), 0.9443881609152163615, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (50, -1.0, &r), 0.980762245565660617, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (50, -1.0e-8, &r), 1.0 -1.0e-8/51.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (50, 1.0e-8, &r), 1.0 +1.0e-8/51.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (50, 1.0, &r), 1.01999216583666790, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (50, 3.0, &r), 1.0624205757460368307, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (50, 48.0, &r), 7.499573876877194416, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (50, 50.1, &r), 9.311803306230992272, TEST_TOL4, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (50, 100.0, &r), 8.175664432485807634e+07, TEST_TOL4, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (50, 500.0, &r), 4.806352370663185330e+146, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (500, -1000.0, &r), 0.3334815803127619256, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (500, -100.0, &r), 0.8335646217536183909, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (500, -10.0, &r), 0.9804297803131823066, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (500, -3.0, &r), 0.9940475488850672997, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (500, -1.0, &r), 0.9980079602383488808, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (500, -1.0e-8, &r), 1.0 -1.0e-8/501.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (500, 1.0e-8, &r), 1.0 +1.0e-8/501.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (500, 1.0, &r), 1.0019999920160634252, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (500, 3.0, &r), 1.0060240236632444934, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (500, 48.0, &r), 1.1059355517981272174, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (500, 100.0, &r), 1.2492221464878287204, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (500, 500.0, &r), 28.363019877927630858, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (500, 1000.0, &r), 2.4037563160335300322e+68, TEST_TOL4, GSL_SUCCESS); TEST_SF(s, gsl_sf_exprel_n_e, (500, 1600.0, &r), 7.899293535320607403e+226, TEST_TOL4, GSL_SUCCESS); return s; } int test_expint(void) { gsl_sf_result r; int s = 0; TEST_SF(s, gsl_sf_expint_E1_e, (-1.0, &r), -1.8951178163559367555, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E1_e, (1.0e-10, &r), 22.448635265138923980, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E1_e, (1.0e-05, &r), 10.935719800043695615, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E1_e, (0.1, &r), 1.82292395841939066610, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E1_e, (1.0, &r), 0.21938393439552027368, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E1_e, (10.0, &r), 4.156968929685324277e-06, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E1_e, (50.0, &r), 3.783264029550459019e-24, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E1_e, (300.0, &r), 1.710384276804510115e-133, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_e, (-1.0, &r), 0.8231640121031084799, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_e, (0.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_e, (1.0/4294967296.0, &r), 0.9999999947372139168, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_e, (1.0/65536.0, &r), 0.9998243233207178845, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_e, (0.1, &r), 0.7225450221940205066, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_e, (1.0, &r), 0.14849550677592204792, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_e, (10.0, &r), 3.830240465631608762e-06, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_e, (50.0, &r), 3.711783318868827367e-24, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_e, (300.0, &r), 1.7047391998483433998e-133, TEST_TOL2, GSL_SUCCESS); /* Tests for E_n(x) */ TEST_SF(s, gsl_sf_expint_En_e, (1,-1.0, &r), -1.8951178163559367555, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (1,1.0e-10, &r), 22.448635265138923980, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (1,1.0e-05, &r), 10.935719800043695615, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (1,0.1, &r), 1.82292395841939066610, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (1,1.0, &r), 0.21938393439552027368, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (1,10.0, &r), 4.156968929685324277e-06, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (1,50.0, &r), 3.783264029550459019e-24, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (1,300.0, &r), 1.710384276804510115e-133, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (2,-1.0, &r), 0.8231640121031084799, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (2,0.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (2,1.0/4294967296.0, &r), 0.9999999947372139168, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (2,1.0/65536.0, &r), 0.9998243233207178845, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (2,0.1, &r), 0.7225450221940205066, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (2,1.0, &r), 0.14849550677592204792, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (2,10.0, &r), 3.830240465631608762e-06, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (2,50.0, &r), 3.711783318868827367e-24, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (2,300.0, &r), 1.7047391998483433998e-133, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (3,0.0, &r), 0.5, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (3,1.0/4294967296.0, &r), 0.499999999767169356972, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (3,1.0/65536.0, &r), 0.4999847426094515610, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (3,0.1, &r), 0.4162914579082787612543, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (3,1.0, &r), 0.10969196719776013683858, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (3,10.0, &r),0.000003548762553084381959981, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (3,50.0, &r), 3.6429094264752049812e-24, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (3,300.0, &r),1.699131143349179084e-133, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (10,0.0, &r), 0.111111111111111111, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (10,1.0/4294967296.0, &r), 0.111111111082007280658, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (10,1.0/65536.0, &r), 0.11110920377910896018606, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (10,0.1, &r), 0.099298432000896813567905, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (10,1.0, &r), 0.036393994031416401634164534, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (10,10.0, &r), 0.00000232530265702821081778968, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (10,50.0, &r), 3.223296586749110919572e-24, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_e, (10,300.0, &r), 1.6608815083360041367294736e-133, TEST_TOL2, GSL_SUCCESS); /* Tests for Ei(x) */ TEST_SF(s, gsl_sf_expint_Ei_e, (-1.0, &r), -0.21938393439552027368, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_Ei_e, (1.0/4294967296.0, &r), -21.603494112783886397, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_Ei_e, (1.0, &r), 1.8951178163559367555, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E1_scaled_e, (-10000.0, &r), -0.00010001000200060024012, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E1_scaled_e, (-1000.0, &r), -0.0010010020060241207251, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E1_scaled_e, (-10.0, &r), -0.11314702047341077803, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E1_scaled_e, (-1.0, &r), -0.69717488323506606877, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E1_scaled_e, (1.0e-10, &r), 22.448635267383787506, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E1_scaled_e, (1.0e-05, &r), 10.935829157788483865, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E1_scaled_e, (0.1, &r), 2.0146425447084516791, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E1_scaled_e, (1.0, &r), 0.59634736232319407434, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E1_scaled_e, (10.0, &r), 0.091563333939788081876, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E1_scaled_e, (50.0, &r), 0.019615109930114870365, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E1_scaled_e, (300.0, &r), 0.0033222955652707070644, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E1_scaled_e, (1000.0, &r), 0.00099900199402388071500, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E1_scaled_e, (10000.0, &r), 0.000099990001999400239880, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_scaled_e, (-10000.0, &r), -0.00010002000600240120072, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_scaled_e, (-1000.0, &r), -0.0010020060241207250807, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_scaled_e, (-10.0, &r), -0.13147020473410778034, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_scaled_e, (-1.0, &r), 0.30282511676493393123, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_scaled_e, (0.0, &r), 1.0, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_scaled_e, (1.0/4294967296.0, &r), 0.99999999497004455927, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_scaled_e, (1.0/65536.0, &r), 0.99983957954556245453, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_scaled_e, (0.1, &r), 0.79853574552915483209, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_scaled_e, (1.0, &r), 0.40365263767680592566, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_scaled_e, (10.0, &r), 0.084366660602119181239, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_scaled_e, (50.0, &r), 0.019244503494256481735, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_scaled_e, (300.0, &r), 0.0033113304187878806691, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_scaled_e, (1000.0, &r), 0.00099800597611928500004, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_E2_scaled_e, (10000.0, &r), 0.000099980005997601199281, TEST_TOL0, GSL_SUCCESS); /* Tests for E_n(x) */ TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,-10000.0, &r), -0.00010001000200060024012, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,-1000.0, &r), -0.0010010020060241207251, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,-10.0, &r), -0.11314702047341077803, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,-1.0, &r), -0.69717488323506606877, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,1.0e-10, &r), 22.448635267383787506, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,1.0e-05, &r), 10.935829157788483865, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,0.1, &r), 2.0146425447084516791, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,1.0, &r), 0.59634736232319407434, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,10.0, &r), 0.091563333939788081876, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,50.0, &r), 0.019615109930114870365, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,300.0, &r), 0.0033222955652707070644, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,1000.0, &r), 0.00099900199402388071500, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,10000.0, &r), 0.000099990001999400239880, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,-10000.0, &r), -0.00010002000600240120072, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,-1000.0, &r), -0.0010020060241207250807, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,-10.0, &r), -0.13147020473410778034, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,-1.0, &r), 0.30282511676493393123, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,0.0, &r), 1.0, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,1.0/4294967296.0, &r), 0.99999999497004455927, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,1.0/65536.0, &r), 0.99983957954556245453, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,0.1, &r), 0.79853574552915483209, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,1.0, &r), 0.40365263767680592566, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,10.0, &r), 0.084366660602119181239, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,50.0, &r), 0.019244503494256481735, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,300.0, &r), 0.0033113304187878806691, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,1000.0, &r), 0.00099800597611928500004, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,10000.0, &r), 0.000099980005997601199281, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (3,0.0, &r), 0.5, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (3,1.0/4294967296.0, &r), 0.4999999998835846787586, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (3,1.0/65536.0, &r), 0.4999923718293796877864492, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (3,0.1, &r), 0.4600732127235422583955, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (3,1.0, &r), 0.298173681161597037170539, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (3,10.0, &r), 0.07816669698940409380349, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (3,50.0, &r), 0.0188874126435879566345, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (3,300.0, &r), 0.00330043718181789963028657675, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (10,0.0, &r), 0.111111111111111111, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (10,1.0/4294967296.0, &r), 0.11111111110787735217158, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (10,1.0/65536.0, &r), 0.1111108991839472074435, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (10,0.1, &r), 0.1097417392579033988025, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (10,1.0, &r), 0.09892913264064615521915, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (10,10.0, &r), 0.0512181994376050593314159875, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (10,50.0, &r), 0.0167118436335939556034579, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_En_scaled_e, (10,300.0, &r), 0.0032261400811599644878615, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_Ei_scaled_e, (-1000.0, &r), -0.00099900199402388071500, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_Ei_scaled_e, (-1.0, &r), -0.59634736232319407434, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_Ei_scaled_e, (1.0/4294967296.0, &r), -21.603494107753930958, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_Ei_scaled_e, (1.0, &r), 0.69717488323506606877, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_Ei_scaled_e, (1000.0, &r), 0.0010010020060241207251, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Shi_e, (-1.0, &r), -1.0572508753757285146, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Shi_e, (1.0/4294967296.0, &r), 2.3283064365386962891e-10, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Shi_e, (1.0/65536.0, &r), 0.00001525878906269737298, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Shi_e, (0.1, &r), 0.1000555722250569955, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Shi_e, (1.0, &r), 1.0572508753757285146, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Shi_e, (10.0, &r), 1246.1144901994233444, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_Shi_e, (50.0, &r), 5.292818448565845482e+19, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_Shi_e, (300.0, &r), 3.248241254044332895e+127, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_Chi_e, (-1.0, &r), 0.8378669409802082409, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Chi_e, (1.0/4294967296.0, &r), -21.603494113016717041, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Chi_e, (1.0/65536.0, &r), -10.513139223999384429, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Chi_e, (1.0/8.0, &r), -1.4983170827635760646, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Chi_e, (1.0, &r), 0.8378669409802082409, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Chi_e, (10.0, &r), 1246.1144860424544147, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_Chi_e, (50.0, &r), 5.292818448565845482e+19, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_Chi_e, (300.0, &r), 3.248241254044332895e+127, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_3_e, (1.0e-10, &r), 1.0e-10, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_3_e, (1.0e-05, &r), 9.9999999999999975e-06, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_3_e, (0.1, &r), 0.09997500714119079665122, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_3_e, (0.5, &r), 0.48491714311363971332427, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_3_e, (1.0, &r), 0.80751118213967145285833, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_3_e, (2.0, &r), 0.89295351429387631138208, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_3_e, (5.0, &r), 0.89297951156924921121856, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_3_e, (10.0, &r), 0.89297951156924921121856, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_expint_3_e, (100.0, &r), 0.89297951156924921121856, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Si_e, (-1.0, &r), -0.9460830703671830149, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Si_e, (1.0e-10, &r), 1.0e-10, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Si_e, (1.0e-05, &r), 9.999999999944444444e-06, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Si_e, (0.1, &r), 0.09994446110827695016, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Si_e, (1.0, &r), 0.9460830703671830149, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Si_e, (10.0, &r), 1.6583475942188740493, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Si_e, (50.0, &r), 1.5516170724859358947, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Si_e, (300.0, &r), 1.5708810882137495193, TEST_TOL0, GSL_SUCCESS); /* TEST_SF(s, gsl_sf_Si_e, (1.0e+20, &r), 1.5707963267948966192, TEST_TOL0, GSL_SUCCESS); */ TEST_SF(s, gsl_sf_Ci_e, (1.0/4294967296.0, &r), -21.603494113016717041, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Ci_e, (1.0/65536.0, &r), -10.513139224115799751, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Ci_e, (1.0/8.0, &r), -1.5061295845296396649, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Ci_e, (1.0, &r), 0.3374039229009681347, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Ci_e, (10.0, &r), -0.04545643300445537263, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Ci_e, (50.0, &r), -0.005628386324116305440, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Ci_e, (300.0, &r), -0.003332199918592111780, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Ci_e, (65536.0, &r), 0.000010560248837656279453, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Ci_e, (4294967296.0, &r), -1.0756463261957757485e-10, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_Ci_e, (1099511627776.0, &r), -3.689865584710764214e-13, 1024.0*TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_atanint_e, (1.0e-10, &r), 1.0e-10, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_atanint_e, (1.0e-05, &r), 9.99999999988888888889e-06, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_atanint_e, (0.1, &r), 0.09988928686033618404, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_atanint_e, (1.0, &r), 0.91596559417721901505, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_atanint_e, (2.0, &r), 1.57601540344632342236, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_atanint_e, (10.0, &r), 3.71678149306806859029, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_atanint_e, (50.0, &r), 6.16499047850274874222, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_atanint_e, (300.0, &r), 8.96281388924518959990, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_atanint_e, (1.0e+5, &r), 18.084471031038661920, TEST_TOL0, GSL_SUCCESS); return s; } int test_fermidirac(void) { gsl_sf_result r; int s = 0; TEST_SF(s, gsl_sf_fermi_dirac_m1_e, (-10.0, &r), 0.00004539786870243439450, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_m1_e, ( -1.0, &r), 0.26894142136999512075, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_m1_e, ( 1.0, &r), 0.7310585786300048793, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_m1_e, ( 10.0, &r), 0.9999546021312975656, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_0_e, (-10.0, &r), 0.00004539889921686464677, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_0_e, ( -1.0, &r), 0.31326168751822283405, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_0_e, ( 1.0, &r), 1.3132616875182228340, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_0_e, ( 10.0, &r), 10.000045398899216865, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_1_e, (-10.0, &r), 0.00004539941448447633524, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( -2.0, &r), 0.13101248471442377127, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( -1.0, &r), 0.3386479964034521798, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( -0.4, &r), 0.5825520806897909028, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( 0.4, &r), 1.1423819861584355337, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( 1.0, &r), 1.8062860704447742567, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( 1.5, &r), 2.5581520872227806402, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( 2.5, &r), 4.689474797599761667, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( 10.0, &r), 51.64488866743374196, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( 12.0, &r), 73.64492792264531092, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( 20.0, &r), 201.64493406478707282, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( 50.0, &r), 1251.6449340668482264, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_2_e, (-10.0, &r), 0.00004539967212174776662, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( -2.0, &r), 0.13313272938565030508, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( -1.0, &r), 0.3525648792978077590, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( -0.4, &r), 0.6229402647001272120, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( 0.4, &r), 1.2915805581060844533, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( 1.0, &r), 2.1641656128127008622, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( 1.5, &r), 3.247184513920792475, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( 2.5, &r), 6.797764392735056317, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( 10.0, &r), 183.11605273482105278, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( 12.0, &r), 307.73921494638635166, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( 20.0, &r), 1366.2320146723590157, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( 50.0, &r), 20915.580036675744655, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_2_e, (200.0, &r), 1.3336623201467029786e+06, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, (-10.0, &r), 0.00004539847236080549532, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( -2.0, &r), 0.12366562180120994266, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( -1.0, &r), 0.29402761761145122022, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( -0.4, &r), 0.4631755336886027800, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( 0.4, &r), 0.7654084737661656915, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( 1.0, &r), 1.0270571254743506890, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( 1.5, &r), 1.2493233478527122008, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( 2.5, &r), 1.6663128834358313625, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( 10.0, &r), 3.552779239536617160, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( 12.0, &r), 3.897268231925439359, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( 20.0, &r), 5.041018507535328603, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( 50.0, &r), 7.977530858581869960, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_half_e, (-10.0, &r), 0.00004539920105264132755, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( -2.0, &r), 0.12929851332007559106, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( -1.0, &r), 0.3277951592607115477, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( -0.4, &r), 0.5522452153690688947, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( 0.4, &r), 1.0386797503389389277, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( 1.0, &r), 1.5756407761513002308, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( 1.5, &r), 2.1448608775831140360, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( 2.5, &r), 3.606975377950373251, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( 10.0, &r), 24.084656964637653615, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( 12.0, &r), 31.540203287044242593, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( 20.0, &r), 67.49151222165892049, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( 50.0, &r), 266.09281252136259343, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_3half_e, (-10.0, &r), 0.00004539956540456176333, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( -2.0, &r), 0.13224678225177236685, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( -1.0, &r), 0.3466747947990574170, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( -0.4, &r), 0.6056120213305040910, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( 0.4, &r), 1.2258236403963668282, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( 1.0, &r), 2.0022581487784644573, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( 1.5, &r), 2.9277494127932173068, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( 2.5, &r), 5.768879312210516582, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( 10.0, &r), 101.00510084332600020, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( 12.0, &r), 156.51518642795728036, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( 20.0, &r), 546.5630100657601959, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( 50.0, &r), 5332.353566687145552, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (3, -2.0, &r), 0.1342199155038680215, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (3, 0.0, &r), 0.9470328294972459176, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (3, 0.1, &r), 1.0414170610956165759, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (3, 1.0, &r), 2.3982260822489407070, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (3, 3.0, &r), 12.621635313399690724, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (3, 100.0, &r), 4.174893231066566793e+06, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (3, 500.0, &r), 2.604372285319088354e+09, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (5, -2.0, &r), 0.13505242246823676478, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (5, 0.0, &r), 0.9855510912974351041, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (5, 0.1, &r), 1.0876519750101492782, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (5, 1.0, &r), 2.6222337848692390539, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (5, 3.0, &r), 17.008801618012113022, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (5, 100.0, &r), 1.3957522531334869874e+09, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (5, 500.0, &r), 2.1705672808114817955e+13, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (7, -2.0, &r), 0.1352641105671255851, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (7, 0.0, &r), 0.9962330018526478992, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (7, 0.1, &r), 1.1005861815180315485, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (7, 1.0, &r), 2.6918878172003129203, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (7, 3.0, &r), 19.033338976999367642, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (7, 10.0, &r), 5654.530932873610014, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (7, 50.0, &r), 1.005005069985066278e+09, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (7, 500.0, &r), 9.691690268341569514e+16, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (9, -2.0, &r), 0.1353174385330242691, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (9, 0.0, &r), 0.9990395075982715656, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (9, 0.1, &r), 1.1039997234712941212, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (9, 1.0, &r), 2.7113648898129249947, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (9, 3.0, &r), 19.768544008138602223, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (9, 10.0, &r), 10388.990167312912478, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (9, 50.0, &r), 2.85466960802601649e+10, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (9, 500.0, &r), 2.69273849842695876e+20, 2*TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (10, -2.0, &r), 0.13532635396712288092, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (10, 0.0, &r), 0.9995171434980607541, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (10, 0.1, &r), 1.1045818238852612296, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (10, 1.0, &r), 2.7147765350346120647, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (10, 3.0, &r), 19.917151938411675171, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (10, 10.0, &r), 12790.918595516495955, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (10, 50.0, &r), 1.3147703201869657654e+11, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (10, 500.0, &r), 1.2241331244469204398e+22, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (11, -2.0, &r), 0.1353308162894847149, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (11, 0.0, &r), 0.9997576851438581909, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (11, 0.1, &r), 1.1048751811565850418, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (11, 1.0, &r), 2.7165128749007313436, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (11, 3.0, &r), 19.997483022044603065, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (11, 10.0, &r), 14987.996005901818036, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (11, 50.0, &r), 5.558322924078990628e+11, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (11, 500.0, &r), 5.101293089606198280e+23, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (20, -2.0, &r), 0.13533527450327238373, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (20, 0.0, &r), 0.9999995232582155428, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (20, 0.1, &r), 1.1051703357941368203, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (20, 1.0, &r), 2.7182783069905721654, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (20, 3.0, &r), 20.085345296028242734, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (20, 10.0, &r), 21898.072920149606475, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (20, 50.0, &r), 1.236873256595717618e+16, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_fermi_dirac_int_e, (20, 500.0, &r), 9.358938204369557277e+36, TEST_TOL2, GSL_SUCCESS); return s; } int test_gegen(void) { gsl_sf_result r; double ga[100]; int s = 0; int sa; TEST_SF(s, gsl_sf_gegenpoly_1_e, (-0.2, 1.0, &r), -0.4, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_1_e, ( 0.0, 1.0, &r), 2.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_1_e, ( 1.0, 1.0, &r), 2.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_1_e, ( 1.0, 0.5, &r), 1.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_1_e, ( 5.0, 1.0, &r), 10.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_1_e, ( 100.0, 0.5, &r), 100.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_2_e, (-0.2, 0.5, &r), 0.12, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_2_e, ( 0.0, 1.0, &r), 1.00, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_2_e, ( 1.0, 1.0, &r), 3.00, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_2_e, ( 1.0, 0.1, &r), -0.96, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_2_e, ( 5.0, 1.0, &r), 55.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_2_e, ( 100.0, 0.5, &r), 4950.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_3_e, (-0.2, 0.5, &r), 0.112, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_3_e, ( 0.0, 1.0, &r), -2.0/3.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_3_e, ( 1.0, 1.0, &r), 4.000, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_3_e, ( 1.0, 0.1, &r), -0.392, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_3_e, ( 5.0, 1.0, &r), 220.000, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_3_e, ( 100.0, 0.5, &r), 161600.000, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_n_e, (1, 1.0, 1.0, &r), 2.000 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_n_e, (10, 1.0, 1.0, &r), 11.000 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_n_e, (10, 1.0, 0.1, &r), -0.4542309376 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_n_e, (10, 5.0, 1.0, &r), 9.23780e+4 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_n_e, (10, 100.0, 0.5, &r), 1.5729338392690000e+13, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_n_e, (1000, 100.0, 1.0, &r), 3.3353666135627322e+232, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_n_e, (100, 2000.0, 1.0, &r), 5.8753432034937579e+202, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_n_e, (103, 207.0, 2.0, &r), 1.4210272202235983e+145, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_gegenpoly_n_e, (103, -0.4, 0.3, &r), -1.64527498094522e-04, TEST_TOL1, GSL_SUCCESS); sa = 0; gsl_sf_gegenpoly_array(99, 5.0, 1.0, ga); sa += ( test_sf_frac_diff( ga[1], 10.0 ) > TEST_TOL0 ); sa += ( test_sf_frac_diff( ga[10], 9.23780e+4 ) > TEST_TOL0 ); gsl_test(sa, " gsl_sf_gegenpoly_array"); s += sa; return s; } int test_jac(void) { double u, m; double sn, cn, dn; int stat_ej; int s = 0; int sa; u = 0.5; m = 0.5; sa = 0; stat_ej = gsl_sf_elljac_e(u, m, &sn, &cn, &dn); sa += test_sf_val(sn, 0.4707504736556572833, TEST_TOL0, "gsl_sf_elljac_e(0.5|0.5) sn"); sa += test_sf_val(cn, 0.8822663948904402865, TEST_TOL0, "gsl_sf_elljac_e(0.5|0.5) cn"); sa += test_sf_val(dn, 0.9429724257773856873, TEST_TOL0, "gsl_sf_elljac_e(0.5|0.5) dn"); gsl_test(s, " gsl_sf_elljac_e(0.5|0.5)"); s += sa; u = 1.0; m = 0.3; sa = 0; stat_ej = gsl_sf_elljac_e(u, m, &sn, &cn, &dn); sa += test_sf_val(sn, 0.8187707145344889190, TEST_TOL0, "gsl_sf_elljac_e(1.0|0.3) sn"); sa += test_sf_val(cn, 0.5741206467465548795, TEST_TOL0, "gsl_sf_elljac_e(1.0|0.3) cn"); sa += test_sf_val(dn, 0.8938033089590823040, TEST_TOL0, "gsl_sf_elljac_e(1.0|0.3) dn"); gsl_test(sa, " gsl_sf_elljac_e(1.0|0.3)"); s += sa; u = 1.0; m = 0.6; sa = 0; stat_ej = gsl_sf_elljac_e(u, m, &sn, &cn, &dn); sa += test_sf_val(sn, 0.7949388393365780943, TEST_TOL0, "gsl_sf_elljac_e(1.0|0.6) sn"); sa += test_sf_val(cn, 0.6066895760718277578, TEST_TOL0, "gsl_sf_elljac_e(1.0|0.6) cn"); sa += test_sf_val(dn, 0.7879361300438814425, TEST_TOL0, "gsl_sf_elljac_e(1.0|0.6) dn"); gsl_test(sa, " gsl_sf_elljac_e(1.0|0.6)"); s += sa; u = 3.0; m = 0.6; sa = 0; stat_ej = gsl_sf_elljac_e(u, m, &sn, &cn, &dn); sa += test_sf_val(sn, 0.7432676860864044186, TEST_TOL0, " gsl_sf_elljac_e(3.0|0.6) sn"); sa += test_sf_val(cn, -0.6689941306317733154, TEST_TOL0, " gsl_sf_elljac_e(3.0|0.6) cn"); sa += test_sf_val(dn, 0.8176379933025723259, TEST_TOL0, " gsl_sf_elljac_e(3.0|0.6) dn"); gsl_test(sa, " gsl_sf_elljac_e(3.0|0.6)"); s += sa; u = 2.0; m = 0.999999; sa = 0; stat_ej = gsl_sf_elljac_e(u, m, &sn, &cn, &dn); sa += test_sf_val(sn, 0.96402778575700186570, TEST_TOL1, "gsl_sf_elljac_e(2.0|0.999999) sn"); sa += test_sf_val(cn, 0.26580148285600686381, TEST_TOL1, "gsl_sf_elljac_e(2.0|0.999999) cn"); sa += test_sf_val(dn, 0.26580323105264131136, TEST_TOL1, "gsl_sf_elljac_e(2.0|0.999999) dn"); gsl_test(sa, " gsl_sf_elljac_e(2.0|0.999999)"); s += sa; /* test supplied by Ivan Panchenko */ u = 1.69695970624443; m = 0.270378013104138; sa = 0; stat_ej = gsl_sf_elljac_e(u, m, &sn, &cn, &dn); sa += test_sf_val(sn, 1.0, TEST_TOL0, "gsl_sf_elljac_e(1.69..|0.27..) sn"); sa += test_sf_val(cn, 0.0, TEST_TOL1, "gsl_sf_elljac_e(1.69..|0.27..) cn"); sa += test_sf_val(dn, 0.8541791304497336, TEST_TOL1, "gsl_sf_elljac_e(1.69..|0.27..) dn"); gsl_test(sa, " gsl_sf_elljac_e(1.69695970624443|0.270378013104138)"); s += sa; /* Check known values from Abramowitz & Stegun, Table 16.5 */ u = 0; m = 0.1; { double mc = 1 - m; /* quarter period K is (pi/2)/agm(1,mc) */ double K = (M_PI_2)/ 0.9741726903999478375938128316; double A = 1.0 / sqrt(1+sqrt(mc)); double B = pow(mc, 0.25) / sqrt(1+sqrt(mc)); double C = pow(mc, 0.25); double C2 = sqrt(mc); double eps = 1e-10; sa = 0; stat_ej = gsl_sf_elljac_e(0.0, m, &sn, &cn, &dn); sa += test_sf_val(sn, 0.0, TEST_TOL0, "gsl_sf_elljac_e(0|0.1) sn"); sa += test_sf_val(cn, 1.0, TEST_TOL0, "gsl_sf_elljac_e(0|0.1) cn"); sa += test_sf_val(dn, 1.0, TEST_TOL0, "gsl_sf_elljac_e(0|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(0|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(-eps, m, &sn, &cn, &dn); sa += test_sf_val(sn, -eps, TEST_TOL0, "gsl_sf_elljac_e(-1e-10|0.1) sn"); sa += test_sf_val(cn, 1.0, TEST_TOL0, "gsl_sf_elljac_e(-1e-10|0.1) cn"); sa += test_sf_val(dn, 1.0, TEST_TOL0, "gsl_sf_elljac_e(-1e-10|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(-1e-10|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(eps, m, &sn, &cn, &dn); sa += test_sf_val(sn, eps, TEST_TOL0, "gsl_sf_elljac_e(1e-10|0.1) sn"); sa += test_sf_val(cn, 1.0, TEST_TOL0, "gsl_sf_elljac_e(1e-10|0.1) cn"); sa += test_sf_val(dn, 1.0, TEST_TOL0, "gsl_sf_elljac_e(1e-10|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(1e-10|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(1e-30, m, &sn, &cn, &dn); sa += test_sf_val(sn, 1e-30, TEST_TOL0, "gsl_sf_elljac_e(1e-30|0.1) sn"); sa += test_sf_val(cn, 1.0, TEST_TOL0, "gsl_sf_elljac_e(1e-30|0.1) cn"); sa += test_sf_val(dn, 1.0, TEST_TOL0, "gsl_sf_elljac_e(1e-30|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(1e-30|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(K / 2.0 - eps, m, &sn, &cn, &dn); sa += test_sf_val(sn, A - eps*B*C, TEST_TOL2, "gsl_sf_elljac_e(K/2-1e-10|0.1) sn"); sa += test_sf_val(cn, B + eps*A*C, TEST_TOL2, "gsl_sf_elljac_e(K/2-1e-10|0.1) cn"); sa += test_sf_val(dn, C + m*eps*A*B, TEST_TOL2, "gsl_sf_elljac_e(K/2-1e-10|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(K/2-1e-10|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(K / 2.0, m, &sn, &cn, &dn); sa += test_sf_val(sn, A, TEST_TOL2, "gsl_sf_elljac_e(K/2|0.1) sn"); sa += test_sf_val(cn, B, TEST_TOL2, "gsl_sf_elljac_e(K/2|0.1) cn"); sa += test_sf_val(dn, C, TEST_TOL2, "gsl_sf_elljac_e(K/2|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(K/2|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(K / 2.0 + eps, m, &sn, &cn, &dn); sa += test_sf_val(sn, A + eps*B*C, TEST_TOL2, "gsl_sf_elljac_e(K/2+1e-10|0.1) sn"); sa += test_sf_val(cn, B - eps*A*C, TEST_TOL2, "gsl_sf_elljac_e(K/2+1e-10|0.1) cn"); sa += test_sf_val(dn, C - m*eps*A*B, TEST_TOL2, "gsl_sf_elljac_e(K/2+1e-10|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(K/2+1e-10|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(K - eps, m, &sn, &cn, &dn); sa += test_sf_val(sn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(K-1e-10|0.1) sn"); sa += test_sf_val(cn, eps*C2, 10*TEST_SNGL, "gsl_sf_elljac_e(K-1e-10|0.1) cn"); sa += test_sf_val(dn, C2, TEST_TOL2, "gsl_sf_elljac_e(K-1e-10|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(K-1e-10|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(K, m, &sn, &cn, &dn); sa += test_sf_val(sn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(K|0.1) sn"); sa += test_sf_val(cn, 0.0, TEST_TOL1, "gsl_sf_elljac_e(K|0.1) cn"); sa += test_sf_val(dn, C2, TEST_TOL2, "gsl_sf_elljac_e(K|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(K|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(K + eps, m, &sn, &cn, &dn); sa += test_sf_val(sn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(K+1e-10|0.1) sn"); sa += test_sf_val(cn, -eps*C2, 10*TEST_SNGL, "gsl_sf_elljac_e(K+1e-10|0.1) cn"); sa += test_sf_val(dn, C2, TEST_TOL2, "gsl_sf_elljac_e(K+1e-10|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(K+1e-10|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(3.0*K / 2.0, m, &sn, &cn, &dn); sa += test_sf_val(sn, A, TEST_TOL2, "gsl_sf_elljac_e(3K/2|0.1) sn"); sa += test_sf_val(cn, -B, TEST_TOL2, "gsl_sf_elljac_e(3K/2|0.1) cn"); sa += test_sf_val(dn, C, TEST_TOL2, "gsl_sf_elljac_e(3K/2|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(3K/2|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(2.0*K - eps, m, &sn, &cn, &dn); sa += test_sf_val(sn, eps, 10*TEST_SNGL, "gsl_sf_elljac_e(2K-1e-10|0.1) sn"); sa += test_sf_val(cn, -1.0, TEST_TOL1, "gsl_sf_elljac_e(2K-1e-10|0.1) cn"); sa += test_sf_val(dn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(2K-1e-10|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(2K-1e-10|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(2.0*K, m, &sn, &cn, &dn); sa += test_sf_val(sn, 0.0, TEST_TOL1, "gsl_sf_elljac_e(2K|0.1) sn"); sa += test_sf_val(cn, -1.0, TEST_TOL1, "gsl_sf_elljac_e(2K|0.1) cn"); sa += test_sf_val(dn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(2K|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(2K|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(2.0*K + eps, m, &sn, &cn, &dn); sa += test_sf_val(sn, -eps, 10*TEST_SNGL, "gsl_sf_elljac_e(2K+1e-10|0.1) sn"); sa += test_sf_val(cn, -1.0, TEST_TOL1, "gsl_sf_elljac_e(2K+1e-10|0.1) cn"); sa += test_sf_val(dn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(2K+1e-10|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(2K+1e-10|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(5.0*K / 2.0, m, &sn, &cn, &dn); sa += test_sf_val(sn, -A, TEST_TOL2, "gsl_sf_elljac_e(5K/2|0.1) sn"); sa += test_sf_val(cn, -B, TEST_TOL2, "gsl_sf_elljac_e(5K/2|0.1) cn"); sa += test_sf_val(dn, C, TEST_TOL2, "gsl_sf_elljac_e(5K/2|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(5K/2|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(3.0*K - eps, m, &sn, &cn, &dn); sa += test_sf_val(sn, -1.0, TEST_TOL1, "gsl_sf_elljac_e(3K-1e-10|0.1) sn"); sa += test_sf_val(cn, -C2 * eps, 10*TEST_SNGL, "gsl_sf_elljac_e(3K-1e-10|0.1) cn"); sa += test_sf_val(dn, C2, TEST_TOL2, "gsl_sf_elljac_e(3K-1e-10|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(3K-1e-10|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(3.0*K, m, &sn, &cn, &dn); sa += test_sf_val(sn, -1.0, TEST_TOL1, "gsl_sf_elljac_e(3K|0.1) sn"); sa += test_sf_val(cn, 0.0, TEST_TOL1, "gsl_sf_elljac_e(3K|0.1) cn"); sa += test_sf_val(dn, C2, TEST_TOL2, "gsl_sf_elljac_e(3K|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(3K|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(3.0*K + eps, m, &sn, &cn, &dn); sa += test_sf_val(sn, -1.0, TEST_TOL1, "gsl_sf_elljac_e(3K+1e-10|0.1) sn"); sa += test_sf_val(cn, +C2 * eps, 10*TEST_SNGL, "gsl_sf_elljac_e(3K+1e-10|0.1) cn"); sa += test_sf_val(dn, C2, TEST_TOL2, "gsl_sf_elljac_e(3K+1e-10|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(3K+1e-10|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(7.0*K / 2.0, m, &sn, &cn, &dn); sa += test_sf_val(sn, -A, TEST_TOL2, "gsl_sf_elljac_e(7K/2|0.1) sn"); sa += test_sf_val(cn, B, TEST_TOL2, "gsl_sf_elljac_e(7K/2|0.1) cn"); sa += test_sf_val(dn, C, TEST_TOL2, "gsl_sf_elljac_e(7K/2|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(7K/2|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(4.0*K - eps, m, &sn, &cn, &dn); sa += test_sf_val(sn, -eps, 10*TEST_SNGL, "gsl_sf_elljac_e(4K-1e-10|0.1) sn"); sa += test_sf_val(cn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(4K-1e-10|0.1) cn"); sa += test_sf_val(dn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(4K-1e-10|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(4K-1e-10|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(4.0*K, m, &sn, &cn, &dn); sa += test_sf_val(sn, 0.0, TEST_TOL1, "gsl_sf_elljac_e(4K|0.1) sn"); sa += test_sf_val(cn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(4K|0.1) cn"); sa += test_sf_val(dn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(4K|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(4K|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(9.0 * K / 2.0, m, &sn, &cn, &dn); sa += test_sf_val(sn, A, TEST_TOL2, "gsl_sf_elljac_e(9K/2|0.1) sn"); sa += test_sf_val(cn, B, TEST_TOL2, "gsl_sf_elljac_e(9K/2|0.1) cn"); sa += test_sf_val(dn, C, TEST_TOL2, "gsl_sf_elljac_e(9K/2|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(9K/2|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(-K / 2.0, m, &sn, &cn, &dn); sa += test_sf_val(sn, -A, TEST_TOL2, "gsl_sf_elljac_e(-K/2|0.1) sn"); sa += test_sf_val(cn, B, TEST_TOL2, "gsl_sf_elljac_e(-K/2|0.1) cn"); sa += test_sf_val(dn, C, TEST_TOL2, "gsl_sf_elljac_e(-K/2|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(-K/2|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(-K, m, &sn, &cn, &dn); sa += test_sf_val(sn, -1.0, TEST_TOL1, "gsl_sf_elljac_e(-K|0.1) sn"); sa += test_sf_val(cn, 0.0, TEST_TOL1, "gsl_sf_elljac_e(-K|0.1) cn"); sa += test_sf_val(dn, C2, TEST_TOL2, "gsl_sf_elljac_e(-K|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(-K|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(-3.0*K / 2.0, m, &sn, &cn, &dn); sa += test_sf_val(sn, -A, TEST_TOL2, "gsl_sf_elljac_e(-3K/2|0.1) sn"); sa += test_sf_val(cn, -B, TEST_TOL2, "gsl_sf_elljac_e(-3K/2|0.1) cn"); sa += test_sf_val(dn, C, TEST_TOL2, "gsl_sf_elljac_e(-3K/2|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(-3K/2|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(-2.0*K, m, &sn, &cn, &dn); sa += test_sf_val(sn, 0.0, TEST_TOL1, "gsl_sf_elljac_e(-2K|0.1) sn"); sa += test_sf_val(cn, -1.0, TEST_TOL1, "gsl_sf_elljac_e(-2K|0.1) cn"); sa += test_sf_val(dn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(-2K|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(-2K|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(-5.0*K / 2.0, m, &sn, &cn, &dn); sa += test_sf_val(sn, A, TEST_TOL2, "gsl_sf_elljac_e(-5K/2|0.1) sn"); sa += test_sf_val(cn, -B, TEST_TOL2, "gsl_sf_elljac_e(-5K/2|0.1) cn"); sa += test_sf_val(dn, C, TEST_TOL2, "gsl_sf_elljac_e(-5K/2|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(-5K/2|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(-3.0*K, m, &sn, &cn, &dn); sa += test_sf_val(sn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(-3K|0.1) sn"); sa += test_sf_val(cn, 0.0, TEST_TOL1, "gsl_sf_elljac_e(-3K|0.1) cn"); sa += test_sf_val(dn, C2, TEST_TOL2, "gsl_sf_elljac_e(-3K|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(-3K|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(-7.0*K / 2.0, m, &sn, &cn, &dn); sa += test_sf_val(sn, A, TEST_TOL2, "gsl_sf_elljac_e(-7K/2|0.1) sn"); sa += test_sf_val(cn, B, TEST_TOL2, "gsl_sf_elljac_e(-7K/2|0.1) cn"); sa += test_sf_val(dn, C, TEST_TOL2, "gsl_sf_elljac_e(-7K/2|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(-7K/2|0.1)"); s += sa; sa = 0; stat_ej = gsl_sf_elljac_e(-4.0*K, m, &sn, &cn, &dn); sa += test_sf_val(sn, 0.0, TEST_TOL1, "gsl_sf_elljac_e(-4K|0.1) sn"); sa += test_sf_val(cn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(-4K|0.1) cn"); sa += test_sf_val(dn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(-4K|0.1) dn"); gsl_test(sa, " gsl_sf_elljac_e(-4K|0.1)"); s += sa; } return s; } int test_laguerre(void) { gsl_sf_result r; int s = 0; TEST_SF(s, gsl_sf_laguerre_1_e, (0.5, -1.0, &r), 2.5, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_1_e, (0.5, 1.0, &r), 0.5, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_1_e, (1.0, 1.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_2_e, ( 0.5, -1.0, &r), 4.875, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_2_e, ( 0.5, 1.0, &r), -0.125, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_2_e, ( 1.0, 1.0, &r), 0.5, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_2_e, (-1.0, 1.0, &r), -0.5, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_2_e, (-2.0, 1.0, &r), 0.5, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_2_e, (-3.0, 1.0, &r), 2.5, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_3_e, (0.5, -1.0, &r), 8.479166666666666667, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_3_e, (0.5, 1.0, &r), -0.6041666666666666667, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_3_e, (1.0, 1.0, &r), -0.16666666666666666667, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_3_e, ( 2.0, 1.0, &r), 2.3333333333333333333, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_3_e, (-2.0, 1.0, &r), 1.0/3.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_3_e, (-3.0, 1.0, &r), -1.0/6.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_3_e, (-4.0, 1.0, &r), -8.0/3.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (1, 0.5, 1.0, &r), 0.5, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (2, 1.0, 1.0, &r), 0.5, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (3, 2.0, 1.0, &r), 2.3333333333333333333, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (4, 2.0, 0.5, &r), 6.752604166666666667, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (90, 2.0, 0.5, &r), -48.79047157201507897, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (90, 2.0, -100.0, &r), 2.5295879275042410902e+63, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (90, 2.0, 100.0, &r), -2.0929042259546928670e+20, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, 2.0, -0.5, &r), 2.2521795545919391405e+07, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, 2.0, 0.5, &r), -28.764832945909097418, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (1000, 2.0, -0.5, &r), 2.4399915170947549589e+21, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (1000, 2.0, 0.5, &r), -306.77440254315317525, TEST_TOL2, GSL_SUCCESS); /**/ TEST_SF(s, gsl_sf_laguerre_n_e, (100000, 2.0, 1.0, &r), 5107.73491348319, TEST_TOL4, GSL_SUCCESS); /* Compute these with the recurrence * L(0,alpha,x)=1; * L(1,alpha,x)=1+alpha-x; * L(n,alpha,x)=((2*n-1+alpha-x)*L(n-1,alpha,x)-(n+alpha-1)*L(n-2,alpha,x))/k */ TEST_SF(s, gsl_sf_laguerre_n_e, (1e5, 2.5, 2.5, &r), -0.41491680394598644969113795e5, TEST_TOL4, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (1e5+1, 2.5, 2.5, &r), -0.41629446949552321027514888e5, TEST_TOL4, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (1e6+1, 2.5, 2.5, &r), -0.48017961545391273151977118e6, TEST_TOL4, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (5e6+1, 2.5, 2.5, &r), -0.15174037401611122446089494e7, TEST_TOL6, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (8e6+1, 2.5, 2.5, &r), 0.63251509472091810994286362e6, TEST_SNGL, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (1e7+1, 2.5, 2.5, &r), 0.15299484685632983178033887e7, TEST_SNGL, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (1e8+1, 2.5, 2.5, &r), 0.23645341644922756725290777e8, TEST_SNGL, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (1e9+1, 2.5, 2.5, &r), -0.17731002248958790286185878e8, 100*TEST_SNGL, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (1, -2.0, 1.0, &r), -2.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (2, -2.0, 1.0, &r), 0.5, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (3, -2.0, 1.0, &r), 1.0/3.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (10, -2.0, 1.0, &r), -0.04654954805996472663, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (10, -5.0, 1.0, &r), -0.0031385030864197530864, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (10, -9.0, 1.0, &r), -2.480158730158730159e-06, TEST_TOL5, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (10, -11.0, 1.0, &r), 2.7182818011463844797, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (10, -11.0, -1.0, &r), 0.3678794642857142857, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, -2.0, 1.0, &r), -0.0027339992019526273866, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, -2.0, -1.0, &r), 229923.09193402028290, TEST_TOL5, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, -10.0, 1.0, &r), 3.25966665871244092e-11, TEST_TOL6, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, -10.0, -1.0, &r), 0.00016484365618205810025, TEST_TOL6, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, -20.0, 1.0, &r), 5.09567630343671251e-21, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, -30.0, 1.0, &r), 3.46063150272466192e-34, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, -50.0, 1.0, &r), 1.20981872933162889e-65, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, -50.0, -1.0, &r), 8.60763477742332922e-65, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, -50.5, 1.0, &r), 4.84021010426688393e-31, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, -50.5, -1.0, &r), 8.49861345212160618e-33, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, -101.0, 1.0, &r), 2.7182818284590452354, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, -101.0, -1.0, &r), 0.3678794411714423216, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, -102.0, 1.0, &r), 271.8281828459045235, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, -102.0, -1.0, &r), 37.52370299948711680, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, -110.0, 1.0, &r), 1.0666955248998831554e+13, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, -110.0, -1.0, &r), 1.7028306108058225871e+12, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, -200.0, 1.0, &r), 7.47851889721356628e+58, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, -200.0, -1.0, &r), 2.73740299754732273e+58, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, -50.0, 10.0, &r), 4.504712811317745591e-21, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, -50.0, -10.0, &r), 1.475165520610679937e-11, TEST_TOL1, GSL_SUCCESS); /* test cases for Ed Smith-Rowland */ TEST_SF(s, gsl_sf_laguerre_n_e, (100, 0.0, 0.5, &r), 0.18682260367692278801, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, 0.0, 10.5, &r), 9.1796907354050059874, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, 0.0, -10.5, &r), 5.6329215744170606488e24, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, 0.0, 100.5, &r), -3.9844782875811907525e20, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_laguerre_n_e, (100, 0.0, 150, &r), -1.4463204337261709595e31, TEST_TOL2, GSL_SUCCESS); return s; } int test_lambert(void) { gsl_sf_result r; int s = 0; TEST_SF(s, gsl_sf_lambert_W0_e, (0.0, &r), 0.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lambert_W0_e, (1.0, &r), 0.567143290409783872999969, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lambert_W0_e, (2.0, &r), 0.852605502013725491346472, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lambert_W0_e, (20.0, &r), 2.205003278024059970493066, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lambert_W0_e, (1000.0, &r), 5.24960285240159622712606, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lambert_W0_e, (1.0e+6, &r), 11.38335808614005262200016, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lambert_W0_e, (1.0e+12, &r), 24.43500440493491313826305, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lambert_W0_e, (1.0e+308, &r), 702.641362034106812081125, TEST_TOL0, GSL_SUCCESS); /* Test case from Katrin Wolff fails under double-precision */ TEST_SF(s, gsl_sf_lambert_W0_e, (1.6849341956993852953416990, &r), 0.775706963944252869680440, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lambert_W0_e, (-1.0/M_E - GSL_DBL_EPSILON, &r), -1.0, TEST_TOL0, GSL_EDOM); TEST_SF(s, gsl_sf_lambert_W0_e, (-1.0/M_E + 1.0/(1024.0*1024.0*1024.0), &r), -0.999928845560308370714970, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lambert_W0_e, (-1.0/M_E + 1.0/(1024.0*1024.0), &r), -0.997724730359774141620354, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lambert_W0_e, (-1.0/M_E + 1.0/512.0, &r), -0.900335676696088773044678, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lambert_W0_e, (-1.0/M_E + 0.25, &r), -0.1349044682661213545487599, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lambert_Wm1_e, (0.0, &r), 0.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lambert_Wm1_e, (1.0, &r), 0.567143290409783872999969, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lambert_Wm1_e, (2.0, &r), 0.852605502013725491346472, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lambert_Wm1_e, (20.0, &r), 2.205003278024059970493066, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lambert_Wm1_e, (-1.0/M_E - GSL_DBL_EPSILON, &r), -1.0, TEST_TOL0, GSL_EDOM); TEST_SF(s, gsl_sf_lambert_Wm1_e, (-1.0/M_E + 1.0/(1024.0*1024.0*1024.0), &r), -1.000071157815154608049055, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_lambert_Wm1_e, (-1.0/M_E + 1.0/(1024.0*1024.0), &r), -1.002278726118593023934693, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_lambert_Wm1_e, (-1.0/M_E + 1.0/512.0, &r), -1.106761200865743124599130, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_lambert_Wm1_e, (-1.0/M_E + 1.0/64.0, &r), -1.324240940341812125489772, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_lambert_Wm1_e, (-1.0/M_E + 0.25, &r), -3.345798131120112, TEST_TOL1, GSL_SUCCESS); return s; } int test_log(void) { gsl_sf_result r; gsl_sf_result r1, r2; int s = 0; TEST_SF(s, gsl_sf_log_e, (0.1, &r), -2.3025850929940456840, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_e, (1.1, &r), 0.09531017980432486004, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_e, (1000.0, &r), 6.907755278982137052, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_abs_e, (-0.1, &r), -2.3025850929940456840, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_abs_e, (-1.1, &r), 0.09531017980432486004, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_abs_e, (-1000.0, &r), 6.907755278982137052, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_abs_e, (0.1, &r), -2.3025850929940456840, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_abs_e, (1.1, &r), 0.09531017980432486004, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_abs_e, (1000.0, &r), 6.907755278982137052, TEST_TOL0, GSL_SUCCESS); TEST_SF_2(s, gsl_sf_complex_log_e, (1.0, 1.0, &r1, &r2), 0.3465735902799726547, TEST_TOL0, 0.7853981633974483096, TEST_TOL0, GSL_SUCCESS); TEST_SF_2(s, gsl_sf_complex_log_e, (1.0, -1.0, &r1, &r2), 0.3465735902799726547, TEST_TOL0, -0.7853981633974483096, TEST_TOL0, GSL_SUCCESS); TEST_SF_2(s, gsl_sf_complex_log_e, (1.0, 100.0, &r1, &r2), 4.605220183488258022, TEST_TOL0, 1.560796660108231381, TEST_TOL0, GSL_SUCCESS); TEST_SF_2(s, gsl_sf_complex_log_e, (-1000.0, -1.0, &r1, &r2), 6.907755778981887052, TEST_TOL0, -3.1405926539231263718, TEST_TOL0, GSL_SUCCESS); TEST_SF_2(s, gsl_sf_complex_log_e, (-1.0, 0.0, &r1, &r2), 0.0, TEST_TOL0, 3.1415926535897932385, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_1plusx_e, (1.0e-10, &r), 9.999999999500000000e-11, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_1plusx_e, (1.0e-8, &r), 9.999999950000000333e-09, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_1plusx_e, (1.0e-4, &r), 0.00009999500033330833533, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_1plusx_e, (0.1, &r), 0.09531017980432486004, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_1plusx_e, (0.49, &r), 0.3987761199573677730, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_1plusx_e, (-0.49, &r), -0.6733445532637655964, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_1plusx_e, (1.0, &r), M_LN2, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_1plusx_e, (-0.99, &r), -4.605170185988091368, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_1plusx_mx_e, (1.0e-10, &r), -4.999999999666666667e-21, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_1plusx_mx_e, (1.0e-8, &r), -4.999999966666666917e-17, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_1plusx_mx_e, (1.0e-4, &r), -4.999666691664666833e-09, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_1plusx_mx_e, (0.1, &r), -0.004689820195675139956, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_1plusx_mx_e, (0.49, &r), -0.09122388004263222704, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_1plusx_mx_e, (-0.49, &r), -0.18334455326376559639, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_1plusx_mx_e, (1.0, &r), M_LN2-1.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_log_1plusx_mx_e, (-0.99, &r), -3.615170185988091368, TEST_TOL0, GSL_SUCCESS); return s; } int test_pow_int(void) { gsl_sf_result r; int status = 0; int s = 0; TEST_SF(s, gsl_sf_pow_int_e, (2.0, 3, &r), 8.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_pow_int_e, (-2.0, 3, &r), -8.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_pow_int_e, (2.0, -3, &r), 1.0/8.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_pow_int_e, (-2.0, -3, &r), -1.0/8.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_pow_int_e, (10.0, 4, &r), 1.0e+4, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_pow_int_e, (10.0, -4, &r), 1.0e-4, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_pow_int_e, (-10.0, 4, &r), 1.0e+4, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_pow_int_e, (-10.0, -4, &r), 1.0e-4, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_pow_int_e, (10.0, 40, &r), 1.0e+40, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_pow_int_e, (8.0, -40, &r), 7.523163845262640051e-37, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_pow_int_e, (-10.0, 40, &r), 1.0e+40, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_pow_int_e, (-8.0, -40, &r), 7.523163845262640051e-37, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_pow_int_e, (10.0, 41, &r), 1.0e+41, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_pow_int_e, (8.0, -41, &r), 9.403954806578300064e-38, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_pow_int_e, (-10.0, 41, &r), -1.0e+41, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_pow_int_e, (-8.0, -41, &r), -9.403954806578300064e-38, TEST_TOL0, GSL_SUCCESS); return status; } int test_psi(void) { gsl_sf_result r; int s = 0; /* Test values taken 1-4 from gp-pari */ TEST_SF(s, gsl_sf_psi_int_e, (1, &r), -0.57721566490153286060, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_int_e, (2, &r), 0.42278433509846713939, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_int_e, (3, &r), 0.92278433509846713939, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_int_e, (4, &r), 1.2561176684318004727, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_int_e, (5, &r), 1.5061176684318004727, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_int_e, (100, &r), 4.600161852738087400, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_int_e, (110, &r), 4.695928024251535633, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_int_e, (5000, &r), 8.517093188082904107, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_e, (5000.0, &r), 8.517093188082904107, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_e, (5.0, &r), 1.5061176684318004727, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_e, (-10.5, &r), 2.3982391295357816134, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_e, (-100.5, &r), 4.615124601338064117, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_e, (-1.0e+5-0.5, &r), 11.512935464924395337, 4.0*TEST_TOL4, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_e, (-262144.0-0.5, &r), 12.476653064769611581, 4.0*TEST_TOL4, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1piy_e, (0.8, &r), -0.07088340212750589223, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1piy_e, (1.0, &r), 0.09465032062247697727, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1piy_e, (5.0, &r), 1.6127848446157465854, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1piy_e, (100.0, &r), 4.605178519404762003, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1piy_e, (2000.0, &r), 7.600902480375416216, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1piy_e, (-0.8, &r), -0.07088340212750589223, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1piy_e, (-1.0, &r), 0.09465032062247697727, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1piy_e, (-5.0, &r), 1.6127848446157465854, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1piy_e, (-100.0, &r), 4.605178519404762003, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1piy_e, (-2000.0, &r), 7.600902480375416216, TEST_TOL0, GSL_SUCCESS); /* Additional test values 1-4 computed using gp-pari and Abramowitz & Stegun 6.4.6 */ TEST_SF(s, gsl_sf_psi_1_int_e, (1, &r), 1.6449340668482264364, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1_int_e, (2, &r), 0.64493406684822643647, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1_int_e, (3, &r), 0.39493406684822643647, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1_int_e, (4, &r), 0.28382295573711532536, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1_int_e, (1, &r), 1.6449340668482264365, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1_int_e, (5, &r), 0.22132295573711532536, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1_int_e, (100, &r), 0.010050166663333571395, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1_int_e, (110, &r), 0.009132356622022545705, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1_int_e, (500, &r), 0.0020020013333322666697, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1_e, (1.0/32.0, &r), 1025.5728544782377089, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1_e, (1.0, &r), 1.6449340668482264365, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1_e, (5.0, &r), 0.22132295573711532536, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1_e, (100.0, &r), 0.010050166663333571395, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1_e, (110.0, &r), 0.009132356622022545705, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1_e, (500.0, &r), 0.0020020013333322666697, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1_e, (-1.0 - 1.0/128.0, &r), 16386.648472598746587, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1_e, (-1.50, &r), 9.3792466449891237539, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1_e, (-10.5, &r), 9.7787577398148123845, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1_e, (-15.5, &r), 9.8071247184113896201, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1_e, (-50.5, &r), 9.8499971860824842274, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_1_e, (-1000.5, &r), 9.8686054001734414233, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_n_e, (1, 1, &r), 1.6449340668482264364, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_n_e, (1, 2, &r), 0.64493406684822643647, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_n_e, (1, 3, &r), 0.39493406684822643647, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_n_e, (1, 4, &r), 0.28382295573711532536, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_n_e, (1, 5, &r), 0.22132295573711532536, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_n_e, (1, 100, &r), 0.010050166663333571395, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_n_e, (1, 110, &r), 0.009132356622022545705, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_n_e, (1, 500, &r), 0.0020020013333322666697, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_n_e, (3, 5.0, &r), 0.021427828192755075022, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_n_e, (3, 500.0, &r), 1.6048063999872000683e-08, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_n_e, (10, 5.0, &r), -0.08675107579196581317, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_n_e, (10, 50.0, &r), -4.101091112731268288e-12, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_n_e, (0, -1.5, &r), 0.70315664064524318723, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_psi_n_e, (1, -1.5, &r), 9.3792466449891237539, TEST_TOL0, GSL_SUCCESS); return s; } int test_psi_complex(void) { gsl_sf_result r1; gsl_sf_result r2; int s = 0; TEST_SF_2(s, gsl_sf_complex_psi_e, (1.0e+07, 1.0e+06, &r1, &r2), 16.1230707668799525, TEST_TOL0, 0.09966865744165720, TEST_TOL0, GSL_SUCCESS); TEST_SF_2(s, gsl_sf_complex_psi_e, (10.0, 50.0, &r1, &r2), 3.92973987174863660, TEST_TOL0, 1.38302847985210276, TEST_TOL0, GSL_SUCCESS); TEST_SF_2(s, gsl_sf_complex_psi_e, (2.0, 21.0, &r1, &r2), 3.04697388853248195, TEST_TOL0, 1.49947549076817824, TEST_TOL0, GSL_SUCCESS); TEST_SF_2(s, gsl_sf_complex_psi_e, (1.5, 0.0, &r1, &r2), 0.0364899739785765206, TEST_TOL2, 0.0, TEST_TOL1, GSL_SUCCESS); TEST_SF_2(s, gsl_sf_complex_psi_e, (1.0, 5.0, &r1, &r2), 1.612784844615747, TEST_TOL1, 1.470796326794968, TEST_TOL1, GSL_SUCCESS); TEST_SF_2(s, gsl_sf_complex_psi_e, (-1.5, 5.0, &r1, &r2), 1.68260717336484070, TEST_TOL0, 1.95230236730713338, TEST_TOL0, GSL_SUCCESS); TEST_SF_2(s, gsl_sf_complex_psi_e, (-20.5, -20.5, &r1, &r2), 3.37919358657933066, TEST_TOL0, -2.36829046481731091, TEST_TOL0, GSL_SUCCESS); return s; } int test_synch(void) { gsl_sf_result r; int s = 0; TEST_SF(s, gsl_sf_synchrotron_1_e, (0.01, &r), 0.444972504114210632, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_synchrotron_1_e, (1.0, &r), 0.651422815355364504, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_synchrotron_1_e, (10.0, &r), 0.000192238264300868882, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_synchrotron_1_e, (100.0, &r), 4.69759366592220221e-43, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_synchrotron_2_e, (0.01, &r), 0.23098077342226277732, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_synchrotron_2_e, (1.0, &r), 0.4944750621042082670, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_synchrotron_2_e, (10.0, &r), 0.00018161187569530204281, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_synchrotron_2_e, (256.0, &r), 1.3272635474353774058e-110, TEST_TOL4, GSL_SUCCESS); /* exp()... not my fault */ return s; } int test_transport(void) { gsl_sf_result r; int s = 0; TEST_SF(s, gsl_sf_transport_2_e, (1.0e-10, &r), 9.9999999999999999999e-11, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_2_e, (1.0, &r), 0.97303256135517012845, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_2_e, (3.0, &r), 2.41105004901695346199, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_2_e, (10.0, &r), 3.28432911449795173575, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_2_e, (100.0, &r), 3.28986813369645287294, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_2_e, (1.0e+05, &r), 3.28986813369645287294, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_3_e, (1.0e-10, &r), 4.999999999999999999997e-21, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_3_e, (1.0, &r), 0.479841006572417499939, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_3_e, (3.0, &r), 3.210604662942246772338, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_3_e, (5.0, &r), 5.614386613842273228585, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_3_e, (10.0, &r), 7.150322712008592975030, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_3_e, (30.0, &r), 7.212341416160946511930, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_3_e, (100.0, &r), 7.212341418957565712398, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_3_e, (1.0e+05, &r), 7.212341418957565712398, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_4_e, (1.0e-10, &r), 3.33333333333333333333e-31, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_4_e, (1.0e-07, &r), 3.33333333333333166666e-22, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_4_e, (1.0e-04, &r), 3.33333333166666666726e-13, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_4_e, (0.1, &r), 0.000333166726172109903824, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_4_e, (1.0, &r), 0.31724404523442648241, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_4_e, (3.0, &r), 5.96482239737147652446, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_4_e, (5.0, &r), 15.3597843168821829816, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_4_e, (10.0, &r), 25.2736676770304417334, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_4_e, (30.0, &r), 25.9757575220840937469, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_4_e, (100.0, &r), 25.9757576090673165963, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_4_e, (1.0e+05, &r), 25.9757576090673165963, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_5_e, (1.0e-10, &r), 2.49999999999999999999e-41, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_5_e, (1.0e-07, &r), 2.49999999999999861111e-29, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_5_e, (1.0e-04, &r), 2.49999999861111111163e-17, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_5_e, (0.1, &r), 0.000024986116317791487410, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_5_e, (1.0, &r), 0.236615879239094789259153, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_5_e, (3.0, &r), 12.77055769104415951115760, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_5_e, (5.0, &r), 50.26309221817518778543615, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_5_e, (10.0, &r), 116.3807454024207107698556, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_5_e, (30.0, &r), 124.4313279083858954839911, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_5_e, (100.0, &r), 124.4313306172043911597639, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_transport_5_e, (1.0e+05, &r), 124.43133061720439115976, TEST_TOL0, GSL_SUCCESS); return s; } int test_trig(void) { gsl_sf_result r; gsl_sf_result r1, r2; double theta; int s = 0; int sa; TEST_SF(s, gsl_sf_sin_e, (-10.0, &r), 0.5440211108893698134, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_sin_e, (1.0, &r), 0.8414709848078965067, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_sin_e, (1000.0, &r), 0.8268795405320025603, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_sin_e, (1048576.75, &r), 0.8851545351115651914, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_sin_e, (62831853.75, &r), 0.6273955953485000827, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_sin_e, (1073741822.5, &r), -0.8284043541754465988, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_sin_e, (1073741824.0, &r), -0.6173264150460421708, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_sin_e, (1073741825.5, &r), 0.7410684679436226926, TEST_SQRT_TOL0, GSL_SUCCESS); /* TEST_SF(s, gsl_sf_sin_e, (1099511627776.0, &r), -0.4057050115328287198, 32.0*TEST_SQRT_TOL0, GSL_SUCCESS); */ TEST_SF(s, gsl_sf_cos_e, (-10.0, &r), -0.8390715290764524523, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_cos_e, (1.0, &r), 0.5403023058681397174, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_cos_e, (1000.0, &r), 0.5623790762907029911, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_cos_e, (1048576.75, &r), 0.4652971620066351799, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_cos_e, (62831853.75, &r), 0.7787006914966116436, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_cos_e, (1073741822.5, &r), -0.5601305436977716102, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_cos_e, (1073741824.0, &r), 0.7867071229411881196, TEST_SQRT_TOL0, GSL_SUCCESS); /* TEST_SF(s, gsl_sf_cos_e, (1099511627776.0, &r), -0.9140040719915570023, 128.0*TEST_SQRT_TOL0, GSL_SUCCESS); */ TEST_SF(s, gsl_sf_sinc_e, (1.0/1024.0, &r), 0.9999984312693665404, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_sinc_e, (1.0/2.0, &r), 2.0/M_PI, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_sinc_e, (80.5, &r), 0.0039541600768172754, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_sinc_e, (100.5, &r), 0.0031672625490924445, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_sinc_e, (1.0e+06 + 0.5, &r), 3.18309727028927157e-07, TEST_TOL0, GSL_SUCCESS); /* TEST_SF(s, gsl_sf_sin_pi_x_e, (1000.5, &r), 1.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_sin_pi_x_e, (10000.0 + 1.0/65536.0, &r), 0.00004793689960306688455, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_sin_pi_x_e, (1099511627776.0 + 1 + 0.125, &r), -0.3826834323650897717, TEST_TOL0, GSL_SUCCESS); */ TEST_SF_2(s, gsl_sf_complex_sin_e, (1.0, 5.0, &r1, &r2), 62.44551846769653403, TEST_TOL0, 40.09216577799840254, TEST_TOL0, GSL_SUCCESS); TEST_SF_2(s, gsl_sf_complex_cos_e, (1.0, 5.0, &r1, &r2), 40.09580630629882573, TEST_TOL0, -62.43984868079963017, TEST_TOL0, GSL_SUCCESS); TEST_SF_2(s, gsl_sf_complex_logsin_e, (1.0, 100.0, &r1, &r2), 99.3068528194400546900, TEST_TOL0, 0.5707963267948966192, TEST_TOL0, GSL_SUCCESS); TEST_SF_2(s, gsl_sf_complex_logsin_e, (1.0, -100.0, &r1, &r2), 99.3068528194400546900, TEST_TOL1, -0.5707963267948966192, TEST_TOL1, GSL_SUCCESS); TEST_SF_2(s, gsl_sf_complex_logsin_e, (5.0, 5.0, &r1, &r2), 4.3068909128079757420, TEST_TOL0, 2.8540063315538773952, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lnsinh_e, (0.1, &r), -2.3009189815304652235, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lnsinh_e, (1.0, &r), 0.16143936157119563361, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lnsinh_e, (5.0, &r), 4.306807418479684201, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lnsinh_e, (100.0, &r), 99.30685281944005469, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lncosh_e, (0.125, &r), 0.007792239318898252791, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lncosh_e, (1.0, &r), 0.4337808304830271870, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lncosh_e, (5.0, &r), 4.306898218339271555, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_lncosh_e, (100.0, &r), 99.30685281944005469, TEST_TOL0, GSL_SUCCESS); TEST_SF_2(s, gsl_sf_polar_to_rect, (10.0, M_PI/6.0, &r1, &r2), (10.0 * sqrt(3) / 2.0), TEST_TOL0, (10.0 * 0.5), TEST_TOL0, GSL_SUCCESS); TEST_SF_2(s, gsl_sf_polar_to_rect, (10.0, -2.0/3.0*M_PI, &r1, &r2), (10.0 * (-0.5)), TEST_TOL1, (10.0 * (-sqrt(3.0)/2.0)), TEST_TOL1, GSL_SUCCESS); /* In double precision M_PI = \pi - 1.2246467991473531772e-16, i.e. the nearest machine number is slightly below the exact value of \pi. The true value of \pi satisfies M_PI < \pi < nextafter(M_PI,+Inf) where nextafter(M_PI,+Inf) = M_PI + 2*DBL_EPSILON This also means that 2*M_PI is less than \pi by 2.449e-16. The true value of 2\pi satisfies 2*M_PI < 2\pi < nextafter(2*M_PI,+Inf) where nextafter(2*M_PI,+Inf) = 2*M_PI + 4*DBL_EPSILON BJG 25/9/06 */ #define DELTA (1.2246467991473531772e-16) TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (2.0*M_PI), 2*M_PI, TEST_TOL1); TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (-2.0*M_PI), 2*DELTA, TEST_TOL1); TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (2.0*M_PI+4*GSL_DBL_EPSILON), 4*GSL_DBL_EPSILON-2*DELTA, TEST_TOL1); TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (-2.0*M_PI-4*GSL_DBL_EPSILON), 2*M_PI-4*GSL_DBL_EPSILON+2*DELTA, TEST_TOL1); TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (4.0*M_PI+8*GSL_DBL_EPSILON), 8*GSL_DBL_EPSILON-4*DELTA, TEST_TOL1); TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (-4.0*M_PI-8*GSL_DBL_EPSILON), 2*M_PI-8*GSL_DBL_EPSILON+4*DELTA, TEST_TOL1); TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (1e9), 0.5773954235013851694, TEST_TOL1); TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (1e12), 5.625560548042800009446, TEST_SNGL); TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (-1e9), 5.7057898836782013075, TEST_TOL1); TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (-1e12), 0.6576247591367864674792517289, 100*TEST_SNGL); #ifdef EXTENDED TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (1e15), 2.1096981170701125979, TEST_TOL1); TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (-1e15), 4.1734871901094738790, TEST_TOL1); #endif TEST_SF(s, gsl_sf_angle_restrict_pos_err_e, (2.0*M_PI, &r), 2*M_PI, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_angle_restrict_pos_err_e, (-2.0*M_PI, &r), 2*DELTA, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_angle_restrict_pos_err_e, (1e9, &r), 0.5773954235013851694, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_angle_restrict_pos_err_e, (1e12, &r), 5.625560548042800009446, TEST_SNGL, GSL_SUCCESS); TEST_SF(s, gsl_sf_angle_restrict_pos_err_e, (-1e9, &r), 5.7057898836782013075, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_angle_restrict_pos_err_e, (-1e12, &r), 0.6576247591367864674792517289, 100*TEST_SNGL, GSL_SUCCESS); TEST_SF (s, gsl_sf_angle_restrict_pos_err_e, (1e15, &r), GSL_NAN, TEST_TOL1, GSL_ELOSS); TEST_SF (s, gsl_sf_angle_restrict_pos_err_e, (-1e15, &r), GSL_NAN, TEST_TOL1, GSL_ELOSS); TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (2.0*M_PI), -2*DELTA, TEST_TOL1); TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (-2.0*M_PI), 2*DELTA, TEST_TOL1); TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (M_PI), M_PI, TEST_TOL1); TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (-M_PI), -M_PI, TEST_TOL1); TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (M_PI+2*GSL_DBL_EPSILON), -M_PI+2*(GSL_DBL_EPSILON-DELTA), TEST_TOL1); TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (-M_PI-2*GSL_DBL_EPSILON), M_PI-2*(GSL_DBL_EPSILON-DELTA), TEST_TOL1); TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (3*M_PI+6*GSL_DBL_EPSILON), -M_PI+6*GSL_DBL_EPSILON-4*DELTA, TEST_TOL1); TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (-3*M_PI-6*GSL_DBL_EPSILON), M_PI-6*GSL_DBL_EPSILON+4*DELTA, TEST_TOL1); TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (1e9), 0.5773954235013851694, TEST_TOL1); TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (1e12), -0.6576247591367864674792517289, 100*TEST_SNGL); TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (-1e9), -0.5773954235013851694, TEST_TOL1); TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (-1e12), 0.6576247591367864674792517289, 100*TEST_SNGL); #ifdef EXTENDED TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (1e15), 2.1096981170701125979, TEST_TOL1); TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (-1e15), -2.1096981170701125979, TEST_TOL1); #endif TEST_SF (s, gsl_sf_angle_restrict_symm_err_e, (2.0*M_PI, &r), -2*DELTA, TEST_TOL1, GSL_SUCCESS); TEST_SF (s, gsl_sf_angle_restrict_symm_err_e, (-2.0*M_PI, &r), 2*DELTA, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_angle_restrict_symm_err_e, (1e9, &r), 0.5773954235013851694, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_angle_restrict_symm_err_e, (1e12, &r), -0.6576247591367864674792517289, 100*TEST_SNGL, GSL_SUCCESS); TEST_SF(s, gsl_sf_angle_restrict_symm_err_e, (-1e9, &r), -0.5773954235013851694, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_angle_restrict_symm_err_e, (-1e12, &r), 0.6576247591367864674792517289, 100*TEST_SNGL, GSL_SUCCESS); TEST_SF (s, gsl_sf_angle_restrict_symm_err_e, (1e15, &r), GSL_NAN, TEST_TOL1, GSL_ELOSS); TEST_SF (s, gsl_sf_angle_restrict_symm_err_e, (-1e15, &r), GSL_NAN, TEST_TOL1, GSL_ELOSS); theta = 5.0*M_PI + 5*DELTA + M_PI/2.0; gsl_sf_angle_restrict_pos_e(&theta); sa = 0; sa += ( test_sf_frac_diff( theta, 3.0/2.0*M_PI ) > TEST_TOL0 ); gsl_test(sa, " gsl_angle_restrict_pos_e: theta = 11/2 Pi"); s += sa; theta = -5.0*M_PI - 5*DELTA - M_PI/2.0; gsl_sf_angle_restrict_pos_e(&theta); sa = 0; sa += ( test_sf_frac_diff( theta, M_PI/2.0 ) > 2.0*TEST_TOL0 ); gsl_test(sa, " gsl_angle_restrict_pos_e: theta = -11/2 Pi"); s += sa; theta = 50000.0 + 1.0/65536.0; gsl_sf_angle_restrict_pos_e(&theta); sa = 0; sa += ( test_sf_frac_diff( theta, 4.6945260308194656055 ) > TEST_TOL0 ); gsl_test(sa, " gsl_angle_restrict_pos_e: theta = 50000.0 + 1.0/65536.0"); s += sa; theta = 5000000.0 + 1.0/65536.0; gsl_sf_angle_restrict_pos_e(&theta); sa = 0; sa += ( test_sf_frac_diff( theta, 4.49537973053997376 ) > TEST_TOL0 ); gsl_test(sa, " gsl_angle_restrict_pos_e: theta = 5000000.0 + 1.0/65536.0"); s += sa; /* theta = 140737488355328.0; gsl_sf_angle_restrict_pos_e(&theta); sa = 0; sa += ( test_sf_frac_diff( theta, 3.20652300406795792638 ) > TEST_TOL0 ); gsl_test(sa, " gsl_angle_restrict_pos_e: theta = 2^47"); s += sa; */ theta = 5.0*M_PI + (5.5*DELTA + M_PI/2.0); gsl_sf_angle_restrict_symm_e(&theta); sa = 0; sa += ( test_sf_frac_diff( theta, -M_PI/2.0 ) > 2.0*TEST_TOL0 ); gsl_test(sa, " gsl_angle_restrict_symm_e: theta = 11/2 Pi"); s += sa; theta = -5.0*M_PI - (5.5*DELTA + M_PI/2.0); gsl_sf_angle_restrict_symm_e(&theta); sa = 0; sa += ( test_sf_frac_diff( theta, M_PI/2.0 ) > 2.0*TEST_TOL0 ); gsl_test(sa, " gsl_angle_restrict_symm_e: theta = -11/2 Pi"); s += sa; theta = 5.0*M_PI + 5*DELTA - M_PI/2.0; gsl_sf_angle_restrict_symm_e(&theta); sa = 0; sa += ( test_sf_frac_diff( theta, M_PI/2.0 ) > TEST_TOL0 ); gsl_test(sa, " gsl_angle_restrict_symm_e: theta = -9/2 Pi"); s += sa; theta = 3.0/2.0*M_PI + 3.0/2.0*DELTA; gsl_sf_angle_restrict_symm_e(&theta); sa = 0; sa += ( test_sf_frac_diff( theta, -M_PI/2.0 ) > TEST_TOL0 ); gsl_test(sa, " gsl_angle_restrict_symm_e: theta = 3/2 Pi"); s += sa; theta = -3.0/2.0*M_PI; gsl_sf_angle_restrict_symm_e(&theta); sa = 0; sa += ( test_sf_frac_diff( theta, M_PI/2.0 ) > TEST_TOL0 ); gsl_test(sa, " gsl_angle_restrict_symm_e: theta = -3/2 Pi"); s += sa; theta = 50000.0 + 1.0/65536.0; gsl_sf_angle_restrict_symm_e(&theta); sa = 0; sa += ( test_sf_frac_diff( theta, -1.5886592763601208714 ) > TEST_TOL0 ); gsl_test(sa, " gsl_angle_restrict_symm_e: theta = 50000.0 + 1.0/65536.0"); s += sa; return s; } /* I computed the values of zeta for s = -1e-10, 0, 1e-10 using the Jensen formula, zeta(s) = -1/2 + 1/(1-s) + integ(sin(s arctan(t))/((1+t^2)^(s/2)(exp(2pi*t)-1)), t, 0, inf) transforming the integral from a semi-infinite range to the range [0,pi/2] using the substitution t = tan(u). After Taylor expansion in s and numerical evaluation of the integrals this gave, zeta(s) = 1/2 + 1/(1-s) + (0.0810614667944862 +/- 2e-16) s + (-3.17822795429232e-3 +/- 2e-17) s^2 + .... for an expansion about s = 0 [BJG 7/01] */ int test_zeta(void) { gsl_sf_result r; int s = 0; TEST_SF(s, gsl_sf_zeta_int_e, (-61.0, &r), -3.30660898765775767257e+34, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_int_e, (-8, &r), 0.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_int_e, (-6, &r), 0.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_int_e, (-5.0, &r), -0.003968253968253968253968, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_int_e, (-4, &r), 0.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_int_e, (-3, &r), 1.0/120.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_int_e, (-2, &r), 0.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_int_e, (-1, &r), -1.0/12.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_int_e, ( 5.0, &r), 1.0369277551433699263313655, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_int_e, (31.0, &r), 1.0000000004656629065033784, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_int_e, (-61.0, &r), -3.30660898765775767257e+34, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_int_e, (-5.0, &r), -1.003968253968253968253968, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_int_e, (-8, &r), -1.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_int_e, (-6, &r), -1.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_int_e, (-4, &r), -1.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_int_e, (-3, &r), -119.0/120.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_int_e, (-2, &r), -1.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_int_e, (-1, &r), -13.0/12.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_int_e, ( 5.0, &r), 0.0369277551433699263313655, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_int_e, (31.0, &r), 0.0000000004656629065033784, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_e, (-151, &r), 8.195215221831378294e+143, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_e, (-51, &r), 9.68995788746359406565e+24, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_e, (-5, &r), -0.003968253968253968253968, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_e, (-8, &r), 0.0, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_e, (-6, &r), 0.0, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_e, (-4, &r), 0.0, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_e, (-3, &r), 1.0/120.0, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_e, (-2, &r), 0.0, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_e, (-1, &r), -1.0/12.0, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_e, (-0.5, &r), -0.207886224977354566017307, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_e, (-1e-10, &r), -0.49999999990810614668948, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_e, (0.0, &r), -0.5, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_e, (1e-10, &r), -0.50000000009189385333058, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_e, (0.5, &r), -1.460354508809586812889499, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_e, (1.0-1.0/1024.0, &r), -1023.4228554489429787, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_e, (1.0+1.0/1048576, &r), 1.0485765772157343441e+06, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_e, (5.0, &r), 1.036927755143369926331365, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zeta_e, (25.5, &r), 1.000000021074106110269959, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_e, (-8, &r), -1.0, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_e, (-6, &r), -1.0, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_e, (-4, &r), -1.0, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_e, (-3, &r), -119.0/120.0, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_e, (-2, &r), -1.0, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_e, (-1, &r), -13.0/12.0, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_e, (-0.5, &r), -1.207886224977354566017307, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_e, (-1e-10, &r), -1.49999999990810614668948, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_e, (0.0, &r), -1.5, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_e, (1e-10, &r), -1.50000000009189385333058, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_e, (0.5, &r), -2.460354508809586812889499, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_e, (2.0, &r), 0.64493406684822643647, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_e, (3.0, &r), 0.20205690315959428540, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_e, (5.0, &r), 0.0369277551433699263314, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_e, (9.5, &r), 0.0014125906121736622712, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_e, (10.5, &r), 0.000700842641736155219500, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_e, (12.5, &r), 0.000173751733643178193390, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_e, (13.5, &r), 0.000086686727462338155188, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_e, (15.5, &r), 0.000021619904246069108133, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_e, (16.5, &r), 0.000010803124900178547671, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_zetam1_e, (25.5, &r), 0.000000021074106110269959, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hzeta_e, (2, 1.0, &r), 1.6449340668482264365, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hzeta_e, (2, 10.0, &r), 0.1051663356816857461, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hzeta_e, (5, 1.0, &r), 1.0369277551433699263, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hzeta_e, (5, 10.0, &r), 0.000030413798676470276, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hzeta_e, (9, 0.1, &r), 1.0000000004253980e+09, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hzeta_e, (30, 0.5, &r), 1.0737418240000053e+09, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hzeta_e, (30, 0.9, &r), 2.3589824880264765e+01, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hzeta_e, (75, 0.25, &r), 1.4272476927059599e+45, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_eta_int_e, (-91, &r), -4.945598888750002040e+94, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_eta_int_e, (-51, &r), -4.363969073121683116e+40, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_eta_int_e, (-5, &r), 0.25, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_eta_int_e, (-1, &r), 0.25, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_eta_int_e, ( 0, &r), 0.5, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_eta_int_e, ( 5, &r), 0.9721197704469093059, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_eta_int_e, ( 6, &r), 0.9855510912974351041, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_eta_int_e, ( 20, &r), 0.9999990466115815221, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_eta_int_e, ( 1000, &r), 1.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_eta_e, (-51.5, &r), -1.2524184036924703656e+41, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_eta_e, (-5, &r), 0.25, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_eta_e, (0.5, &r), 0.6048986434216303702, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_eta_e, (0.999, &r), 0.6929872789683383574, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_eta_e, (1.0, &r), 0.6931471805599453094, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_eta_e, (1.0+1.0e-10, &r), 0.6931471805759321998, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_eta_e, ( 5, &r), 0.9721197704469093059, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_eta_e, ( 5.2, &r), 0.9755278712546684682, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_eta_e, ( 6, &r), 0.9855510912974351041, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_eta_e, ( 20, &r), 0.9999990466115815221, TEST_TOL0, GSL_SUCCESS); return s; } int test_results(void) { int s = 0; gsl_sf_result_e10 re; gsl_sf_result r; re.val = -1.0; re.err = 0.5; re.e10 = 0; gsl_sf_result_smash_e(&re, &r); s += ( test_sf_frac_diff(r.val, -1.0) > TEST_TOL0 ); s += ( test_sf_frac_diff(r.err, 0.5) > TEST_TOL0 ); re.val = -1.0; re.err = 0.5; re.e10 = 10; gsl_sf_result_smash_e(&re, &r); s += ( test_sf_frac_diff(r.val, -1.0e+10) > TEST_TOL1 ); s += ( test_sf_frac_diff(r.err, 0.5e+10) > TEST_TOL1 ); re.val = 1.0; re.err = 0.5; re.e10 = 10000; s += ( gsl_sf_result_smash_e(&re, &r) != GSL_EOVRFLW ); re.val = 1.0; re.err = 0.5; re.e10 = -10000; s += ( gsl_sf_result_smash_e(&re, &r) != GSL_EUNDRFLW ); return s; } int main(int argc, char * argv[]) { gsl_ieee_env_setup (); gsl_set_error_handler_off (); gsl_test(test_airy(), "Airy Functions"); gsl_test(test_bessel(), "Bessel Functions"); gsl_test(test_clausen(), "Clausen Integral"); gsl_test(test_coulomb(), "Coulomb Wave Functions"); gsl_test(test_coupling(), "Coupling Coefficients"); gsl_test(test_dawson(), "Dawson Integral"); gsl_test(test_debye(), "Debye Functions"); gsl_test(test_dilog(), "Dilogarithm"); gsl_test(test_elementary(), "Elementary Functions (Misc)"); gsl_test(test_ellint(), "Elliptic Integrals"); gsl_test(test_jac(), "Elliptic Functions (Jacobi)"); gsl_test(test_erf(), "Error Functions"); gsl_test(test_exp(), "Exponential Functions"); gsl_test(test_expint(), "Exponential/Sine/Cosine Integrals"); gsl_test(test_fermidirac(), "Fermi-Dirac Functions"); gsl_test(test_gamma(), "Gamma Functions"); gsl_test(test_gegen(), "Gegenbauer Polynomials"); gsl_test(test_hyperg(), "Hypergeometric Functions"); gsl_test(test_laguerre(), "Laguerre Polynomials"); gsl_test(test_lambert(), "Lambert W Functions"); gsl_test(test_legendre(), "Legendre Functions"); gsl_test(test_log(), "Logarithm"); gsl_test(test_mathieu(), "Mathieu Functions"); gsl_test(test_pow_int(), "Integer Powers"); gsl_test(test_psi(), "Psi Functions"); gsl_test(test_psi_complex(), "Psi Function for complex argument"); gsl_test(test_synch(), "Synchrotron Functions"); gsl_test(test_transport(), "Transport Functions"); gsl_test(test_trig(), "Trigonometric and Related Functions"); gsl_test(test_zeta(), "Zeta Functions"); gsl_test(test_results(), "Result Methods"); exit (gsl_test_summary()); } gsl-1.0.8/inst/test_hyperg_corr.c0000644000175000017500000012270511201030403014605 0ustar shsh/* specfunc/test_hyperg.c * * Copyright (C) 2007 Brian Gough * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004 Gerard Jungman * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 3 of the License, or (at * your option) any later version. * * This program is distributed in the hope that it will be useful, but * WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */ /* Author: G. Jungman */ #include #include #include #include "test_sf.h" int test_hyperg(void) { gsl_sf_result r; int s = 0; /* 0F1 */ TEST_SF(s, gsl_sf_hyperg_0F1_e, (1, 0.5, &r), 1.5660829297563505373, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_0F1_e, (5, 0.5, &r), 1.1042674404828684574, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_0F1_e, (100, 30, &r), 1.3492598639485110176, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_0F1_e, (-0.5, 3, &r), -39.29137997543434276, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_0F1_e, (-100.5, 50, &r), 0.6087930289227538496, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_0F1_e, (1, -5.0, &r), -0.3268752818235339109, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_0F1_e, (-0.5, -5.0, &r),-4.581634759005381184, TEST_TOL1, GSL_SUCCESS); /* 1F1 for integer parameters */ TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (1, 1, 0.5, &r), 1.6487212707001281468, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (1, 2, 500.0, &r), 2.8071844357056748215e+214, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (1, 2, -500.0, &r), 0.002, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (8, 1, 0.5, &r), 13.108875178030540372, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 1, 1.0, &r), 131.63017574352619931, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 1, 10.0, &r), 8.514625476546280796e+09, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 1, 100.0, &r), 1.5671363646800353320e+56, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 20, 1.0, &r), 1.6585618002669675465, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 20, 10.0, &r), 265.26686430340188871, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 20, 100.0, &r), 3.640477355063227129e+34, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, 1.0, &r), 1.1056660194025527099, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, 10.0, &r), 2.8491063634727594206, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, 40.0, &r), 133.85880835831230986, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, 80.0, &r), 310361.16228011433406, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, 100.0, &r), 8.032171336754168282e+07, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, 500.0, &r), 7.633961202528731426e+123, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 1, 1.0, &r), 6.892842729046469965e+07, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 1, 10.0, &r), 2.4175917112200409098e+28, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 1, 100.0, &r), 1.9303216896309102993e+110, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 200, 1.0, &r), 1.6497469106162459226, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 200, 10.0, &r), 157.93286197349321981, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 200, 100.0, &r), 2.1819577501255075240e+24, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 200, 400.0, &r), 3.728975529926573300e+119, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 400, 10.0, &r), 12.473087623658878813, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 400, 100.0, &r), 9.071230376818550241e+11, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 400, 150.0, &r), 7.160949515742170775e+18, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 400, 200.0, &r), 2.7406690412731576823e+26, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 400, 300.0, &r), 6.175110613473276193e+43, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 400, 400.0, &r), 1.1807417662711371440e+64, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 400, 600.0, &r), 2.4076076354888886030e+112, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 1, -1.0, &r), 0.11394854824644542810, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 1, -10.0, &r), 0.0006715506365396127863, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 1, -100.0, &r), -4.208138537480269868e-32, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 50, -1.0, &r), 0.820006196079380, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, -10.0, &r), 0.38378859043466243, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, -100.0, &r), 0.0008460143401464189061, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, -500.0, &r), 1.1090822141973655929e-08, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, -10000.0, &r), 5.173783508088272292e-21, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (50, 1, -90.0, &r), -1.6624258547648311554e-21, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (50, 1, -100.0, &r), 4.069661775122048204e-24, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (50, 1, -110.0, &r), 1.0072444993946236025e-25, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 10, -100.0, &r), -2.7819353611733941962e-37, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 1, -90.0, &r), 7.501705041159802854e-22, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 1, -100.0, &r), 6.305128893152291187e-25, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 1, -110.0, &r), -7.007122115422439755e-26, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 10, -100.0, &r), -2.7819353611733941962e-37, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (200, 50, -1.0, &r), 0.016087060191732290813, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (200, 50, -300.0, &r), -4.294975979706421471e-121, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (200, 100, -1.0, &r), 0.13397521083325179687, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (200, 100, -10.0, &r), 5.835134393749807387e-10, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (200, 100, -100.0, &r), 4.888460453078914804e-74, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (200, 100, -500.0, &r), -1.4478509059582015053e-195, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-1, 1, 2.0, &r), -1.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-1, -2, 2.0, &r), 2.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-2, -3, 2.0, &r), 3.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, 1, 1.0, &r), 0.4189459325396825397, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, 1, 10.0, &r), 27.984126984126984127, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, 1, 100.0, &r), 9.051283795429571429e+12, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-100, 20, 1.0, &r), 0.0020203016320697069566, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -20, 1.0, &r), 1.6379141878548080173, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -20, 10.0, &r), 78.65202404521289970, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -20, 100.0, &r), 4.416169713262624315e+08, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -100, 1.0, &r), 1.1046713999681950919, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -100, 10.0, &r), 2.6035952191039006838, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -100, 100.0, &r), 1151.6852040836932392, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-100, -200, 1.0, &r), 1.6476859702535324743, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-100, -200, 10.0, &r), 139.38026829540687270, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-100, -200, 100.0, &r), 1.1669433576237933752e+19, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -20, -1.0, &r), 0.6025549561148035735, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -20, -10.0, &r), 0.00357079636732993491, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -20, -100.0, &r), 1.64284868563391159e-35, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -100, -1.0, &r), 0.90442397250313899, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -100, -10.0, &r), 0.35061515251367215, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -100, -100.0, &r), 8.19512187960476424e-09, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-100, -200, -1.0, &r), 0.6061497939628952629, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-100, -200, -10.0, &r), 0.0063278543908877674, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-100, -200, -100.0, &r), 4.34111795007336552e-25, TEST_TOL2, GSL_SUCCESS); /* 1F1 */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, 1, &r), 2.0300784692787049755, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, 10, &r), 6172.859561078406855, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, 100, &r), 2.3822817898485692114e+42, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, 500, &r), 5.562895351723513581e+215, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1.5, 2.5, 1, &r), 1.8834451238277954398, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1.5, 2.5, 10, &r), 3128.7352996840916381, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, 1, &r), 110.17623733873889579, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, 10, &r), 6.146657975268385438e+09, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, 100, &r), 9.331833897230312331e+55, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, 500, &r), 4.519403368795715843e+235, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 50.1, 2, &r), 1.5001295507968071788, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 50.1, 10, &r), 8.713385849265044908, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 50.1, 100, &r), 5.909423932273380330e+18, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 50.1, 500, &r), 9.740060618457198900e+165, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, 1, &r), 5.183531067116809033e+07, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, 10, &r), 1.6032649110096979462e+28, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, 100, &r), 1.1045151213192280064e+110, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 50.1, 1, &r), 7.222953133216603757, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 50.1, 10, &r), 1.0998696410887171538e+08, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 50.1, 100, &r), 7.235304862322283251e+63, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, -1, &r), 0.5380795069127684191, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, -10, &r), 0.05303758099290164485, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, -100, &r), 0.005025384718759852803, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, -500, &r), 0.0010010030151059555322, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.1, -500, &r), 0.00020036137599690208265, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, -1, &r), 0.07227645648935938168, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, -10, &r), 0.0003192415409695588126, TEST_TOL1, GSL_SUCCESS); /* sensitive to the pair_ratio hack in hyperg_1F1.c TEST_SF_RLX(s, gsl_sf_hyperg_1F1_e, (10, 1.1, -100, &r), -8.293425316123158950e-16, 50.0*TEST_SNGL, GSL_SUCCESS); */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, -500, &r), -3.400379216707701408e-23, TEST_TOL2, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_1F1_e, (50, 1.1, -90, &r), -7.843129411802921440e-22, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (50, 1.1, -100, &r), 4.632883869540640460e-24, TEST_SQRT_TOL0, GSL_SUCCESS); /* FIXME: tolerance is poor, but is consistent within reported error */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (50, 1.1, -110.0, &r), 5.642684651305310023e-26, 0.03, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -1, &r), 0.0811637344096042096, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -10, &r), 0.00025945610092231574387, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -50, &r), 2.4284830988994084452e-13, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -90, &r), 2.4468224638378426461e-22, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -99, &r), 1.0507096272617608461e-23, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -100, &r), 1.8315497474210138602e-24, TEST_TOL2, GSL_SUCCESS); /* FIXME: Reported error is too small. TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -101, &r), -2.3916306291344452490e-24, 0.04, GSL_SUCCESS); */ /* FIXME: Reported error is too small. // TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -110, &r), -4.517581986037732280e-26, TEST_TOL0, GSL_SUCCESS); */ /* FIXME: Result is terrible, but reported error is very large, so consistent. // TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 10.1, -220, &r), -4.296130300021696573e-64, TEST_TOL1, GSL_SUCCESS); */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -10.1, 10.0, &r), 10959.603204633058116, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -10.1, 1000.0, &r), 2.0942691895502242831e+23, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -100.1, 10.0, &r), 2.6012036337980078062, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-1000, -1000.1, 10.0, &r), 22004.341698908631636, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-1000, -1000.1, 200.0, &r), 7.066514294896245043e+86, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-8.1, -10.1, -10.0, &r), 0.00018469685276347199258, TEST_TOL0, GSL_SUCCESS); /* TEST_SF(s, gsl_sf_hyperg_1F1_e, (-8.1, -1000.1, -10.0, &r), 0.9218280185080036020, TEST_TOL0, GSL_SUCCESS); */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -5.1, 1, &r), 16.936141866089601635, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -5.1, 10, &r), 771534.0349543820541, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -5.1, 100, &r), 2.2733956505084964469e+17, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, -1, &r), 0.13854540373629275583, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, -10, &r), -9.142260314353376284e+19, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, -100, &r), -1.7437371339223929259e+87, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, 1, &r), 7.516831748170351173, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, 10, &r), 1.0551632286359671976e+11, TEST_SQRT_TOL0, GSL_SUCCESS); /* These come out way off. On the other hand, the error estimates are also very large; so much so that the answers are consistent within the reported error. Something will need to be done about this eventually // TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, 50, &r), -7.564755600940346649e+36, TEST_TOL3, GSL_SUCCESS); // TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, 100, &r), 4.218776962675977e+55, TEST_TOL3, GSL_SUCCESS); */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10.5, -8.1, 0.1, &r), 1.1387201443786421724, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10.5, -11.1, 1, &r), 2.5682766147138452362, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100.5, -80.1, 10, &r), 355145.4517305220603, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100.5, -102.1, 10, &r), 18678.558725244365016, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100.5, -500.1, 10, &r), 7.342209011101454, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100.5, -500.1, 100, &r), 1.2077443075367177662e+8, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-500.5, -80.1, 2, &r), 774057.8541325341699, TEST_TOL4, GSL_SUCCESS); /* UNIMPL TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, 1, &r), -2.1213846338338567395e+12, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, 10, &r), -6.624849346145112398e+39, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, 100, &r), -1.2413466759089171904e+129, TEST_TOL0, GSL_SUCCESS); */ /* UNIMPL // TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, -1, &r), 34456.29405305551691, TEST_TOL0, GSL_SUCCESS); // TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, -10, &r), -7.809224251467710833e+07, TEST_TOL0, GSL_SUCCESS); // TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, -100, &r), -5.214065452753988395e-07, TEST_TOL0, GSL_SUCCESS); */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, 1, &r), 0.21519810496314438414, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, 10, &r), 8.196123715597869948, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, 100, &r), -1.4612966715976530293e+20, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 20.1, 1, &r), 0.0021267655527278456412, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 20.1, 10, &r), 2.0908665169032186979e-11, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 20.1, 100, &r), -0.04159447537001340412, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, -1, &r), 2.1214770215694685282e+07, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, -10, &r), 1.0258848879387572642e+24, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, -100, &r), 1.1811367147091759910e+67, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 50.1, -1, &r), 6.965259317271427390, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 50.1, -10, &r), 1.0690052487716998389e+07, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 50.1, -100, &r), 6.889644435777096248e+36, TEST_TOL3, GSL_SUCCESS); /* Bug report from Fernando Pilotto */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (-2.05, 1.0, 5.05, &r), 3.79393389516785e+00, TEST_TOL3, GSL_SUCCESS); /* Bug reports from Ivan Liu */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (-26, 2.0, 100.0, &r), 1.444786781107436954e+19, TEST_TOL3, GSL_SUCCESS); #if 0 /* This one is computed with a huge error, there is loss of precision but the error estimate flags the problem (assuming the user looks at it). We should probably trap any return with err>|val| and signal loss of precision */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (-26.1, 2.0, 100.0, &r), 1.341557199575986995e+19, TEST_TOL3, GSL_SUCCESS); #endif /* Bug report H.Moseby */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (1.2, 1.1e-15, 1.5, &r), 8254503159672429.02, TEST_TOL3, GSL_SUCCESS); // TEST_SF(s, gsl_sf_hyperg_1F1_e, (1.0, 1000000.5, 0.8e6 + 0.5, &r), 4.999922505099443804e+00, TEST_TOL3, GSL_SUCCESS); // TEST_SF(s, gsl_sf_hyperg_1F1_e, (1.0, 1000000.5, 1001000.5, &r), 3480.3699557431856166, TEST_TOL4, GSL_SUCCESS); #if 0 /* FIX THESE NEXT RELEASE */ // TEST_SF(s, gsl_sf_hyperg_1F1_e, (1.1, 1000000.5, 1001000.5, &r), 7304.6126942641350122, TEST_TOL3, GSL_SUCCESS); // TEST_SF(s, gsl_sf_hyperg_1F1_e, (0.9, 1000000.5, 1001000.5, &r), 1645.4879293475410982, TEST_TOL3, GSL_SUCCESS); #endif TEST_SF(s, gsl_sf_hyperg_1F1_e, (-1.1, 1000000.5, 1001000.5, &r), -5.30066488697455e-04, TEST_TOL3, GSL_SUCCESS); // TEST_SF(s, gsl_sf_hyperg_1F1_e, (1.5, 1000000.5, 0.8e6 + 0.5, &r), 11.18001288977894650469927615, TEST_TOL4, GSL_SUCCESS); /* U for integer parameters */ TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 0.0001, &r), 8.634088070212725330, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 0.01, &r), 4.078511443456425847, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 0.5, &r), 0.9229106324837304688, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 2.0, &r), 0.3613286168882225847, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 100, &r), 0.009901942286733018406, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 1000, &r), 0.0009990019940238807150, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 0.01, &r), 7.272361203006010000e+16, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 1, &r), 1957.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 5, &r), 1.042496, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 8, &r), 0.3207168579101562500, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 50, &r), 0.022660399001600000000, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 100, &r), 0.010631236727200000000, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 1000, &r), 0.0010060301203607207200, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 20, 1, &r), 1.7403456103284421000e+16, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 20, 20, &r), 0.22597813610531052969, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 50, 1, &r), 3.374452117521520758e+61, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 50, 50, &r), 0.15394136814987651785, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 0.1, &r), 1.0418325171990852858e+253, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 1, &r), 2.5624945006073464385e+154, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 50, &r), 3.0978624160896431391e+07, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 100, &r), 0.11323192555773717475, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 200, &r), 0.009715680951406713589, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 1000, &r), 0.0011085142546061528661, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1000, 2000, &r), 0.0009970168547036318206, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -1, 1, &r), 0.29817368116159703717, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -1, 10, &r), 0.07816669698940409380, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -10, 1, &r), 0.08271753756946041959, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -10, 5, &r), 0.06127757419425055261, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -10, 10, &r), 0.04656199948873187212, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -10, 20, &r), 0.031606421847946077709, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 0.01, &r), 0.009900000099999796950, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 1, &r), 0.009802970197050404429, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 10, &r), 0.009001648897173103447, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 20, &r), 0.008253126487166557546, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 50, &r), 0.006607993916432051008, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 90, &r), 0.005222713769726871937, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 110, &r), 0.004727658137692606210, TEST_TOL2, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_U_int_e, (1, -1000, 1, &r), 0.0009980029970019970050, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -1000, 1010, &r), 0.0004971408839859245170, TEST_TOL4, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 1, 0.001, &r), 0.0007505359326875706975, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 1, 0.5, &r), 6.449509938973479986e-06, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 1, 8, &r), 6.190694573035761284e-10, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 1, 20, &r), 3.647213845460374016e-12, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 8, 1, &r), 0.12289755012652317578, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 8, 10, &r), 5.687710359507564272e-09, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 8, 20, &r), 2.8175404594901039724e-11, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (100, 100, 0.01, &r), 1.0099979491941914867e+196, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (100, 100, 0.1, &r), 1.0090713562719862833e+97, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (100, 100, 1, &r), 0.009998990209084729106, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (100, 100, 20, &r), 1.3239363905866130603e-131, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 1, 0.01, &r), 3.274012540759009536e+06, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 1, 1, &r), 1.5202710000000000000e+06, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 1, 10, &r), 1.0154880000000000000e+08, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 1, 100, &r), 3.284529863685482880e+19, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 10, 1, &r), 1.1043089864100000000e+11, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 100, 1, &r), 1.3991152402448957897e+20, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 100, 10, &r), 5.364469916567136000e+19, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 100, 100, &r), 3.909797568000000000e+12, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 100, 500, &r), 8.082625576697984130e+25, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 1, 0.01, &r), 1.6973422555823855798e+64, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 1, 1, &r), 7.086160198304780325e+63, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 1, 10, &r), 5.332862895528712200e+65, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 10, 1, &r), -7.106713471565790573e+71, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 100, 1, &r), 2.4661377199407186476e+104, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 10, 10, &r), 5.687538583671241287e+68, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 100, 10, &r), 1.7880761664553373445e+102, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 1, 0.01, &r), 4.185245354032917715e+137, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 1, 0.1, &r), 2.4234043408007841358e+137, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 1, 10, &r), -1.8987677149221888807e+139, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 10, 10, &r), -5.682999988842066677e+143, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 100, 10, &r), 2.3410029853990624280e+189, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 1000, 10, &r), 1.9799451517572225316e+271, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, -1, 10, &r), -9.083195466262584149e+64, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, -10, 10, &r), -1.4418257327071634407e+62, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, -100, 0.01, &r), 3.0838993811468983931e+93, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, -100, 10, &r), 4.014552630378340665e+95, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-100, -100, 10, &r), 2.0556466922347982030e+162, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-100, -200, 10, &r), 1.1778399522973555582e+219, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-100, -200, 100, &r), 9.861313408898201873e+235, TEST_TOL3, GSL_SUCCESS); /* U */ TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 0.0001, 0.0001, &r), 1.0000576350699863577, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 0.0001, 1.0, &r), 0.9999403679233247536, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 0.0001, 100.0, &r), 0.9995385992657260887, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 1, 0.0001, &r), 1.0009210608660065989, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 1.0, 1.0, &r), 0.9999999925484179084, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 10, 1, &r), 13.567851006281412726, TEST_TOL3, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.0001, 10, 5, &r), 1.0006265020064596364, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 10, 10, &r), 0.9999244381454633265, TEST_TOL0, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.0001, 100, 1, &r), 2.5890615708804247881e+150, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.0001, 100, 10, &r), 2.3127845417739661466e+55, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.0001, 100, 50, &r), 6402.818715083582554, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 100, 98, &r), 0.9998517867411840044, TEST_TOL2, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.0001, 1000, 300, &r), 2.5389557274938010716e+213, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 1000, 999, &r), 0.9997195294193261604, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 1000, 1100, &r), 0.9995342990014584713, TEST_TOL1, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.5, 1000, 300, &r), 1.1977955438214207486e+217, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.5, 1000, 800, &r), 9.103916020464797207e+08, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.5, 1000, 998, &r), 0.21970269691801966806, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.5, 0.5, 1.0, &r), 0.7578721561413121060, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (1, 0.0001, 0.0001, &r), 0.9992361337764090785, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (1, 0.0001, 1, &r), 0.4036664068111504538, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (1, 0.0001, 100, &r), 0.009805780851264329587, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (1, 1.2, 2.0, &r), 0.3835044780075602550, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (1, -0.0001, 1, &r), 0.4036388693605999482, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (8, 10.5, 1, &r), 27.981926466707438538, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (8, 10.5, 10, &r), 2.4370135607662056809e-8, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (8, 10.5, 100, &r), 1.1226567526311488330e-16, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (10, -2.5, 10, &r), 6.734690720346560349e-14, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (10, 2.5, 10, &r), 6.787780794037971638e-13, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (10, 2.5, 50, &r), 2.4098720076596087125e-18, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 1, &r), -3.990841457734147e+6, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 10, &r), 1.307472052129343e+8, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 50, &r), 3.661978424114088e+16, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 90, &r), 8.09469542130868e+19, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 99, &r), 2.546328328942063e+20, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 100, &r), 2.870463201832814e+20, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 200, &r), 8.05143453769373e+23, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 10.1, 0.1, &r), -3.043016255306515e+20, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 10.1, 1, &r), -3.194745265896115e+12, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 10.1, 4, &r), -6.764203430361954e+07, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 10.1, 10, &r), -2.067399425480545e+09, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 10.1, 50, &r), 4.661837330822824e+14, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 100.4, 10, &r), -6.805460513724838e+66, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 100.4, 50, &r), -2.081052558162805e+18, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 100.4, 80, &r), 2.034113191014443e+14, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 100.4, 100, &r), 6.85047268436107e+13, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 100.4, 200, &r), 1.430815706105649e+20, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-19.5, 82.1, 10, &r), 5.464313196201917432e+60, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-50.5, 100.1, 10, &r), -5.5740216266953e+126, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-50.5, 100.1, 40, &r), 5.937463786613894e+91, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-50.5, 100.1, 50, &r), -1.631898534447233e+89, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-50.5, 100.1, 70, &r), 3.249026971618851e+84, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-50.5, 100.1, 100, &r), 1.003401902126641e+85, TEST_TOL1, GSL_SUCCESS); /* 2F1 */ TEST_SF(s, gsl_sf_hyperg_2F1_e, (1, 1, 1, 0.5, &r), 2.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, 8, 1, 0.5, &r), 12451584.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, -8, 1, 0.5, &r), 0.13671875, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, -8.1, 1, 0.5, &r), 0.14147385378899930422, TEST_TOL4, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, -8, 1, -0.5, &r), 4945.136718750000000, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, -8, -5.5, 0.5, &r), -906.6363636363636364, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, -8, -5.5, -0.5, &r), 24565.363636363636364, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, 8, 1, -0.5, &r), -0.006476312098196747669, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, 8, 5, 0.5, &r), 4205.714285714285714, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, 8, 5, -0.5, &r), 0.0028489656290296436616, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, 1, 0.99, &r), 1.2363536673577259280e+38 , TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -1.5, 0.99, &r), 3.796186436458346579e+46, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -1.5, -0.99, &r), 0.14733409946001025146, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -8.5, 0.99, &r), -1.1301780432998743440e+65, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -8.5, -0.99, &r), -8.856462606575344483, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -21.5, 0.99, &r), 2.0712920991876073253e+95, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -21.5, -0.99, &r), -74.30517015382249216, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -100.5, 0.99, &r), -3.186778061428268980e+262, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -100.5, -0.99, &r), 2.4454358338375677520, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (25, 25, 1, -0.5, &r), -2.9995530823639545027e-06, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, 1.0-1.0/64.0, &r), 3.17175539044729373926, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, 1.0-1.0/128.0, &r), 3.59937243502024563424, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, 1.0-1.0/256.0, &r), 4.03259299524392504369, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, 1.0-1.0/1024.0, &r), 4.90784159359675398250, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, 1.0-1.0/65536.0, &r), 7.552266033399683914, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, 1.0-1.0/16777216.0, &r), 11.08235454026043830363, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, -1.0+1.0/1024.0, &r), 0.762910940909954974527, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, -1.0+1.0/65536.0, &r), 0.762762124908845424449, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, -1.0+1.0/1048576.0, &r), 0.762759911089064738044, TEST_TOL0, GSL_SUCCESS); /* added special handling with x == 1.0 , Richard J. Mathar, 2008-01-09 */ TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 3.0, 1.0, &r), 1.6976527263135502482014268 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, -4.2, 3.0, 1.0, &r), .15583601560025710649555254 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (-7.4, 0.7, -1.5, 1.0, &r), -.34478866959246584996859 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (0.1, -2.7, -1.5, 1.0, &r), 1.059766766063610122925 , TEST_TOL0, GSL_SUCCESS); /* 2F1 conj */ TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (1, 1, 1, 0.5, &r), 3.352857095662929028, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (8, 8, 1, 0.5, &r), 1.7078067538891293983e+09, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (8, 8, 5, 0.5, &r), 285767.15696901140627, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (8, 8, 1, -0.5, &r), 0.007248196261471276276, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (8, 8, 5, -0.5, &r), 0.00023301916814505902809, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (25, 25, 1, -0.5, &r), 5.1696944096e-06, TEST_SQRT_TOL0, GSL_SUCCESS); /* updated correct values, testing enabled, Richard J. Mathar, 2008-01-09 */ TEST_SF(s, gsl_sf_hyperg_2F0_e, (0.01, 1.0, -0.02, &r), .99980388665511730901180717 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F0_e, (0.1, 0.5, -0.02, &r), .99901595171179281891589794 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F0_e, (1, 1, -0.02, &r), .98075549650574351826538049000 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F0_e, (8, 8, -0.02, &r), .32990592849626965538692141 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F0_e, (50, 50, -0.02, &r), .2688995263772964415245902e-12 , TEST_TOL0, GSL_SUCCESS); /* 2F1 renorm */ TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (1, 1, 1, 0.5, &r), 2.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, 8, 1, 0.5, &r), 12451584.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, -8, 1, 0.5, &r), 0.13671875, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, -8, 1, -0.5, &r), 4945.13671875, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, -8, -5.5, 0.5, &r), -83081.19167659493609, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, -8, -5.5, -0.5, &r), 2.2510895952730178518e+06, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, 8, 5, 0.5, &r), 175.2380952380952381, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (9, 9, -1.5, 0.99, &r), 1.6063266334913066551e+46, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (9, 9, -1.5, -0.99, &r), 0.06234327316254516616, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (5, 5, -1, 0.5, &r), 4949760.0, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (5, 5, -10, 0.5, &r), 139408493229637632000.0, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (5, 5, -100, 0.5, &r), 3.0200107544594411315e+206, TEST_TOL3, GSL_SUCCESS); /* 2F1 conj renorm */ TEST_SF(s, gsl_sf_hyperg_2F1_conj_renorm_e, (9, 9, -1.5, 0.99, &r), 5.912269095984229412e+49, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_renorm_e, (9, 9, -1.5, -0.99, &r), 0.10834020229476124874, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_renorm_e, (5, 5, -1, 0.5, &r), 1.4885106335357933625e+08, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_renorm_e, (5, 5, -10, 0.5, &r), 7.968479361426355095e+21, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_renorm_e, (5, 5, -100, 0.5, &r), 3.1113180227052313057e+208, TEST_TOL3, GSL_SUCCESS); return s; } gsl-1.0.8/inst/test_ellint.m0000644000175000017500000000767611201030403013574 0ustar shsh## Copyright (C) 2008 Raymond E. Rogers ## ## This program is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; if not, see . # # # # R. Rogers v1, testing gsl_sf_ellint_Kcomp_e, gsl_sf_ellint_Ecomp_e # implementation in octave as ellint_Kcomp, ellint_Ecomp # against the gsl tests # Some array verification is done; since I messed it up once. global GSL_DBL_EPSILON= 2.2204460492503131e-16 global GSL_SQRT_DBL_EPSILON= 1.4901161193847656e-08 global TEST_TOL0= (2.0*GSL_DBL_EPSILON) global TEST_TOL1= (16.0*GSL_DBL_EPSILON) global TEST_TOL2= (256.0*GSL_DBL_EPSILON) global TEST_TOL3= (2048.0*GSL_DBL_EPSILON) global TEST_TOL4= (16384.0*GSL_DBL_EPSILON) global TEST_TOL5= (131072.0*GSL_DBL_EPSILON) global TEST_TOL6= (1048576.0*GSL_DBL_EPSILON) global TEST_SQRT_TOL0= (2.0*GSL_SQRT_DBL_EPSILON) global TEST_SNGL= (1.0e-06) global TEST_SF_INCONS= 1 global TEST_SF_ERRNEG= 2 global TEST_SF_TOLBAD= 4 global TEST_SF_RETBAD= 8 global TEST_SF_ERRBAD= 16 global TEST_SF_ERRBIG= 32 global TEST_SF_EXPBAD= 64 global TEST_FACTOR= 100 function res=READ_TEST_SF_ellint(input_name) global GSL_DBL_EPSILON global GSL_SQRT_DBL_EPSILON global TEST_TOL0 global TEST_TOL1 global TEST_TOL2 global TEST_TOL3 global TEST_TOL4 global TEST_TOL5 global TEST_TOL6 global TEST_SQRT_TOL0 global TEST_SNGL global TEST_SF_INCONS global TEST_SF_ERRNEG global TEST_SF_TOLBAD global TEST_SF_RETBAD global TEST_SF_ERRBAD global TEST_SF_ERRBIG global TEST_SF_EXPBAD global TEST_FACTOR [source_id,source_msg]=fopen(input_name,"r","native") while (! feof(source_id)) do input_line=fgetl(source_id); until( index(input_line,"//") == 0); str_p=index(input_line,"gsl_sf_ellint_Kcomp_e"); if (str_p != 0) # Take it apart string_split=split(input_line,","); arg1=str2double(substr(string_split(3,:),3)); arg2=str2double(string_split(4,:)); arg3=(string_split(5,:)); val=str2double(string_split(6,:)); tol=eval(string_split(7,:)); [ret,err]=ellint_Kcomp(arg1,arg2); # This is to prevent extanious stops on some errors if ret==NaN ret=Inf endif if (abs((ret-val)/val) $$pkgdir/packinfo/on_uninstall.m; \ echo " error ('Can not uninstall %s installed by the $(DISTPKG) package manager', desc.name);" >> $$pkgdir/packinfo/on_uninstall.m; \ echo "endfunction" >> $$pkgdir/packinfo/on_uninstall.m; \ echo "#! /bin/sh -f" > $$pkgdir/packinfo/dist_admin; \ echo "if [ \"\$$1\" == \"install\" ]; then" >> $$pkgdir/packinfo/dist_admin; \ echo " octave -H -q --no-site-file --eval \"pkg('rebuild');\"" >> $$pkgdir/packinfo/dist_admin; \ echo "else" >> $$pkgdir/packinfo/dist_admin; \ echo " pkgdir=\`octave -H -q --no-site-file --eval \"pkg('rebuild');l=pkg('list');disp(l{cellfun(@(x)strcmp(x.name,'$(PKG)'),l)}.dir);\"\`" >> $$pkgdir/packinfo/dist_admin; \ echo " rm \$$pkgdir/packinfo/on_uninstall.m" >> $$pkgdir/packinfo/dist_admin; \ echo " if [ -e \$$pkgdir/packinfo/on_uninstall.m.orig ]; then" >> $$pkgdir/packinfo/dist_admin; \ echo " mv \$$pkgdir/packinfo/on_uninstall.m.orig \$$pkgdir/packinfo/on_uninstall.m" >> $$pkgdir/packinfo/dist_admin; \ echo " cd \$$pkgdir/packinfo" >> $$pkgdir/packinfo/dist_admin; \ echo " octave -q -H --no-site-file --eval \"l=pkg('list');on_uninstall(l{cellfun(@(x)strcmp(x.name,'$(PKG)'),l)});\"" >> $$pkgdir/packinfo/dist_admin; \ echo " fi" >> $$pkgdir/packinfo/dist_admin; \ echo "fi" >> $$pkgdir/packinfo/dist_admin; \ chmod a+x $$pkgdir/packinfo/dist_admin; \ fi; clean: rm $(PACKAGE) $(MAKE) -C src clean gsl-1.0.8/doc/0000755000175000017500000000000011201031723010646 5ustar shshgsl-1.0.8/doc/gsl_sf.log0000644000175000017500000244220711201030403012633 0ustar shshThis is pdfeTeXk, Version 3.141592-1.21a-2.2 (Web2C 7.5.4) (format=pdfetex 2008.5.11) 20 JUN 2008 15:45 entering extended mode file:line:error style messages enabled. **\nonstopmode \input ./gsl_sf.texi (./gsl_sf.texi (./texinfo.tex Loading texinfo [version 2004-11-25.16]: Basics, \bindingoffset=\dimen16 \normaloffset=\dimen17 \pagewidth=\dimen18 \pageheight=\dimen19 \outerhsize=\dimen20 \outervsize=\dimen21 \cornerlong=\dimen22 \cornerthick=\dimen23 \topandbottommargin=\dimen24 \headlinebox=\box16 \footlinebox=\box17 \margin=\insert252 \EMsimple=\toks13 \groupbox=\box18 \groupinvalidhelp=\toks14 \mil=\dimen25 \exdentamount=\skip18 \inmarginspacing=\skip19 pdf, \tempnum=\count27 \lnkcount=\count28 \filename=\toks15 \filenamelength=\count29 \pgn=\count30 \toksA=\toks16 \toksB=\toks17 \toksC=\toks18 \toksD=\toks19 \boxA=\box19 \countA=\count31 (/usr/share/texmf/tex/plain/pdfcolor/pdfcolor.tex) fonts, \sffam=\fam8 \textleading=\dimen26 \fontdepth=\count32 page headings, \titlepagetopglue=\skip20 \titlepagebottomglue=\skip21 \evenheadline=\toks20 \oddheadline=\toks21 \evenfootline=\toks22 \oddfootline=\toks23 tables, \tableindent=\dimen27 \itemindent=\dimen28 \itemmargin=\dimen29 \itemmax=\dimen30 \itemno=\count33 \multitableparskip=\skip22 \multitableparindent=\skip23 \multitablecolspace=\dimen31 \multitablelinespace=\skip24 \colcount=\count34 \everytab=\toks24 conditionals, \doignorecount=\count35 indexing, \secondaryindent=\skip25 \partialpage=\box20 \doublecolumnhsize=\dimen32 sectioning, \unnumberedno=\count36 \chapno=\count37 \secno=\count38 \subsecno=\count39 \subsubsecno=\count40 \appendixno=\count41 \absseclevel=\count42 \secbase=\count43 \chapheadingskip=\skip26 \secheadingskip=\skip27 \subsecheadingskip=\skip28 toc, \tocfile=\write0 \contentsrightmargin=\skip29 \savepageno=\count44 \lastnegativepageno=\count45 \tocindent=\dimen33 environments, \errorbox=\box21 \lispnarrowing=\skip30 \envskipamount=\skip31 \circthick=\dimen34 \cartouter=\dimen35 \cartinner=\dimen36 \normbskip=\skip32 \normpskip=\skip33 \normlskip=\skip34 \lskip=\skip35 \rskip=\skip36 \tabw=\dimen37 defuns, \defbodyindent=\skip37 \defargsindent=\skip38 \deflastargmargin=\skip39 \parencount=\count46 \brackcount=\count47 macros, \paramno=\count48 \macname=\toks25 cross references, \auxfile=\write1 \savesfregister=\count49 insertions, \footnoteno=\count50 \SAVEfootins=\box22 \SAVEmargin=\box23 (/usr/share/texmf/tex/generic/epsf/epsf.tex \epsffilein=\read1 \epsfframemargin=\dimen38 \epsfframethickness=\dimen39 \epsfrsize=\dimen40 \epsftmp=\dimen41 \epsftsize=\dimen42 \epsfxsize=\dimen43 \epsfysize=\dimen44 \pspoints=\dimen45 \epsfnoopenhelp=\toks26 ) \noepsfhelp=\toks27 localization, \nolanghelp=\toks28 \defaultparindent=\dimen46 and turning on texinfo input format.) ./gsl_sf.texi:8: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gsl_sf}{\folio }{\code {gsl_sf}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.8 @deftypefn {Loadable Function} {} gsl_sf () A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:16: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{clausen}{\folio }{\code {clausen}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.16 ...le Function} {@var{y} =} clausen (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:17: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{clausen}{\folio }{\code {clausen}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.17 ...{[@var{y}, @var{err}] =} clausen (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:21: Use of \ doesn't match its definition. l.21 Cl_2(x) = - \\ int_0^x dt \\log(2 \\sin(t/2)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:21: Use of \ doesn't match its definition. l.21 Cl_2(x) = - \\int_0^x dt \\ log(2 \\sin(t/2)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:21: Use of \ doesn't match its definition. l.21 Cl_2(x) = - \\int_0^x dt \\log(2 \\ sin(t/2)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:23: Use of \ doesn't match its definition. l.23 It is related to the dilogarithm by Cl_2(\\ theta) = \\Im Li_2(\\exp(i \... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:23: Use of \ doesn't match its definition. l.23 ...d to the dilogarithm by Cl_2(\\theta) = \\ Im Li_2(\\exp(i \\theta)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:23: Use of \ doesn't match its definition. l.23 ...ilogarithm by Cl_2(\\theta) = \\Im Li_2(\\ exp(i \\theta)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:23: Use of \ doesn't match its definition. l.23 ...hm by Cl_2(\\theta) = \\Im Li_2(\\exp(i \\ theta)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 27--29 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:34: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{dawson}{\folio }{\code {dawson}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.34 ...ble Function} {@var{y} =} dawson (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:35: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{dawson}{\folio }{\code {dawson}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.35 ... {[@var{y}, @var{err}] =} dawson (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:37: Use of \ doesn't match its definition. l.37 The Dawson integral is defined by \\ exp(-x^2) \\int_0^x dt \\exp(t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:37: Use of \ doesn't match its definition. l.37 ...wson integral is defined by \\exp(-x^2) \\ int_0^x dt \\exp(t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:37: Use of \ doesn't match its definition. l.37 ... is defined by \\exp(-x^2) \\int_0^x dt \\ exp(t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 42--44 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:49: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_1}{\folio }{\code {debye_1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.49 ...le Function} {@var{y} =} debye_1 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:50: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_1}{\folio }{\code {debye_1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.50 ...{[@var{y}, @var{err}] =} debye_1 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:54: Use of \ doesn't match its definition. l.54 D_n(x) = n/x^n \\ int_0^x dt (t^n/(e^t - 1)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 60--62 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:67: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_2}{\folio }{\code {debye_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.67 ...le Function} {@var{y} =} debye_2 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:68: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_2}{\folio }{\code {debye_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.68 ...{[@var{y}, @var{err}] =} debye_2 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:72: Use of \ doesn't match its definition. l.72 D_n(x) = n/x^n \\ int_0^x dt (t^n/(e^t - 1)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 78--80 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:85: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_3}{\folio }{\code {debye_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.85 ...le Function} {@var{y} =} debye_3 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [1{/usr/share/texmf-var/fonts/map/pdftex/updmap/pdftex.map} \entry{gsl_sf}{1}{\code {gsl_sf}} \entry{clausen}{1}{\code {clausen}} \entry{clausen}{1}{\code {clausen}} \entry{dawson}{1}{\code {dawson}} \entry{dawson}{1}{\code {dawson}} \entry{debye_1}{1}{\code {debye_1}} \entry{debye_1}{1}{\code {debye_1}} \entry{debye_2}{1}{\code {debye_2}} \entry{debye_2}{1}{\code {debye_2}} ] ./gsl_sf.texi:86: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_3}{\folio }{\code {debye_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.86 ...{[@var{y}, @var{err}] =} debye_3 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:90: Use of \ doesn't match its definition. l.90 D_n(x) = n/x^n \\ int_0^x dt (t^n/(e^t - 1)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 96--98 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:103: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_4}{\folio }{\code {debye_4}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.103 ...e Function} {@var{y} =} debye_4 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:104: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_4}{\folio }{\code {debye_4}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.104 ...[@var{y}, @var{err}] =} debye_4 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:108: Use of \ doesn't match its definition. l.108 D_n(x) = n/x^n \\ int_0^x dt (t^n/(e^t - 1)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 114--116 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:121: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_gsl}{\folio }{\code {erf_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.121 ...e Function} {@var{y} =} erf_gsl (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:122: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_gsl}{\folio }{\code {erf_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.122 ...[@var{y}, @var{err}] =} erf_gsl (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:125: Use of \ doesn't match its definition. l.125 erf(x) = (2/\\ sqrt(\\pi)) \\int_0^x dt \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:125: Use of \ doesn't match its definition. l.125 erf(x) = (2/\\sqrt(\\ pi)) \\int_0^x dt \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:125: Use of \ doesn't match its definition. l.125 erf(x) = (2/\\sqrt(\\pi)) \\ int_0^x dt \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:125: Use of \ doesn't match its definition. l.125 erf(x) = (2/\\sqrt(\\pi)) \\int_0^x dt \\ exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 129--131 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:136: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erfc_gsl}{\folio }{\code {erfc_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.136 ... Function} {@var{y} =} erfc_gsl (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:137: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erfc_gsl}{\folio }{\code {erfc_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.137 ...@var{y}, @var{err}] =} erfc_gsl (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:140: Use of \ doesn't match its definition. l.140 erfc(x) = 1 - erf(x) = (2/\\ sqrt(\\pi)) \\int_x^\\infty \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:140: Use of \ doesn't match its definition. l.140 erfc(x) = 1 - erf(x) = (2/\\sqrt(\\ pi)) \\int_x^\\infty \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:140: Use of \ doesn't match its definition. l.140 erfc(x) = 1 - erf(x) = (2/\\sqrt(\\pi)) \\ int_x^\\infty \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:140: Use of \ doesn't match its definition. l.140 ... 1 - erf(x) = (2/\\sqrt(\\pi)) \\int_x^\\ infty \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:140: Use of \ doesn't match its definition. l.140 ...(x) = (2/\\sqrt(\\pi)) \\int_x^\\infty \\ exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 144--146 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:151: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_erfc}{\folio }{\code {log_erfc}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.151 ... Function} {@var{y} =} log_erfc (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:152: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_erfc}{\folio }{\code {log_erfc}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.152 ...@var{y}, @var{err}] =} log_erfc (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:155: Use of \ doesn't match its definition. l.155 function \\ log(\\erfc(x)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:155: Use of \ doesn't match its definition. l.155 function \\log(\\ erfc(x)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 159--161 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. [2 \entry{debye_3}{2}{\code {debye_3}} \entry{debye_3}{2}{\code {debye_3}} \entry{debye_4}{2}{\code {debye_4}} \entry{debye_4}{2}{\code {debye_4}} \entry{erf_gsl}{2}{\code {erf_gsl}} \entry{erf_gsl}{2}{\code {erf_gsl}} \entry{erfc_gsl}{2}{\code {erfc_gsl}} \entry{erfc_gsl}{2}{\code {erfc_gsl}} \entry{log_erfc}{2}{\code {log_erfc}} \entry{log_erfc}{2}{\code {log_erfc}} ] ./gsl_sf.texi:166: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_Z}{\folio }{\code {erf_Z}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.166 ...ble Function} {@var{y} =} erf_Z (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:167: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_Z}{\folio }{\code {erf_Z}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.167 ... {[@var{y}, @var{err}] =} erf_Z (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:170: Use of \ doesn't match its definition. l.170 Z(x) = (1/(2\\ pi)) \\exp(-x^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:170: Use of \ doesn't match its definition. l.170 Z(x) = (1/(2\\pi)) \\ exp(-x^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 174--176 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:181: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_Q}{\folio }{\code {erf_Q}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.181 ...ble Function} {@var{y} =} erf_Q (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:182: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_Q}{\folio }{\code {erf_Q}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.182 ... {[@var{y}, @var{err}] =} erf_Q (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:185: Use of \ doesn't match its definition. l.185 function Q(x) = (1/(2\\ pi)) \\int_x^\\infty dt \\exp(-t^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:185: Use of \ doesn't match its definition. l.185 function Q(x) = (1/(2\\pi)) \\ int_x^\\infty dt \\exp(-t^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:185: Use of \ doesn't match its definition. l.185 function Q(x) = (1/(2\\pi)) \\int_x^\\ infty dt \\exp(-t^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:185: Use of \ doesn't match its definition. l.185 ... Q(x) = (1/(2\\pi)) \\int_x^\\infty dt \\ exp(-t^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 189--191 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:196: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hazard}{\folio }{\code {hazard}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.196 ...le Function} {@var{y} =} hazard (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:197: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hazard}{\folio }{\code {hazard}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.197 ...{[@var{y}, @var{err}] =} hazard (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:200: Use of \ doesn't match its definition. l.200 inverse Mill\\ 's ratio, is defined as If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:201: Use of \ doesn't match its definition. l.201 h(x) = Z(x)/Q(x) = \\ sqrt@{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2)@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:201: Use of \ doesn't match its definition. l.201 h(x) = Z(x)/Q(x) = \\sqrt@{2/\\ pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2)@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:201: Use of \ doesn't match its definition. l.201 h(x) = Z(x)/Q(x) = \\sqrt@{2/\\pi \\ exp(-x^2 / 2) / \\erfc(x/\\sqrt 2)@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:201: Use of \ doesn't match its definition. l.201 ...(x) = \\sqrt@{2/\\pi \\exp(-x^2 / 2) / \\ erfc(x/\\sqrt 2)@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:201: Use of \ doesn't match its definition. l.201 ...qrt@{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\ sqrt 2)@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:202: Use of \ doesn't match its definition. l.202 It decreases rapidly as x approaches -\\ infty and asymptotes to If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:203: Use of \ doesn't match its definition. l.203 h(x) \\ sim x as x approaches +\\infty. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:203: Use of \ doesn't match its definition. l.203 h(x) \\sim x as x approaches +\\ infty. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 207--209 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:214: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expm1}{\folio }{\code {expm1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.214 ...ble Function} {@var{y} =} expm1 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:215: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expm1}{\folio }{\code {expm1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.215 ... {[@var{y}, @var{err}] =} expm1 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:217: Use of \ doesn't match its definition. l.217 These routines compute the quantity \\ exp(x)-1 using an algorithm that If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 222--224 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:229: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel}{\folio }{\code {exprel}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.229 ...le Function} {@var{y} =} exprel (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:230: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel}{\folio }{\code {exprel}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.230 ...{[@var{y}, @var{err}] =} exprel (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:232: Use of \ doesn't match its definition. l.232 These routines compute the quantity (\\ exp(x)-1)/x using an algorithm If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:234: Use of \ doesn't match its definition. l.234 the expansion (\\ exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\d... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:234: Use of \ doesn't match its definition. l.234 ... = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\ dots. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [3 \entry{erf_Z}{3}{\code {erf_Z}} \entry{erf_Z}{3}{\code {erf_Z}} \entry{erf_Q}{3}{\code {erf_Q}} \entry{erf_Q}{3}{\code {erf_Q}} \entry{hazard}{3}{\code {hazard}} \entry{hazard}{3}{\code {hazard}} \entry{expm1}{3}{\code {expm1}} \entry{expm1}{3}{\code {expm1}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 238--240 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:245: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel_2}{\folio }{\code {exprel_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.245 ... Function} {@var{y} =} exprel_2 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:246: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel_2}{\folio }{\code {exprel_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.246 ...@var{y}, @var{err}] =} exprel_2 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:248: Use of \ doesn't match its definition. l.248 These routines compute the quantity 2(\\ exp(x)-1-x)/x^2 using an If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:251: Use of \ doesn't match its definition. l.251 2(\\ exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\dots. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:251: Use of \ doesn't match its definition. l.251 ... = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\ dots. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 255--257 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:262: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_E1}{\folio }{\code {expint_E1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.262 ...Function} {@var{y} =} expint_E1 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:263: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_E1}{\folio }{\code {expint_E1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.263 ...var{y}, @var{err}] =} expint_E1 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:267: Use of \ doesn't match its definition. l.267 E_1(x) := Re \\ int_1^\\infty dt \\exp(-xt)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:267: Use of \ doesn't match its definition. l.267 E_1(x) := Re \\int_1^\\ infty dt \\exp(-xt)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:267: Use of \ doesn't match its definition. l.267 E_1(x) := Re \\int_1^\\infty dt \\ exp(-xt)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 271--273 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:278: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_E2}{\folio }{\code {expint_E2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.278 ...Function} {@var{y} =} expint_E2 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:279: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_E2}{\folio }{\code {expint_E2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.279 ...var{y}, @var{err}] =} expint_E2 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:283: Use of \ doesn't match its definition. l.283 E_2(x) := \\ Re \\int_1^\\infty dt \\exp(-xt)/t^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:283: Use of \ doesn't match its definition. l.283 E_2(x) := \\Re \\ int_1^\\infty dt \\exp(-xt)/t^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:283: Use of \ doesn't match its definition. l.283 E_2(x) := \\Re \\int_1^\\ infty dt \\exp(-xt)/t^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:283: Use of \ doesn't match its definition. l.283 E_2(x) := \\Re \\int_1^\\infty dt \\ exp(-xt)/t^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 287--289 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:294: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_Ei}{\folio }{\code {expint_Ei}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.294 ...Function} {@var{y} =} expint_Ei (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:295: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_Ei}{\folio }{\code {expint_Ei}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.295 ...var{y}, @var{err}] =} expint_Ei (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:299: Use of \ doesn't match its definition. l.299 Ei(x) := - PV(\\ int_@{-x@}^\\infty dt \\exp(-t)/t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:299: Use of \ doesn't match its definition. l.299 Ei(x) := - PV(\\int_@{-x@}^\\ infty dt \\exp(-t)/t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:299: Use of \ doesn't match its definition. l.299 Ei(x) := - PV(\\int_@{-x@}^\\infty dt \\ exp(-t)/t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 305--307 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. [4 \entry{exprel}{4}{\code {exprel}} \entry{exprel}{4}{\code {exprel}} \entry{exprel_2}{4}{\code {exprel_2}} \entry{exprel_2}{4}{\code {exprel_2}} \entry{expint_E1}{4}{\code {expint_E1}} \entry{expint_E1}{4}{\code {expint_E1}} \entry{expint_E2}{4}{\code {expint_E2}} \entry{expint_E2}{4}{\code {expint_E2}} \entry{expint_Ei}{4}{\code {expint_Ei}} \entry{expint_Ei}{4}{\code {expint_Ei}} ] ./gsl_sf.texi:312: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Shi}{\folio }{\code {Shi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.312 ...dable Function} {@var{y} =} Shi (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:313: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Shi}{\folio }{\code {Shi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.313 ...n} {[@var{y}, @var{err}] =} Shi (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:315: Use of \ doesn't match its definition. l.315 ...routines compute the integral Shi(x) = \\ int_0^x dt \\sinh(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:315: Use of \ doesn't match its definition. l.315 ...ute the integral Shi(x) = \\int_0^x dt \\ sinh(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 319--321 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:326: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Chi}{\folio }{\code {Chi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.326 ...dable Function} {@var{y} =} Chi (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:327: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Chi}{\folio }{\code {Chi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.327 ...n} {[@var{y}, @var{err}] =} Chi (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:331: Use of \ doesn't match its definition. l.331 Chi(x) := Re[ \\ gamma_E + \\log(x) + \\int_0^x dt (\\cosh[t]-1)/t] , If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:331: Use of \ doesn't match its definition. l.331 Chi(x) := Re[ \\gamma_E + \\ log(x) + \\int_0^x dt (\\cosh[t]-1)/t] , If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:331: Use of \ doesn't match its definition. l.331 Chi(x) := Re[ \\gamma_E + \\log(x) + \\ int_0^x dt (\\cosh[t]-1)/t] , If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:331: Use of \ doesn't match its definition. l.331 ...[ \\gamma_E + \\log(x) + \\int_0^x dt (\\ cosh[t]-1)/t] , If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:333: Use of \ doesn't match its definition. l.333 where \\ gamma_E is the Euler constant. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 337--339 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:344: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_3}{\folio }{\code {expint_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.344 ... Function} {@var{y} =} expint_3 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:345: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_3}{\folio }{\code {expint_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.345 ...@var{y}, @var{err}] =} expint_3 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:348: Use of \ doesn't match its definition. l.348 Ei_3(x) = \\ int_0^x dt \\exp(-t^3) for x >= 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:348: Use of \ doesn't match its definition. l.348 Ei_3(x) = \\int_0^x dt \\ exp(-t^3) for x >= 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 352--354 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:359: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Si}{\folio }{\code {Si}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.359 ...adable Function} {@var{y} =} Si (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:360: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Si}{\folio }{\code {Si}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.360 ...on} {[@var{y}, @var{err}] =} Si (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:362: Use of \ doesn't match its definition. l.362 ...ines compute the Sine integral Si(x) = \\ int_0^x dt \\sin(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:362: Use of \ doesn't match its definition. l.362 ...the Sine integral Si(x) = \\int_0^x dt \\ sin(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 366--368 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:373: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Ci}{\folio }{\code {Ci}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.373 ...adable Function} {@var{y} =} Ci (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:374: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Ci}{\folio }{\code {Ci}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.374 ...on} {[@var{y}, @var{err}] =} Ci (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:377: Use of \ doesn't match its definition. l.377 Ci(x) = -\\ int_x^\\infty dt \\cos(t)/t for x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:377: Use of \ doesn't match its definition. l.377 Ci(x) = -\\int_x^\\ infty dt \\cos(t)/t for x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:377: Use of \ doesn't match its definition. l.377 Ci(x) = -\\int_x^\\infty dt \\ cos(t)/t for x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 381--383 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. [5 \entry{Shi}{5}{\code {Shi}} \entry{Shi}{5}{\code {Shi}} \entry{Chi}{5}{\code {Chi}} \entry{Chi}{5}{\code {Chi}} \entry{expint_3}{5}{\code {expint_3}} \entry{expint_3}{5}{\code {expint_3}} \entry{Si}{5}{\code {Si}} \entry{Si}{5}{\code {Si}} ] ./gsl_sf.texi:388: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{atanint}{\folio }{\code {atanint}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.388 ...e Function} {@var{y} =} atanint (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:389: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{atanint}{\folio }{\code {atanint}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.389 ...[@var{y}, @var{err}] =} atanint (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:392: Use of \ doesn't match its definition. l.392 AtanInt(x) = \\ int_0^x dt \\arctan(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:392: Use of \ doesn't match its definition. l.392 AtanInt(x) = \\int_0^x dt \\ arctan(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 396--398 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:403: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_mhalf}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.403 ...} {@var{y} =} fermi_dirac_mhalf (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:404: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_mhalf}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.404 ...@var{err}] =} fermi_dirac_mhalf (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 410--412 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:417: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_half}{\folio }{\code {fermi_di... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.417 ...n} {@var{y} =} fermi_dirac_half (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:418: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_half}{\folio }{\code {fermi_di... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.418 ... @var{err}] =} fermi_dirac_half (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 424--426 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:431: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_3half}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.431 ...} {@var{y} =} fermi_dirac_3half (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:432: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_3half}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.432 ...@var{err}] =} fermi_dirac_3half (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 438--440 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:445: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_gsl}{\folio }{\code {gamma_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.445 ...Function} {@var{y} =} gamma_gsl (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:446: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_gsl}{\folio }{\code {gamma_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.446 ...var{y}, @var{err}] =} gamma_gsl (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:448: Use of \ doesn't match its definition. l.448 These routines compute the Gamma function \\ Gamma(x), subject to x not If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:450: Use of \ doesn't match its definition. l.450 ...thod. The maximum value of x such that \\ Gamma(x) is not If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [6 \entry{Ci}{6}{\code {Ci}} \entry{Ci}{6}{\code {Ci}} \entry{atanint}{6}{\code {atanint}} \entry{atanint}{6}{\code {atanint}} \entry{fermi_dirac_mhalf}{6}{\code {fermi_dirac_mhalf}} \entry{fermi_dirac_mhalf}{6}{\code {fermi_dirac_mhalf}} \entry{fermi_dirac_half}{6}{\code {fermi_dirac_half}} \entry{fermi_dirac_half}{6}{\code {fermi_dirac_half}} \entry{fermi_dirac_3half}{6}{\code {fermi_dirac_3half}} \entry{fermi_dirac_3half}{6}{\code {fermi_dirac_3half}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 455--457 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:462: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lngamma_gsl}{\folio }{\code {lngamma_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.462 ...nction} {@var{y} =} lngamma_gsl (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:463: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lngamma_gsl}{\folio }{\code {lngamma_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.463 ...r{y}, @var{err}] =} lngamma_gsl (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:466: Use of \ doesn't match its definition. l.466 \\ log(\\Gamma(x)), subject to x not a being negative integer. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:466: Use of \ doesn't match its definition. l.466 \\log(\\ Gamma(x)), subject to x not a being negative integer. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:467: Use of \ doesn't match its definition. l.467 For x<0 the real part of \\ log(\\Gamma(x)) is returned, which is If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:467: Use of \ doesn't match its definition. l.467 For x<0 the real part of \\log(\\ Gamma(x)) is returned, which is If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:468: Use of \ doesn't match its definition. l.468 equivalent to \\ log(|\\Gamma(x)|). The function is computed using If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:468: Use of \ doesn't match its definition. l.468 equivalent to \\log(|\\ Gamma(x)|). The function is computed using If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 473--475 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:480: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gammastar}{\folio }{\code {gammastar}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.480 ...Function} {@var{y} =} gammastar (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:481: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gammastar}{\folio }{\code {gammastar}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.481 ...var{y}, @var{err}] =} gammastar (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:483: Use of \ doesn't match its definition. l.483 ...s compute the regulated Gamma Function \\ Gamma^*(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:486: Use of \ doesn't match its definition. l.486 \\ Gamma^*(x) = \\Gamma(x)/(\\sqrt@{2\\pi@} x^@{(x-1/2)@} \\exp(-x)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:486: Use of \ doesn't match its definition. l.486 \\Gamma^*(x) = \\ Gamma(x)/(\\sqrt@{2\\pi@} x^@{(x-1/2)@} \\exp(-x)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:486: Use of \ doesn't match its definition. l.486 \\Gamma^*(x) = \\Gamma(x)/(\\ sqrt@{2\\pi@} x^@{(x-1/2)@} \\exp(-x)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:486: Use of \ doesn't match its definition. l.486 \\Gamma^*(x) = \\Gamma(x)/(\\sqrt@{2\\ pi@} x^@{(x-1/2)@} \\exp(-x)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:486: Use of \ doesn't match its definition. l.486 ...amma(x)/(\\sqrt@{2\\pi@} x^@{(x-1/2)@} \\ exp(-x)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:487: Use of \ doesn't match its definition. l.487 = (1 + (1/12x) + ...) for x \\ to \\infty If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:487: Use of \ doesn't match its definition. l.487 ... = (1 + (1/12x) + ...) for x \\to \\ infty If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 493--495 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:500: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gammainv_gsl}{\folio }{\code {gammainv_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.500 ...ction} {@var{y} =} gammainv_gsl (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:501: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gammainv_gsl}{\folio }{\code {gammainv_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.501 ...{y}, @var{err}] =} gammainv_gsl (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:503: Use of \ doesn't match its definition. l.503 ...he reciprocal of the gamma function, 1/\\ Gamma(x) using the real La... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 507--509 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:514: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lambert_W0}{\folio }{\code {lambert_W0}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.514 ...unction} {@var{y} =} lambert_W0 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:515: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lambert_W0}{\folio }{\code {lambert_W0}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.515 ...ar{y}, @var{err}] =} lambert_W0 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [7 \entry{gamma_gsl}{7}{\code {gamma_gsl}} \entry{gamma_gsl}{7}{\code {gamma_gsl}} \entry{lngamma_gsl}{7}{\code {lngamma_gsl}} \entry{lngamma_gsl}{7}{\code {lngamma_gsl}} \entry{gammastar}{7}{\code {gammastar}} \entry{gammastar}{7}{\code {gammastar}} \entry{gammainv_gsl}{7}{\code {gammainv_gsl}} \entry{gammainv_gsl}{7}{\code {gammainv_gsl}} ] ./gsl_sf.texi:519: Use of \ doesn't match its definition. l.519 Lambert\\ 's W functions, W(x), are defined to be solutions of the If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:520: Use of \ doesn't match its definition. l.520 equation W(x) \\ exp(W(x)) = x. This function has multiple branches If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 527--529 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:534: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lambert_Wm1}{\folio }{\code {lambert_Wm1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.534 ...nction} {@var{y} =} lambert_Wm1 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:535: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lambert_Wm1}{\folio }{\code {lambert_Wm1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.535 ...r{y}, @var{err}] =} lambert_Wm1 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:540: Use of \ doesn't match its definition. l.540 Lambert\\ 's W functions, W(x), are defined to be solutions of the If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:541: Use of \ doesn't match its definition. l.541 equation W(x) \\ exp(W(x)) = x. This function has multiple branches If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 548--550 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:555: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_1plusx}{\folio }{\code {log_1plusx}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.555 ...unction} {@var{y} =} log_1plusx (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:556: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_1plusx}{\folio }{\code {log_1plusx}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.556 ...ar{y}, @var{err}] =} log_1plusx (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:558: Use of \ doesn't match its definition. l.558 These routines compute \\ log(1 + x) for x > -1 using an algorithm that If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 563--565 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:570: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_1plusx_mx}{\folio }{\code {log_1plusx_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.570 ...tion} {@var{y} =} log_1plusx_mx (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:571: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_1plusx_mx}{\folio }{\code {log_1plusx_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.571 ...y}, @var{err}] =} log_1plusx_mx (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:573: Use of \ doesn't match its definition. l.573 These routines compute \\ log(1 + x) - x for x > -1 using an algorithm If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 578--580 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:585: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi}{\folio }{\code {psi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.585 ...dable Function} {@var{y} =} psi (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:586: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi}{\folio }{\code {psi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.586 ...n} {[@var{y}, @var{err}] =} psi (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:588: Use of \ doesn't match its definition. l.588 ... routines compute the digamma function \\ psi(x) for general x, If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:589: Use of \ doesn't match its definition. l.589 x \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [8 \entry{lambert_W0}{8}{\code {lambert_W0}} \entry{lambert_W0}{8}{\code {lambert_W0}} \entry{lambert_Wm1}{8}{\code {lambert_Wm1}} \entry{lambert_Wm1}{8}{\code {lambert_Wm1}} \entry{log_1plusx}{8}{\code {log_1plusx}} \entry{log_1plusx}{8}{\code {log_1plusx}} \entry{log_1plusx_mx}{8}{\code {log_1plusx_mx}} \entry{log_1plusx_mx}{8}{\code {log_1plusx_mx}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 594--596 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:601: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_1piy}{\folio }{\code {psi_1piy}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.601 ... Function} {@var{y} =} psi_1piy (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:602: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_1piy}{\folio }{\code {psi_1piy}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.602 ...@var{y}, @var{err}] =} psi_1piy (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:605: Use of \ doesn't match its definition. l.605 the line 1+i y, Re[\\ psi(1 + i y)]. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 609--611 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:616: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{synchrotron_1}{\folio }{\code {synchrotron... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.616 ...tion} {@var{y} =} synchrotron_1 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:617: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{synchrotron_1}{\folio }{\code {synchrotron... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.617 ...y}, @var{err}] =} synchrotron_1 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:620: Use of \ doesn't match its definition. l.620 x \\ int_x^\\infty dt K_@{5/3@}(t) for x >= 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:620: Use of \ doesn't match its definition. l.620 x \\int_x^\\ infty dt K_@{5/3@}(t) for x >= 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 624--626 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:631: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{synchrotron_2}{\folio }{\code {synchrotron... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.631 ...tion} {@var{y} =} synchrotron_2 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:632: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{synchrotron_2}{\folio }{\code {synchrotron... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.632 ...y}, @var{err}] =} synchrotron_2 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 639--641 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:646: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_2}{\folio }{\code {transport_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.646 ...nction} {@var{y} =} transport_2 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:647: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_2}{\folio }{\code {transport_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.647 ...r{y}, @var{err}] =} transport_2 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:652: Use of \ doesn't match its definition. l.652 representations J(n,x) := \\ int_0^x dt t^n e^t /(e^t - 1)^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 656--658 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:663: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_3}{\folio }{\code {transport_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.663 ...nction} {@var{y} =} transport_3 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:664: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_3}{\folio }{\code {transport_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.664 ...r{y}, @var{err}] =} transport_3 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [9 \entry{psi}{9}{\code {psi}} \entry{psi}{9}{\code {psi}} \entry{psi_1piy}{9}{\code {psi_1piy}} \entry{psi_1piy}{9}{\code {psi_1piy}} \entry{synchrotron_1}{9}{\code {synchrotron_1}} \entry{synchrotron_1}{9}{\code {synchrotron_1}} \entry{synchrotron_2}{9}{\code {synchrotron_2}} \entry{synchrotron_2}{9}{\code {synchrotron_2}} \entry{transport_2}{9}{\code {transport_2}} \entry{transport_2}{9}{\code {transport_2}} ] ./gsl_sf.texi:669: Use of \ doesn't match its definition. l.669 representations J(n,x) := \\ int_0^x dt t^n e^t /(e^t - 1)^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 673--675 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:680: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_4}{\folio }{\code {transport_4}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.680 ...nction} {@var{y} =} transport_4 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:681: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_4}{\folio }{\code {transport_4}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.681 ...r{y}, @var{err}] =} transport_4 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:686: Use of \ doesn't match its definition. l.686 representations J(n,x) := \\ int_0^x dt t^n e^t /(e^t - 1)^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 690--692 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:697: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_5}{\folio }{\code {transport_5}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.697 ...nction} {@var{y} =} transport_5 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:698: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_5}{\folio }{\code {transport_5}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.698 ...r{y}, @var{err}] =} transport_5 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:703: Use of \ doesn't match its definition. l.703 representations J(n,x) := \\ int_0^x dt t^n e^t /(e^t - 1)^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 707--709 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:714: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{sinc_gsl}{\folio }{\code {sinc_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.714 ... Function} {@var{y} =} sinc_gsl (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:715: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{sinc_gsl}{\folio }{\code {sinc_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.715 ...@var{y}, @var{err}] =} sinc_gsl (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:717: Use of \ doesn't match its definition. l.717 These routines compute \\ sinc(x) = \\sin(\\pi x) / (\\pi x) for any va... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:717: Use of \ doesn't match its definition. l.717 These routines compute \\sinc(x) = \\ sin(\\pi x) / (\\pi x) for any va... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:717: Use of \ doesn't match its definition. l.717 These routines compute \\sinc(x) = \\sin(\\ pi x) / (\\pi x) for any va... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:717: Use of \ doesn't match its definition. l.717 ...s compute \\sinc(x) = \\sin(\\pi x) / (\\ pi x) for any value of x. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 721--723 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:728: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnsinh}{\folio }{\code {lnsinh}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.728 ...le Function} {@var{y} =} lnsinh (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:729: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnsinh}{\folio }{\code {lnsinh}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.729 ...{[@var{y}, @var{err}] =} lnsinh (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:731: Use of \ doesn't match its definition. l.731 These routines compute \\ log(\\sinh(x)) for x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:731: Use of \ doesn't match its definition. l.731 These routines compute \\log(\\ sinh(x)) for x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 735--737 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. [10 \entry{transport_3}{10}{\code {transport_3}} \entry{transport_3}{10}{\code {transport_3}} \entry{transport_4}{10}{\code {transport_4}} \entry{transport_4}{10}{\code {transport_4}} \entry{transport_5}{10}{\code {transport_5}} \entry{transport_5}{10}{\code {transport_5}} \entry{sinc_gsl}{10}{\code {sinc_gsl}} \entry{sinc_gsl}{10}{\code {sinc_gsl}} \entry{lnsinh}{10}{\code {lnsinh}} \entry{lnsinh}{10}{\code {lnsinh}} ] ./gsl_sf.texi:742: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lncosh}{\folio }{\code {lncosh}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.742 ...le Function} {@var{y} =} lncosh (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:743: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lncosh}{\folio }{\code {lncosh}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.743 ...{[@var{y}, @var{err}] =} lncosh (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:745: Use of \ doesn't match its definition. l.745 These routines compute \\ log(\\cosh(x)) for any x. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:745: Use of \ doesn't match its definition. l.745 These routines compute \\log(\\ cosh(x)) for any x. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 749--751 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:756: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{zeta}{\folio }{\code {zeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.756 ...able Function} {@var{y} =} zeta (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:757: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{zeta}{\folio }{\code {zeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.757 ...} {[@var{y}, @var{err}] =} zeta (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:759: Use of \ doesn't match its definition. l.759 ...ines compute the Riemann zeta function \\ zeta(s) for If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:760: Use of \ doesn't match its definition. l.760 arbitrary s, s \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:764: Use of \ doesn't match its definition. l.764 \\ zeta(s) = \\sum_@{k=1@}^\\infty k^@{-s@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:764: Use of \ doesn't match its definition. l.764 \\zeta(s) = \\ sum_@{k=1@}^\\infty k^@{-s@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:764: Use of \ doesn't match its definition. l.764 \\zeta(s) = \\sum_@{k=1@}^\\ infty k^@{-s@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 768--770 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:775: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{eta}{\folio }{\code {eta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.775 ...dable Function} {@var{y} =} eta (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:776: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{eta}{\folio }{\code {eta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.776 ...n} {[@var{y}, @var{err}] =} eta (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:778: Use of \ doesn't match its definition. l.778 These routines compute the eta function \\ eta(s) for arbitrary s. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:780: Use of \ doesn't match its definition. l.780 The eta function is defined by \\ eta(s) = (1-2^@{1-s@}) \\zeta(s). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:780: Use of \ doesn't match its definition. l.780 ...is defined by \\eta(s) = (1-2^@{1-s@}) \\ zeta(s). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 784--786 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:791: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Jn}{\folio }{\code {bessel_Jn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.791 ... {@var{y} =} bessel_Jn (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:792: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Jn}{\folio }{\code {bessel_Jn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.792 ...var{y}, @var{err}] =} bessel_Jn (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 799--801 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:806: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Yn}{\folio }{\code {bessel_Yn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.806 ... {@var{y} =} bessel_Yn (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:807: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Yn}{\folio }{\code {bessel_Yn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.807 ...var{y}, @var{err}] =} bessel_Yn (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 814--816 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:821: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_In}{\folio }{\code {bessel_In}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.821 ... {@var{y} =} bessel_In (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [11 \entry{lncosh}{11}{\code {lncosh}} \entry{lncosh}{11}{\code {lncosh}} \entry{zeta}{11}{\code {zeta}} \entry{zeta}{11}{\code {zeta}} \entry{eta}{11}{\code {eta}} \entry{eta}{11}{\code {eta}} \entry{bessel_Jn}{11}{\code {bessel_Jn}} \entry{bessel_Jn}{11}{\code {bessel_Jn}} \entry{bessel_Yn}{11}{\code {bessel_Yn}} \entry{bessel_Yn}{11}{\code {bessel_Yn}} ] ./gsl_sf.texi:822: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_In}{\folio }{\code {bessel_In}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.822 ...var{y}, @var{err}] =} bessel_In (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 829--831 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:836: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_In_scaled}{\folio }{\code {bessel_I... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.836 ...y} =} bessel_In_scaled (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:837: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_In_scaled}{\folio }{\code {bessel_I... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.837 ... @var{err}] =} bessel_In_scaled (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:840: Use of \ doesn't match its definition. l.840 function of order n, \\ exp(-|x|) I_n(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 844--846 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:851: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Kn}{\folio }{\code {bessel_Kn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.851 ... {@var{y} =} bessel_Kn (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:852: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Kn}{\folio }{\code {bessel_Kn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.852 ...var{y}, @var{err}] =} bessel_Kn (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 859--861 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:866: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Kn_scaled}{\folio }{\code {bessel_K... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.866 ...y} =} bessel_Kn_scaled (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:867: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Kn_scaled}{\folio }{\code {bessel_K... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.867 ... @var{err}] =} bessel_Kn_scaled (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 873--875 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:880: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_jl}{\folio }{\code {bessel_jl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.880 ... {@var{y} =} bessel_jl (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:881: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_jl}{\folio }{\code {bessel_jl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.881 ...var{y}, @var{err}] =} bessel_jl (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 888--890 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:895: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_yl}{\folio }{\code {bessel_yl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.895 ... {@var{y} =} bessel_yl (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:896: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_yl}{\folio }{\code {bessel_yl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.896 ...var{y}, @var{err}] =} bessel_yl (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [12 \entry{bessel_In}{12}{\code {bessel_In}} \entry{bessel_In}{12}{\code {bessel_In}} \entry{bessel_In_scaled}{12}{\code {bessel_In_scaled}} \entry{bessel_In_scaled}{12}{\code {bessel_In_scaled}} \entry{bessel_Kn}{12}{\code {bessel_Kn}} \entry{bessel_Kn}{12}{\code {bessel_Kn}} \entry{bessel_Kn_scaled}{12}{\code {bessel_Kn_scaled}} \entry{bessel_Kn_scaled}{12}{\code {bessel_Kn_scaled}} \entry{bessel_jl}{12}{\code {bessel_jl}} \entry{bessel_jl}{12}{\code {bessel_jl}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 903--905 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:910: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_il_scaled}{\folio }{\code {bessel_i... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.910 ...y} =} bessel_il_scaled (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:911: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_il_scaled}{\folio }{\code {bessel_i... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.911 ... @var{err}] =} bessel_il_scaled (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:914: Use of \ doesn't match its definition. l.914 function of order l, \\ exp(-|x|) i_l(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 918--920 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:925: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_kl_scaled}{\folio }{\code {bessel_k... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.925 ...y} =} bessel_kl_scaled (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:926: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_kl_scaled}{\folio }{\code {bessel_k... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.926 ... @var{err}] =} bessel_kl_scaled (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:929: Use of \ doesn't match its definition. l.929 function of order l, \\ exp(x) k_l(x), for x>0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 933--935 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:940: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel_n}{\folio }{\code {exprel_n}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.940 ...} {@var{y} =} exprel_n (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:941: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel_n}{\folio }{\code {exprel_n}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.941 ...@var{y}, @var{err}] =} exprel_n (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:947: Use of \ doesn't match its definition. l.947 exprel_N(x) = N!/x^N (\\ exp(x) - \\sum_@{k=0@}^@{N-1@} x^k/k!) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:947: Use of \ doesn't match its definition. l.947 exprel_N(x) = N!/x^N (\\exp(x) - \\ sum_@{k=0@}^@{N-1@} x^k/k!) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 953--955 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:960: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_int}{\folio }{\code {fermi_dir... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.960 ...{y} =} fermi_dirac_int (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:961: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_int}{\folio }{\code {fermi_dir... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.961 ..., @var{err}] =} fermi_dirac_int (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:964: Use of \ doesn't match its definition. l.964 integer index of j, F_j(x) = (1/\\ Gamma(j+1)) \\int_0^\\infty dt (t^j If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:964: Use of \ doesn't match its definition. l.964 ... index of j, F_j(x) = (1/\\Gamma(j+1)) \\ int_0^\\infty dt (t^j If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:964: Use of \ doesn't match its definition. l.964 ...f j, F_j(x) = (1/\\Gamma(j+1)) \\int_0^\\ infty dt (t^j If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:965: Use of \ doesn't match its definition. l.965 /(\\ exp(t-x)+1)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 969--971 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. [13 \entry{bessel_yl}{13}{\code {bessel_yl}} \entry{bessel_yl}{13}{\code {bessel_yl}} \entry{bessel_il_scaled}{13}{\code {bessel_il_scaled}} \entry{bessel_il_scaled}{13}{\code {bessel_il_scaled}} \entry{bessel_kl_scaled}{13}{\code {bessel_kl_scaled}} \entry{bessel_kl_scaled}{13}{\code {bessel_kl_scaled}} \entry{exprel_n}{13}{\code {exprel_n}} \entry{exprel_n}{13}{\code {exprel_n}} ] ./gsl_sf.texi:976: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{taylorcoeff}{\folio }{\code {taylorcoeff}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.976 ...@var{y} =} taylorcoeff (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:977: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{taylorcoeff}{\folio }{\code {taylorcoeff}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.977 ...r{y}, @var{err}] =} taylorcoeff (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 984--986 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:991: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Pl}{\folio }{\code {legendre_Pl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.991 ...@var{y} =} legendre_Pl (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:992: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Pl}{\folio }{\code {legendre_Pl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.992 ...r{y}, @var{err}] =} legendre_Pl (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 999--1001 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1006: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Ql}{\folio }{\code {legendre_Ql}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1006 ...var{y} =} legendre_Ql (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1007: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Ql}{\folio }{\code {legendre_Ql}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1007 ...{y}, @var{err}] =} legendre_Ql (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1014--1016 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1021: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_n}{\folio }{\code {psi_n}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1021 ...on} {@var{y} =} psi_n (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1022: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_n}{\folio }{\code {psi_n}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1022 ...{[@var{y}, @var{err}] =} psi_n (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1024: Use of \ doesn't match its definition. l.1024 ...utines compute the polygamma function \\ psi^@{(m)@}(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1029--1031 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1036: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Jnu}{\folio }{\code {bessel_Jnu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1036 ...@var{z} =} bessel_Jnu (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1037: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Jnu}{\folio }{\code {bessel_Jnu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1037 ...r{z}, @var{err}] =} bessel_Jnu (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1040: Use of \ doesn't match its definition. l.1040 fractional order nu, J_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [14 \entry{fermi_dirac_int}{14}{\code {fermi_dirac_int}} \entry{fermi_dirac_int}{14}{\code {fermi_dirac_int}} \entry{taylorcoeff}{14}{\code {taylorcoeff}} \entry{taylorcoeff}{14}{\code {taylorcoeff}} \entry{legendre_Pl}{14}{\code {legendre_Pl}} \entry{legendre_Pl}{14}{\code {legendre_Pl}} \entry{legendre_Ql}{14}{\code {legendre_Ql}} \entry{legendre_Ql}{14}{\code {legendre_Ql}} \entry{psi_n}{14}{\code {psi_n}} \entry{psi_n}{14}{\code {psi_n}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 1045--1047 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1052: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Ynu}{\folio }{\code {bessel_Ynu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1052 ...@var{z} =} bessel_Ynu (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1053: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Ynu}{\folio }{\code {bessel_Ynu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1053 ...r{z}, @var{err}] =} bessel_Ynu (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1056: Use of \ doesn't match its definition. l.1056 fractional order nu, Y_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1061--1063 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1068: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Inu}{\folio }{\code {bessel_Inu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1068 ...@var{z} =} bessel_Inu (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1069: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Inu}{\folio }{\code {bessel_Inu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1069 ...r{z}, @var{err}] =} bessel_Inu (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1072: Use of \ doesn't match its definition. l.1072 fractional order nu, I_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1073: Use of \ doesn't match its definition. l.1073 u(x) for x>0, \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1078--1080 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1085: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Inu_scaled}{\folio }{\code {bessel_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1085 ... =} bessel_Inu_scaled (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1086: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Inu_scaled}{\folio }{\code {bessel_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1086 ...var{err}] =} bessel_Inu_scaled (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1089: Use of \ doesn't match its definition. l.1089 fractional order nu, \\ exp(-|x|)I_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1089: Use of \ doesn't match its definition. l.1089 fractional order nu, \\exp(-|x|)I_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1090: Use of \ doesn't match its definition. l.1090 u(x) for x>0, \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1095--1097 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1102: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Knu}{\folio }{\code {bessel_Knu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1102 ...@var{z} =} bessel_Knu (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1103: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Knu}{\folio }{\code {bessel_Knu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1103 ...r{z}, @var{err}] =} bessel_Knu (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1106: Use of \ doesn't match its definition. l.1106 fractional order nu, K_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1107: Use of \ doesn't match its definition. l.1107 u(x) for x>0, \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1112--1114 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1119: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_lnKnu}{\folio }{\code {bessel_lnKnu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1119 ...ar{z} =} bessel_lnKnu (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [15 \entry{bessel_Jnu}{15}{\code {bessel_Jnu}} \entry{bessel_Jnu}{15}{\code {bessel_Jnu}} \entry{bessel_Ynu}{15}{\code {bessel_Ynu}} \entry{bessel_Ynu}{15}{\code {bessel_Ynu}} \entry{bessel_Inu}{15}{\code {bessel_Inu}} \entry{bessel_Inu}{15}{\code {bessel_Inu}} \entry{bessel_Inu_scaled}{15}{\code {bessel_Inu_scaled}} \entry{bessel_Inu_scaled}{15}{\code {bessel_Inu_scaled}} \entry{bessel_Knu}{15}{\code {bessel_Knu}} \entry{bessel_Knu}{15}{\code {bessel_Knu}} ] ./gsl_sf.texi:1120: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_lnKnu}{\folio }{\code {bessel_lnKnu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1120 ...z}, @var{err}] =} bessel_lnKnu (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1123: Use of \ doesn't match its definition. l.1123 function of fractional order nu, \\ ln(K_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1123: Use of \ doesn't match its definition. l.1123 function of fractional order nu, \\ln(K_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1124: Use of \ doesn't match its definition. l.1124 u(x)) for x>0, \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1129--1131 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1136: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Knu_scaled}{\folio }{\code {bessel_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1136 ... =} bessel_Knu_scaled (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1137: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Knu_scaled}{\folio }{\code {bessel_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1137 ...var{err}] =} bessel_Knu_scaled (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1140: Use of \ doesn't match its definition. l.1140 of fractional order nu, \\ exp(+|x|) K_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1140: Use of \ doesn't match its definition. l.1140 of fractional order nu, \\exp(+|x|) K_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1141: Use of \ doesn't match its definition. l.1141 u(x) for x>0, \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1146--1148 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1153: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exp_mult}{\folio }{\code {exp_mult}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1153 ... {@var{z} =} exp_mult (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1154: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exp_mult}{\folio }{\code {exp_mult}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1154 ...var{z}, @var{err}] =} exp_mult (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1157: Use of \ doesn't match its definition. l.1157 the product y \\ exp(x). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1161--1163 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1168: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_inc_0}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1168 ... =} fermi_dirac_inc_0 (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1169: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_inc_0}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1169 ...var{err}] =} fermi_dirac_inc_0 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1172: Use of \ doesn't match its definition. l.1172 index of zero, F_0(x,b) = \\ ln(1 + e^@{b-x@}) - (b-x). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1176--1178 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1183: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{poch}{\folio }{\code {poch}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1183 ...ion} {@var{z} =} poch (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1184: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{poch}{\folio }{\code {poch}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1184 ... {[@var{z}, @var{err}] =} poch (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1188: Use of \ doesn't match its definition. l.1188 (a)_x := \\ Gamma(a + x)/\\Gamma(a), If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1188: Use of \ doesn't match its definition. l.1188 (a)_x := \\Gamma(a + x)/\\ Gamma(a), If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1195--1197 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. [16 \entry{bessel_lnKnu}{16}{\code {bessel_lnKnu}} \entry{bessel_lnKnu}{16}{\code {bessel_lnKnu}} \entry{bessel_Knu_scaled}{16}{\code {bessel_Knu_scaled}} \entry{bessel_Knu_scaled}{16}{\code {bessel_Knu_scaled}} \entry{exp_mult}{16}{\code {exp_mult}} \entry{exp_mult}{16}{\code {exp_mult}} \entry{fermi_dirac_inc_0}{16}{\code {fermi_dirac_inc_0}} \entry{fermi_dirac_inc_0}{16}{\code {fermi_dirac_inc_0}} \entry{poch}{16}{\code {poch}} \entry{poch}{16}{\code {poch}} ] ./gsl_sf.texi:1202: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnpoch}{\folio }{\code {lnpoch}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1202 ...n} {@var{z} =} lnpoch (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1203: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnpoch}{\folio }{\code {lnpoch}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1203 ...[@var{z}, @var{err}] =} lnpoch (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1206: Use of \ doesn't match its definition. l.1206 \\ log((a)_x) = \\log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1206: Use of \ doesn't match its definition. l.1206 \\log((a)_x) = \\ log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1206: Use of \ doesn't match its definition. l.1206 \\log((a)_x) = \\log(\\ Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1206: Use of \ doesn't match its definition. l.1206 \\log((a)_x) = \\log(\\Gamma(a + x)/\\ Gamma(a)) for a > 0, a+x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1210--1212 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1217: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{pochrel}{\folio }{\code {pochrel}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1217 ...} {@var{z} =} pochrel (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1218: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{pochrel}{\folio }{\code {pochrel}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1218 ...@var{z}, @var{err}] =} pochrel (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1221: Use of \ doesn't match its definition. l.1221 where (a,x) = (a)_x := \\ Gamma(a + x)/\\Gamma(a). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1221: Use of \ doesn't match its definition. l.1221 where (a,x) = (a)_x := \\Gamma(a + x)/\\ Gamma(a). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1225--1227 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1232: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc_Q}{\folio }{\code {gamma_inc_Q}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1232 ...var{z} =} gamma_inc_Q (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1233: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc_Q}{\folio }{\code {gamma_inc_Q}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1233 ...{z}, @var{err}] =} gamma_inc_Q (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1236: Use of \ doesn't match its definition. l.1236 Q(a,x) = 1/\\ Gamma(a) \\int_x\\infty dt t^@{a-1@} \\exp(-t) for a > 0... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1236: Use of \ doesn't match its definition. l.1236 Q(a,x) = 1/\\Gamma(a) \\ int_x\\infty dt t^@{a-1@} \\exp(-t) for a > 0... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1236: Use of \ doesn't match its definition. l.1236 Q(a,x) = 1/\\Gamma(a) \\int_x\\ infty dt t^@{a-1@} \\exp(-t) for a > 0... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1236: Use of \ doesn't match its definition. l.1236 ...\Gamma(a) \\int_x\\infty dt t^@{a-1@} \\ exp(-t) for a > 0, x >= 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1240--1242 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1247: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc_P}{\folio }{\code {gamma_inc_P}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1247 ...var{z} =} gamma_inc_P (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1248: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc_P}{\folio }{\code {gamma_inc_P}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1248 ...{z}, @var{err}] =} gamma_inc_P (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1251: Use of \ doesn't match its definition. l.1251 Function P(a,x) = 1/\\ Gamma(a) \\int_0^x dt t^@{a-1@} \\exp(-t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1251: Use of \ doesn't match its definition. l.1251 Function P(a,x) = 1/\\Gamma(a) \\ int_0^x dt t^@{a-1@} \\exp(-t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1251: Use of \ doesn't match its definition. l.1251 ...= 1/\\Gamma(a) \\int_0^x dt t^@{a-1@} \\ exp(-t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1256--1258 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1263: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc}{\folio }{\code {gamma_inc}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1263 ...{@var{z} =} gamma_inc (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1264: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc}{\folio }{\code {gamma_inc}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1264 ...ar{z}, @var{err}] =} gamma_inc (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1268: Use of \ doesn't match its definition. l.1268 \\ Gamma(a,x) = \\int_x\\infty dt t^@{a-1@} \\exp(-t) for a real and x... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1268: Use of \ doesn't match its definition. l.1268 \\Gamma(a,x) = \\ int_x\\infty dt t^@{a-1@} \\exp(-t) for a real and x... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1268: Use of \ doesn't match its definition. l.1268 \\Gamma(a,x) = \\int_x\\ infty dt t^@{a-1@} \\exp(-t) for a real and x... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1268: Use of \ doesn't match its definition. l.1268 ...ma(a,x) = \\int_x\\infty dt t^@{a-1@} \\ exp(-t) for a real and x >... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [17 \entry{lnpoch}{17}{\code {lnpoch}} \entry{lnpoch}{17}{\code {lnpoch}} \entry{pochrel}{17}{\code {pochrel}} \entry{pochrel}{17}{\code {pochrel}} \entry{gamma_inc_Q}{17}{\code {gamma_inc_Q}} \entry{gamma_inc_Q}{17}{\code {gamma_inc_Q}} \entry{gamma_inc_P}{17}{\code {gamma_inc_P}} \entry{gamma_inc_P}{17}{\code {gamma_inc_P}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 1272--1274 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1279: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{beta_gsl}{\folio }{\code {beta_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1279 ... {@var{z} =} beta_gsl (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1280: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{beta_gsl}{\folio }{\code {beta_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1280 ...var{z}, @var{err}] =} beta_gsl (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1283: Use of \ doesn't match its definition. l.1283 B(a,b) = \\ Gamma(a)\\Gamma(b)/\\Gamma(a+b) for a > 0, b > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1283: Use of \ doesn't match its definition. l.1283 B(a,b) = \\Gamma(a)\\ Gamma(b)/\\Gamma(a+b) for a > 0, b > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1283: Use of \ doesn't match its definition. l.1283 B(a,b) = \\Gamma(a)\\Gamma(b)/\\ Gamma(a+b) for a > 0, b > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (20.37637pt too wide) in paragraph at lines 1282--1284 []@textrm These rou-tines com-pute the Beta Func-tion, B(a,b) = Gamma(a)Gamma( b)/Gamma(a+b)| @hbox(8.2125+2.73749)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm e .etc. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1287--1289 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1294: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnbeta}{\folio }{\code {lnbeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1294 ...n} {@var{z} =} lnbeta (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1295: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnbeta}{\folio }{\code {lnbeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1295 ...[@var{z}, @var{err}] =} lnbeta (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1298: Use of \ doesn't match its definition. l.1298 \\ log(B(a,b)) for a > 0, b > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1302--1304 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1309: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_0F1}{\folio }{\code {hyperg_0F1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1309 ...@var{z} =} hyperg_0F1 (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1310: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_0F1}{\folio }{\code {hyperg_0F1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1310 ...r{z}, @var{err}] =} hyperg_0F1 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1316--1318 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1323: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_half}{\folio }{\code {conicalP_ha... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1323 ...r{z} =} conicalP_half (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1324: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_half}{\folio }{\code {conicalP_ha... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1324 ...}, @var{err}] =} conicalP_half (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1327: Use of \ doesn't match its definition. l.1327 P^@{1/2@}_@{-1/2 + i \\ lambda@}(x) for x > -1. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1331--1333 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1338: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_mhalf}{\folio }{\code {conicalP_m... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1338 ...{z} =} conicalP_mhalf (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [18 \entry{gamma_inc}{18}{\code {gamma_inc}} \entry{gamma_inc}{18}{\code {gamma_inc}} \entry{beta_gsl}{18}{\code {beta_gsl}} \entry{beta_gsl}{18}{\code {beta_gsl}} \entry{lnbeta}{18}{\code {lnbeta}} \entry{lnbeta}{18}{\code {lnbeta}} \entry{hyperg_0F1}{18}{\code {hyperg_0F1}} \entry{hyperg_0F1}{18}{\code {hyperg_0F1}} \entry{conicalP_half}{18}{\code {conicalP_half}} \entry{conicalP_half}{18}{\code {conicalP_half}} ] ./gsl_sf.texi:1339: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_mhalf}{\folio }{\code {conicalP_m... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1339 ..., @var{err}] =} conicalP_mhalf (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1342: Use of \ doesn't match its definition. l.1342 P^@{-1/2@}_@{-1/2 + i \\ lambda@}(x) for x > -1. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1346--1348 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1353: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_0}{\folio }{\code {conicalP_0}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1353 ...@var{z} =} conicalP_0 (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1354: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_0}{\folio }{\code {conicalP_0}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1354 ...r{z}, @var{err}] =} conicalP_0 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1356: Use of \ doesn't match its definition. l.1356 ...e the conical function P^0_@{-1/2 + i \\ lambda@}(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1361--1363 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1368: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_1}{\folio }{\code {conicalP_1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1368 ...@var{z} =} conicalP_1 (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1369: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_1}{\folio }{\code {conicalP_1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1369 ...r{z}, @var{err}] =} conicalP_1 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1371: Use of \ doesn't match its definition. l.1371 ...e the conical function P^1_@{-1/2 + i \\ lambda@}(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1376--1378 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1383: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hzeta}{\folio }{\code {hzeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1383 ...on} {@var{z} =} hzeta (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1384: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hzeta}{\folio }{\code {hzeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1384 ...{[@var{z}, @var{err}] =} hzeta (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1386: Use of \ doesn't match its definition. l.1386 ...nes compute the Hurwitz zeta function \\ zeta(s,q) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1391--1393 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1398: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai}{\folio }{\code {airy_Ai}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1398 ...@var{y} =} airy_Ai (@var{x}, @var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1399: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai}{\folio }{\code {airy_Ai}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1399 ...@var{y}, @var{err}] =} airy_Ai (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [19 \entry{conicalP_mhalf}{19}{\code {conicalP_mhalf}} \entry{conicalP_mhalf}{19}{\code {conicalP_mhalf}} \entry{conicalP_0}{19}{\code {conicalP_0}} \entry{conicalP_0}{19}{\code {conicalP_0}} \entry{conicalP_1}{19}{\code {conicalP_1}} \entry{conicalP_1}{19}{\code {conicalP_1}} \entry{hzeta}{19}{\code {hzeta}} \entry{hzeta}{19}{\code {hzeta}} \entry{airy_Ai}{19}{\code {airy_Ai}} \entry{airy_Ai}{19}{\code {airy_Ai}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 1417--1419 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1424: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi}{\folio }{\code {airy_Bi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1424 ...@var{y} =} airy_Bi (@var{x}, @var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1425: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi}{\folio }{\code {airy_Bi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1425 ...@var{y}, @var{err}] =} airy_Bi (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1443--1445 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1450: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_scaled}{\folio }{\code {airy_Ai_sc... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1450 ... =} airy_Ai_scaled (@var{x}, @var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1451: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_scaled}{\folio }{\code {airy_Ai_sc... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1451 ..., @var{err}] =} airy_Ai_scaled (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1454: Use of \ doesn't match its definition. l.1454 ... For x>0 the scaling factor S_A(x) is \\ exp(+(2/3) x^(3/2)), and If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1470--1472 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1477: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_scaled}{\folio }{\code {airy_Bi_sc... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1477 ... =} airy_Bi_scaled (@var{x}, @var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1478: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_scaled}{\folio }{\code {airy_Bi_sc... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1478 ..., @var{err}] =} airy_Bi_scaled (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [20 \entry{airy_Bi}{20}{\code {airy_Bi}} \entry{airy_Bi}{20}{\code {airy_Bi}} \entry{airy_Ai_scaled}{20}{\code {airy_Ai_scaled}} \entry{airy_Ai_scaled}{20}{\code {airy_Ai_scaled}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 1497--1499 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1504: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_deriv}{\folio }{\code {airy_Ai_der... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1504 ...} =} airy_Ai_deriv (@var{x}, @var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1505: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_deriv}{\folio }{\code {airy_Ai_der... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1505 ...}, @var{err}] =} airy_Ai_deriv (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1523--1525 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1530: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_deriv}{\folio }{\code {airy_Bi_der... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1530 ...} =} airy_Bi_deriv (@var{x}, @var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1531: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_deriv}{\folio }{\code {airy_Bi_der... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1531 ...}, @var{err}] =} airy_Bi_deriv (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [21 \entry{airy_Bi_scaled}{21}{\code {airy_Bi_scaled}} \entry{airy_Bi_scaled}{21}{\code {airy_Bi_scaled}} \entry{airy_Ai_deriv}{21}{\code {airy_Ai_deriv}} \entry{airy_Ai_deriv}{21}{\code {airy_Ai_deriv}} \entry{airy_Bi_deriv}{21}{\code {airy_Bi_deriv}} \entry{airy_Bi_deriv}{21}{\code {airy_Bi_deriv}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 1549--1551 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1556: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_deriv_scaled}{\folio }{\code {airy... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1556 ...ry_Ai_deriv_scaled (@var{x}, @var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1557: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_deriv_scaled}{\folio }{\code {airy... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1557 ...{err}] =} airy_Ai_deriv_scaled (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1575--1577 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1582: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_deriv_scaled}{\folio }{\code {airy... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1582 ...ry_Bi_deriv_scaled (@var{x}, @var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1583: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_deriv_scaled}{\folio }{\code {airy... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1583 ...{err}] =} airy_Bi_deriv_scaled (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1601--1603 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1608: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{ellint_Kcomp}{\folio }{\code {ellint_Kcomp}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1608 ...y} =} ellint_Kcomp (@var{x}, @var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1609: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{ellint_Kcomp}{\folio }{\code {ellint_Kcomp}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1609 ...y}, @var{err}] =} ellint_Kcomp (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1613: Undefined control sequence. l.1613 \beforedisplay The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ./gsl_sf.texi:1619: Undefined control sequence. l.1619 \afterdisplay The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ./gsl_sf.texi:1655: Undefined control sequence. l.1655 @seealso {ellipj, ellipke} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. [22 \entry{airy_Ai_deriv_scaled}{22}{\code {airy_Ai_deriv_scaled}} \entry{airy_Ai_deriv_scaled}{22}{\code {airy_Ai_deriv_scaled}} \entry{airy_Bi_deriv_scaled}{22}{\code {airy_Bi_deriv_scaled}} \entry{airy_Bi_deriv_scaled}{22}{\code {airy_Bi_deriv_scaled}} \entry{ellint_Kcomp}{22}{\code {ellint_Kcomp}} \entry{ellint_Kcomp}{22}{\code {ellint_Kcomp}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 1676--1678 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1683: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{ellint_Ecomp}{\folio }{\code {ellint_Ecomp}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1683 ...y} =} ellint_Ecomp (@var{x}, @var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1684: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{ellint_Ecomp}{\folio }{\code {ellint_Ecomp}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1684 ...y}, @var{err}] =} ellint_Ecomp (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1690: Undefined control sequence. l.1690 \beforedisplay The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ./gsl_sf.texi:1696: Undefined control sequence. l.1696 \afterdisplay The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ./gsl_sf.texi:1733: Undefined control sequence. l.1733 @seealso {ellipj, ellipke} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1753--1755 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. [23 \entry{ellint_Ecomp}{23}{\code {ellint_Ecomp}} \entry{ellint_Ecomp}{23}{\code {ellint_Ecomp}} ] ./gsl_sf.texi:1760: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Ai}{\folio }{\code {airy_zero_Ai}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1760 ...tion} {@var{y} =} airy_zero_Ai (@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1761: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Ai}{\folio }{\code {airy_zero_Ai}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1761 ...y}, @var{err}] =} airy_zero_Ai (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1768--1770 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1775: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Bi}{\folio }{\code {airy_zero_Bi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1775 ...tion} {@var{y} =} airy_zero_Bi (@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1776: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Bi}{\folio }{\code {airy_zero_Bi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1776 ...y}, @var{err}] =} airy_zero_Bi (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1783--1785 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1790: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Ai_deriv}{\folio }{\code {airy_z... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1790 ...{@var{y} =} airy_zero_Ai_deriv (@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1791: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Ai_deriv}{\folio }{\code {airy_z... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1791 ...ar{err}] =} airy_zero_Ai_deriv (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1798--1800 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1805: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Bi_deriv}{\folio }{\code {airy_z... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1805 ...{@var{y} =} airy_zero_Bi_deriv (@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1806: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Bi_deriv}{\folio }{\code {airy_z... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1806 ...ar{err}] =} airy_zero_Bi_deriv (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1813--1815 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1820: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_zero_J0}{\folio }{\code {bessel_zer... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1820 ...on} {@var{y} =} bessel_zero_J0 (@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1821: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_zero_J0}{\folio }{\code {bessel_zer... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1821 ..., @var{err}] =} bessel_zero_J0 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1828--1830 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. [24 \entry{airy_zero_Ai}{24}{\code {airy_zero_Ai}} \entry{airy_zero_Ai}{24}{\code {airy_zero_Ai}} \entry{airy_zero_Bi}{24}{\code {airy_zero_Bi}} \entry{airy_zero_Bi}{24}{\code {airy_zero_Bi}} \entry{airy_zero_Ai_deriv}{24}{\code {airy_zero_Ai_deriv}} \entry{airy_zero_Ai_deriv}{24}{\code {airy_zero_Ai_deriv}} \entry{airy_zero_Bi_deriv}{24}{\code {airy_zero_Bi_deriv}} \entry{airy_zero_Bi_deriv}{24}{\code {airy_zero_Bi_deriv}} \entry{bessel_zero_J0}{24}{\code {bessel_zero_J0}} \entry{bessel_zero_J0}{24}{\code {bessel_zero_J0}} ] ./gsl_sf.texi:1835: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_zero_J1}{\folio }{\code {bessel_zer... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1835 ...on} {@var{y} =} bessel_zero_J1 (@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1836: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_zero_J1}{\folio }{\code {bessel_zer... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1836 ..., @var{err}] =} bessel_zero_J1 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1843--1845 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1850: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_1_int}{\folio }{\code {psi_1_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1850 ...unction} {@var{y} =} psi_1_int (@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1851: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_1_int}{\folio }{\code {psi_1_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1851 ...ar{y}, @var{err}] =} psi_1_int (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1853: Use of \ doesn't match its definition. l.1853 ...outines compute the Trigamma function \\ psi(n) for positive If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1858--1860 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1865: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{zeta_int}{\folio }{\code {zeta_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1865 ...Function} {@var{y} =} zeta_int (@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1866: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{zeta_int}{\folio }{\code {zeta_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1866 ...var{y}, @var{err}] =} zeta_int (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1868: Use of \ doesn't match its definition. l.1868 ...nes compute the Riemann zeta function \\ zeta(n) for If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1869: Use of \ doesn't match its definition. l.1869 integer n, n \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1874--1876 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1881: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{eta_int}{\folio }{\code {eta_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1881 ... Function} {@var{y} =} eta_int (@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1882: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{eta_int}{\folio }{\code {eta_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1882 ...@var{y}, @var{err}] =} eta_int (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1884: Use of \ doesn't match its definition. l.1884 These routines compute the eta function \\ eta(n) for integer n. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1888--1890 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1895: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Plm}{\folio }{\code {legendre_Plm}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1895 ...legendre_Plm (@var{n}, @var{m}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1896: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Plm}{\folio }{\code {legendre_Plm}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1896 ...y}, @var{err}] =} legendre_Plm (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1903--1905 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. [25 \entry{bessel_zero_J1}{25}{\code {bessel_zero_J1}} \entry{bessel_zero_J1}{25}{\code {bessel_zero_J1}} \entry{psi_1_int}{25}{\code {psi_1_int}} \entry{psi_1_int}{25}{\code {psi_1_int}} \entry{zeta_int}{25}{\code {zeta_int}} \entry{zeta_int}{25}{\code {zeta_int}} \entry{eta_int}{25}{\code {eta_int}} \entry{eta_int}{25}{\code {eta_int}} \entry{legendre_Plm}{25}{\code {legendre_Plm}} \entry{legendre_Plm}{25}{\code {legendre_Plm}} ] ./gsl_sf.texi:1910: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_sphPlm}{\folio }{\code {legendre_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1910 ...endre_sphPlm (@var{n}, @var{m}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1911: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_sphPlm}{\folio }{\code {legendre_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1911 ... @var{err}] =} legendre_sphPlm (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1914: Use of \ doesn't match its definition. l.1914 $\\ sqrt@{(2l+1)/(4\\pi)@} \\sqrt@{(l-m)!/(l+m)!@} P_l^m(x)$ suitable ... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1914: Use of \ doesn't match its definition. l.1914 $\\sqrt@{(2l+1)/(4\\ pi)@} \\sqrt@{(l-m)!/(l+m)!@} P_l^m(x)$ suitable ... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1914: Use of \ doesn't match its definition. l.1914 $\\sqrt@{(2l+1)/(4\\pi)@} \\ sqrt@{(l-m)!/(l+m)!@} P_l^m(x)$ suitable ... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Underfull \hbox (badness 10000) in paragraph at lines 1913--1918 []@textrm These rou-tines com-pute the nor-mal-ized as-so-ci-ated Leg-en-dre p oly-no-mial @hbox(7.60416+2.12917)x433.62, glue set 4.66573 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm e .etc. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1921--1923 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1928: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_U}{\folio }{\code {hyperg_U}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1928 ... hyperg_U (@var{x0}, @var{x1}, @var{x2}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1929: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_U}{\folio }{\code {hyperg_U}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1929 ...r{out}, @var{err}] =} hyperg_U (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1936--1938 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1943: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_1F1}{\folio }{\code {hyperg_1F1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1943 ...yperg_1F1 (@var{x0}, @var{x1}, @var{x2}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1944: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_1F1}{\folio }{\code {hyperg_1F1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1944 ...out}, @var{err}] =} hyperg_1F1 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1951--1953 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1958: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gsl_sf}{\folio }{\code {gsl_sf}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1958 @deftypefn {Loadable Function} {} gsl_sf () A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1966: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{clausen}{\folio }{\code {clausen}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1966 ... Function} {@var{y} =} clausen (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1967: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{clausen}{\folio }{\code {clausen}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1967 ...@var{y}, @var{err}] =} clausen (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1971: Use of \ doesn't match its definition. l.1971 Cl_2(x) = - \\ int_0^x dt \\log(2 \\sin(t/2)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1971: Use of \ doesn't match its definition. l.1971 Cl_2(x) = - \\int_0^x dt \\ log(2 \\sin(t/2)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1971: Use of \ doesn't match its definition. l.1971 Cl_2(x) = - \\int_0^x dt \\log(2 \\ sin(t/2)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1973: Use of \ doesn't match its definition. l.1973 It is related to the dilogarithm by Cl_2(\\ theta) = \\Im Li_2(\\exp(i... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1973: Use of \ doesn't match its definition. l.1973 ...to the dilogarithm by Cl_2(\\theta) = \\ Im Li_2(\\exp(i \\theta)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1973: Use of \ doesn't match its definition. l.1973 ...ogarithm by Cl_2(\\theta) = \\Im Li_2(\\ exp(i \\theta)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1973: Use of \ doesn't match its definition. l.1973 ... by Cl_2(\\theta) = \\Im Li_2(\\exp(i \\ theta)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1977--1979 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1984: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{dawson}{\folio }{\code {dawson}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1984 ...e Function} {@var{y} =} dawson (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [26 \entry{legendre_sphPlm}{26}{\code {legendre_sphPlm}} \entry{legendre_sphPlm}{26}{\code {legendre_sphPlm}} \entry{hyperg_U}{26}{\code {hyperg_U}} \entry{hyperg_U}{26}{\code {hyperg_U}} \entry{hyperg_1F1}{26}{\code {hyperg_1F1}} \entry{hyperg_1F1}{26}{\code {hyperg_1F1}} \entry{gsl_sf}{26}{\code {gsl_sf}} \entry{clausen}{26}{\code {clausen}} \entry{clausen}{26}{\code {clausen}} ] ./gsl_sf.texi:1985: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{dawson}{\folio }{\code {dawson}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1985 ...[@var{y}, @var{err}] =} dawson (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:1987: Use of \ doesn't match its definition. l.1987 The Dawson integral is defined by \\ exp(-x^2) \\int_0^x dt \\exp(t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1987: Use of \ doesn't match its definition. l.1987 ...on integral is defined by \\exp(-x^2) \\ int_0^x dt \\exp(t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:1987: Use of \ doesn't match its definition. l.1987 ...s defined by \\exp(-x^2) \\int_0^x dt \\ exp(t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1992--1994 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:1999: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_1}{\folio }{\code {debye_1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1999 ... Function} {@var{y} =} debye_1 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2000: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_1}{\folio }{\code {debye_1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2000 ...@var{y}, @var{err}] =} debye_1 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2004: Use of \ doesn't match its definition. l.2004 D_n(x) = n/x^n \\ int_0^x dt (t^n/(e^t - 1)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2010--2012 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2017: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_2}{\folio }{\code {debye_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2017 ... Function} {@var{y} =} debye_2 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2018: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_2}{\folio }{\code {debye_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2018 ...@var{y}, @var{err}] =} debye_2 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2022: Use of \ doesn't match its definition. l.2022 D_n(x) = n/x^n \\ int_0^x dt (t^n/(e^t - 1)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2028--2030 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2035: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_3}{\folio }{\code {debye_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2035 ... Function} {@var{y} =} debye_3 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2036: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_3}{\folio }{\code {debye_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2036 ...@var{y}, @var{err}] =} debye_3 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2040: Use of \ doesn't match its definition. l.2040 D_n(x) = n/x^n \\ int_0^x dt (t^n/(e^t - 1)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2046--2048 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2053: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_4}{\folio }{\code {debye_4}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2053 ... Function} {@var{y} =} debye_4 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2054: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_4}{\folio }{\code {debye_4}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2054 ...@var{y}, @var{err}] =} debye_4 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2058: Use of \ doesn't match its definition. l.2058 D_n(x) = n/x^n \\ int_0^x dt (t^n/(e^t - 1)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [27 \entry{dawson}{27}{\code {dawson}} \entry{dawson}{27}{\code {dawson}} \entry{debye_1}{27}{\code {debye_1}} \entry{debye_1}{27}{\code {debye_1}} \entry{debye_2}{27}{\code {debye_2}} \entry{debye_2}{27}{\code {debye_2}} \entry{debye_3}{27}{\code {debye_3}} \entry{debye_3}{27}{\code {debye_3}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 2064--2066 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2071: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_gsl}{\folio }{\code {erf_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2071 ... Function} {@var{y} =} erf_gsl (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2072: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_gsl}{\folio }{\code {erf_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2072 ...@var{y}, @var{err}] =} erf_gsl (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2075: Use of \ doesn't match its definition. l.2075 erf(x) = (2/\\ sqrt(\\pi)) \\int_0^x dt \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2075: Use of \ doesn't match its definition. l.2075 erf(x) = (2/\\sqrt(\\ pi)) \\int_0^x dt \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2075: Use of \ doesn't match its definition. l.2075 erf(x) = (2/\\sqrt(\\pi)) \\ int_0^x dt \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2075: Use of \ doesn't match its definition. l.2075 erf(x) = (2/\\sqrt(\\pi)) \\int_0^x dt \\ exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2079--2081 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2086: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erfc_gsl}{\folio }{\code {erfc_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2086 ...Function} {@var{y} =} erfc_gsl (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2087: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erfc_gsl}{\folio }{\code {erfc_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2087 ...var{y}, @var{err}] =} erfc_gsl (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2090: Use of \ doesn't match its definition. l.2090 erfc(x) = 1 - erf(x) = (2/\\ sqrt(\\pi)) \\int_x^\\infty \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2090: Use of \ doesn't match its definition. l.2090 erfc(x) = 1 - erf(x) = (2/\\sqrt(\\ pi)) \\int_x^\\infty \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2090: Use of \ doesn't match its definition. l.2090 erfc(x) = 1 - erf(x) = (2/\\sqrt(\\pi)) \\ int_x^\\infty \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2090: Use of \ doesn't match its definition. l.2090 ...1 - erf(x) = (2/\\sqrt(\\pi)) \\int_x^\\ infty \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2090: Use of \ doesn't match its definition. l.2090 ...x) = (2/\\sqrt(\\pi)) \\int_x^\\infty \\ exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2094--2096 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2101: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_erfc}{\folio }{\code {log_erfc}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2101 ...Function} {@var{y} =} log_erfc (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2102: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_erfc}{\folio }{\code {log_erfc}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2102 ...var{y}, @var{err}] =} log_erfc (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2105: Use of \ doesn't match its definition. l.2105 function \\ log(\\erfc(x)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2105: Use of \ doesn't match its definition. l.2105 function \\log(\\ erfc(x)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2109--2111 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2116: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_Z}{\folio }{\code {erf_Z}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2116 ...le Function} {@var{y} =} erf_Z (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2117: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_Z}{\folio }{\code {erf_Z}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2117 ...{[@var{y}, @var{err}] =} erf_Z (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2120: Use of \ doesn't match its definition. l.2120 Z(x) = (1/(2\\ pi)) \\exp(-x^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2120: Use of \ doesn't match its definition. l.2120 Z(x) = (1/(2\\pi)) \\ exp(-x^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2124--2126 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2131: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_Q}{\folio }{\code {erf_Q}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2131 ...le Function} {@var{y} =} erf_Q (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [28 \entry{debye_4}{28}{\code {debye_4}} \entry{debye_4}{28}{\code {debye_4}} \entry{erf_gsl}{28}{\code {erf_gsl}} \entry{erf_gsl}{28}{\code {erf_gsl}} \entry{erfc_gsl}{28}{\code {erfc_gsl}} \entry{erfc_gsl}{28}{\code {erfc_gsl}} \entry{log_erfc}{28}{\code {log_erfc}} \entry{log_erfc}{28}{\code {log_erfc}} \entry{erf_Z}{28}{\code {erf_Z}} \entry{erf_Z}{28}{\code {erf_Z}} ] ./gsl_sf.texi:2132: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_Q}{\folio }{\code {erf_Q}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2132 ...{[@var{y}, @var{err}] =} erf_Q (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2135: Use of \ doesn't match its definition. l.2135 function Q(x) = (1/(2\\ pi)) \\int_x^\\infty dt \\exp(-t^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2135: Use of \ doesn't match its definition. l.2135 function Q(x) = (1/(2\\pi)) \\ int_x^\\infty dt \\exp(-t^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2135: Use of \ doesn't match its definition. l.2135 function Q(x) = (1/(2\\pi)) \\int_x^\\ infty dt \\exp(-t^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2135: Use of \ doesn't match its definition. l.2135 ...Q(x) = (1/(2\\pi)) \\int_x^\\infty dt \\ exp(-t^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2139--2141 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2146: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hazard}{\folio }{\code {hazard}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2146 ...e Function} {@var{y} =} hazard (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2147: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hazard}{\folio }{\code {hazard}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2147 ...[@var{y}, @var{err}] =} hazard (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2150: Use of \ doesn't match its definition. l.2150 inverse Mill\\ 's ratio, is defined as If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2151: Use of \ doesn't match its definition. l.2151 h(x) = Z(x)/Q(x) = \\ sqrt@{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2151: Use of \ doesn't match its definition. l.2151 h(x) = Z(x)/Q(x) = \\sqrt@{2/\\ pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2151: Use of \ doesn't match its definition. l.2151 h(x) = Z(x)/Q(x) = \\sqrt@{2/\\pi \\ exp(-x^2 / 2) / \\erfc(x/\\sqrt 2... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2151: Use of \ doesn't match its definition. l.2151 ...x) = \\sqrt@{2/\\pi \\exp(-x^2 / 2) / \\ erfc(x/\\sqrt 2)@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2151: Use of \ doesn't match its definition. l.2151 ...rt@{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\ sqrt 2)@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2152: Use of \ doesn't match its definition. l.2152 It decreases rapidly as x approaches -\\ infty and asymptotes to If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2153: Use of \ doesn't match its definition. l.2153 h(x) \\ sim x as x approaches +\\infty. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2153: Use of \ doesn't match its definition. l.2153 h(x) \\sim x as x approaches +\\ infty. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2157--2159 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2164: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expm1}{\folio }{\code {expm1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2164 ...le Function} {@var{y} =} expm1 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2165: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expm1}{\folio }{\code {expm1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2165 ...{[@var{y}, @var{err}] =} expm1 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2167: Use of \ doesn't match its definition. l.2167 These routines compute the quantity \\ exp(x)-1 using an algorithm that If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2172--2174 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2179: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel}{\folio }{\code {exprel}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2179 ...e Function} {@var{y} =} exprel (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2180: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel}{\folio }{\code {exprel}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2180 ...[@var{y}, @var{err}] =} exprel (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2182: Use of \ doesn't match its definition. l.2182 These routines compute the quantity (\\ exp(x)-1)/x using an algorithm If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2184: Use of \ doesn't match its definition. l.2184 the expansion (\\ exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2184: Use of \ doesn't match its definition. l.2184 ...= 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\ dots. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2188--2190 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2195: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel_2}{\folio }{\code {exprel_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2195 ...Function} {@var{y} =} exprel_2 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2196: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel_2}{\folio }{\code {exprel_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2196 ...var{y}, @var{err}] =} exprel_2 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2198: Use of \ doesn't match its definition. l.2198 These routines compute the quantity 2(\\ exp(x)-1-x)/x^2 using an If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2201: Use of \ doesn't match its definition. l.2201 2(\\ exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\dots. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2201: Use of \ doesn't match its definition. l.2201 ...= 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\ dots. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [29 \entry{erf_Q}{29}{\code {erf_Q}} \entry{erf_Q}{29}{\code {erf_Q}} \entry{hazard}{29}{\code {hazard}} \entry{hazard}{29}{\code {hazard}} \entry{expm1}{29}{\code {expm1}} \entry{expm1}{29}{\code {expm1}} \entry{exprel}{29}{\code {exprel}} \entry{exprel}{29}{\code {exprel}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 2205--2207 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2212: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_E1}{\folio }{\code {expint_E1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2212 ...unction} {@var{y} =} expint_E1 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2213: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_E1}{\folio }{\code {expint_E1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2213 ...ar{y}, @var{err}] =} expint_E1 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2217: Use of \ doesn't match its definition. l.2217 E_1(x) := Re \\ int_1^\\infty dt \\exp(-xt)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2217: Use of \ doesn't match its definition. l.2217 E_1(x) := Re \\int_1^\\ infty dt \\exp(-xt)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2217: Use of \ doesn't match its definition. l.2217 E_1(x) := Re \\int_1^\\infty dt \\ exp(-xt)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2221--2223 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2228: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_E2}{\folio }{\code {expint_E2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2228 ...unction} {@var{y} =} expint_E2 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2229: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_E2}{\folio }{\code {expint_E2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2229 ...ar{y}, @var{err}] =} expint_E2 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2233: Use of \ doesn't match its definition. l.2233 E_2(x) := \\ Re \\int_1^\\infty dt \\exp(-xt)/t^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2233: Use of \ doesn't match its definition. l.2233 E_2(x) := \\Re \\ int_1^\\infty dt \\exp(-xt)/t^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2233: Use of \ doesn't match its definition. l.2233 E_2(x) := \\Re \\int_1^\\ infty dt \\exp(-xt)/t^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2233: Use of \ doesn't match its definition. l.2233 E_2(x) := \\Re \\int_1^\\infty dt \\ exp(-xt)/t^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2237--2239 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2244: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_Ei}{\folio }{\code {expint_Ei}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2244 ...unction} {@var{y} =} expint_Ei (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2245: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_Ei}{\folio }{\code {expint_Ei}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2245 ...ar{y}, @var{err}] =} expint_Ei (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2249: Use of \ doesn't match its definition. l.2249 Ei(x) := - PV(\\ int_@{-x@}^\\infty dt \\exp(-t)/t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2249: Use of \ doesn't match its definition. l.2249 Ei(x) := - PV(\\int_@{-x@}^\\ infty dt \\exp(-t)/t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2249: Use of \ doesn't match its definition. l.2249 Ei(x) := - PV(\\int_@{-x@}^\\infty dt \\ exp(-t)/t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2255--2257 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2262: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Shi}{\folio }{\code {Shi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2262 ...able Function} {@var{y} =} Shi (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2263: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Shi}{\folio }{\code {Shi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2263 ...} {[@var{y}, @var{err}] =} Shi (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2265: Use of \ doesn't match its definition. l.2265 ...outines compute the integral Shi(x) = \\ int_0^x dt \\sinh(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2265: Use of \ doesn't match its definition. l.2265 ...te the integral Shi(x) = \\int_0^x dt \\ sinh(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2269--2271 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. [30 \entry{exprel_2}{30}{\code {exprel_2}} \entry{exprel_2}{30}{\code {exprel_2}} \entry{expint_E1}{30}{\code {expint_E1}} \entry{expint_E1}{30}{\code {expint_E1}} \entry{expint_E2}{30}{\code {expint_E2}} \entry{expint_E2}{30}{\code {expint_E2}} \entry{expint_Ei}{30}{\code {expint_Ei}} \entry{expint_Ei}{30}{\code {expint_Ei}} \entry{Shi}{30}{\code {Shi}} \entry{Shi}{30}{\code {Shi}} ] ./gsl_sf.texi:2276: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Chi}{\folio }{\code {Chi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2276 ...able Function} {@var{y} =} Chi (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2277: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Chi}{\folio }{\code {Chi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2277 ...} {[@var{y}, @var{err}] =} Chi (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2281: Use of \ doesn't match its definition. l.2281 Chi(x) := Re[ \\ gamma_E + \\log(x) + \\int_0^x dt (\\cosh[t]-1)/t] , If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2281: Use of \ doesn't match its definition. l.2281 Chi(x) := Re[ \\gamma_E + \\ log(x) + \\int_0^x dt (\\cosh[t]-1)/t] , If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2281: Use of \ doesn't match its definition. l.2281 Chi(x) := Re[ \\gamma_E + \\log(x) + \\ int_0^x dt (\\cosh[t]-1)/t] , If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2281: Use of \ doesn't match its definition. l.2281 ... \\gamma_E + \\log(x) + \\int_0^x dt (\\ cosh[t]-1)/t] , If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2283: Use of \ doesn't match its definition. l.2283 where \\ gamma_E is the Euler constant. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2287--2289 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2294: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_3}{\folio }{\code {expint_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2294 ...Function} {@var{y} =} expint_3 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2295: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_3}{\folio }{\code {expint_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2295 ...var{y}, @var{err}] =} expint_3 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2298: Use of \ doesn't match its definition. l.2298 Ei_3(x) = \\ int_0^x dt \\exp(-t^3) for x >= 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2298: Use of \ doesn't match its definition. l.2298 Ei_3(x) = \\int_0^x dt \\ exp(-t^3) for x >= 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2302--2304 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2309: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Si}{\folio }{\code {Si}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2309 ...dable Function} {@var{y} =} Si (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2310: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Si}{\folio }{\code {Si}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2310 ...n} {[@var{y}, @var{err}] =} Si (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2312: Use of \ doesn't match its definition. l.2312 ...nes compute the Sine integral Si(x) = \\ int_0^x dt \\sin(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2312: Use of \ doesn't match its definition. l.2312 ...he Sine integral Si(x) = \\int_0^x dt \\ sin(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2316--2318 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2323: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Ci}{\folio }{\code {Ci}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2323 ...dable Function} {@var{y} =} Ci (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2324: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Ci}{\folio }{\code {Ci}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2324 ...n} {[@var{y}, @var{err}] =} Ci (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2327: Use of \ doesn't match its definition. l.2327 Ci(x) = -\\ int_x^\\infty dt \\cos(t)/t for x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2327: Use of \ doesn't match its definition. l.2327 Ci(x) = -\\int_x^\\ infty dt \\cos(t)/t for x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2327: Use of \ doesn't match its definition. l.2327 Ci(x) = -\\int_x^\\infty dt \\ cos(t)/t for x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2331--2333 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2338: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{atanint}{\folio }{\code {atanint}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2338 ... Function} {@var{y} =} atanint (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2339: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{atanint}{\folio }{\code {atanint}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2339 ...@var{y}, @var{err}] =} atanint (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2342: Use of \ doesn't match its definition. l.2342 AtanInt(x) = \\ int_0^x dt \\arctan(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2342: Use of \ doesn't match its definition. l.2342 AtanInt(x) = \\int_0^x dt \\ arctan(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2346--2348 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2353: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_mhalf}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2353 ... {@var{y} =} fermi_dirac_mhalf (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2354: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_mhalf}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2354 ...var{err}] =} fermi_dirac_mhalf (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [31 \entry{Chi}{31}{\code {Chi}} \entry{Chi}{31}{\code {Chi}} \entry{expint_3}{31}{\code {expint_3}} \entry{expint_3}{31}{\code {expint_3}} \entry{Si}{31}{\code {Si}} \entry{Si}{31}{\code {Si}} \entry{Ci}{31}{\code {Ci}} \entry{Ci}{31}{\code {Ci}} \entry{atanint}{31}{\code {atanint}} \entry{atanint}{31}{\code {atanint}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 2360--2362 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2367: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_half}{\folio }{\code {fermi_di... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2367 ...} {@var{y} =} fermi_dirac_half (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2368: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_half}{\folio }{\code {fermi_di... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2368 ...@var{err}] =} fermi_dirac_half (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2374--2376 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2381: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_3half}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2381 ... {@var{y} =} fermi_dirac_3half (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2382: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_3half}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2382 ...var{err}] =} fermi_dirac_3half (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2388--2390 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2395: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_gsl}{\folio }{\code {gamma_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2395 ...unction} {@var{y} =} gamma_gsl (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2396: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_gsl}{\folio }{\code {gamma_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2396 ...ar{y}, @var{err}] =} gamma_gsl (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2398: Use of \ doesn't match its definition. l.2398 ...e routines compute the Gamma function \\ Gamma(x), subject to x not If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2400: Use of \ doesn't match its definition. l.2400 ...hod. The maximum value of x such that \\ Gamma(x) is not If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2405--2407 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2412: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lngamma_gsl}{\folio }{\code {lngamma_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2412 ...ction} {@var{y} =} lngamma_gsl (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2413: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lngamma_gsl}{\folio }{\code {lngamma_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2413 ...{y}, @var{err}] =} lngamma_gsl (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2416: Use of \ doesn't match its definition. l.2416 \\ log(\\Gamma(x)), subject to x not a being negative integer. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2416: Use of \ doesn't match its definition. l.2416 \\log(\\ Gamma(x)), subject to x not a being negative integer. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2417: Use of \ doesn't match its definition. l.2417 For x<0 the real part of \\ log(\\Gamma(x)) is returned, which is If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2417: Use of \ doesn't match its definition. l.2417 For x<0 the real part of \\log(\\ Gamma(x)) is returned, which is If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2418: Use of \ doesn't match its definition. l.2418 equivalent to \\ log(|\\Gamma(x)|). The function is computed using If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2418: Use of \ doesn't match its definition. l.2418 equivalent to \\log(|\\ Gamma(x)|). The function is computed using If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2423--2425 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. [32 \entry{fermi_dirac_mhalf}{32}{\code {fermi_dirac_mhalf}} \entry{fermi_dirac_mhalf}{32}{\code {fermi_dirac_mhalf}} \entry{fermi_dirac_half}{32}{\code {fermi_dirac_half}} \entry{fermi_dirac_half}{32}{\code {fermi_dirac_half}} \entry{fermi_dirac_3half}{32}{\code {fermi_dirac_3half}} \entry{fermi_dirac_3half}{32}{\code {fermi_dirac_3half}} \entry{gamma_gsl}{32}{\code {gamma_gsl}} \entry{gamma_gsl}{32}{\code {gamma_gsl}} \entry{lngamma_gsl}{32}{\code {lngamma_gsl}} \entry{lngamma_gsl}{32}{\code {lngamma_gsl}} ] ./gsl_sf.texi:2430: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gammastar}{\folio }{\code {gammastar}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2430 ...unction} {@var{y} =} gammastar (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2431: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gammastar}{\folio }{\code {gammastar}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2431 ...ar{y}, @var{err}] =} gammastar (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2433: Use of \ doesn't match its definition. l.2433 ... compute the regulated Gamma Function \\ Gamma^*(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2436: Use of \ doesn't match its definition. l.2436 \\ Gamma^*(x) = \\Gamma(x)/(\\sqrt@{2\\pi@} x^@{(x-1/2)@} \\exp(-x)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2436: Use of \ doesn't match its definition. l.2436 \\Gamma^*(x) = \\ Gamma(x)/(\\sqrt@{2\\pi@} x^@{(x-1/2)@} \\exp(-x)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2436: Use of \ doesn't match its definition. l.2436 \\Gamma^*(x) = \\Gamma(x)/(\\ sqrt@{2\\pi@} x^@{(x-1/2)@} \\exp(-x)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2436: Use of \ doesn't match its definition. l.2436 \\Gamma^*(x) = \\Gamma(x)/(\\sqrt@{2\\ pi@} x^@{(x-1/2)@} \\exp(-x)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2436: Use of \ doesn't match its definition. l.2436 ...mma(x)/(\\sqrt@{2\\pi@} x^@{(x-1/2)@} \\ exp(-x)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2437: Use of \ doesn't match its definition. l.2437 = (1 + (1/12x) + ...) for x \\ to \\infty If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2437: Use of \ doesn't match its definition. l.2437 ... = (1 + (1/12x) + ...) for x \\to \\ infty If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2443--2445 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2450: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gammainv_gsl}{\folio }{\code {gammainv_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2450 ...tion} {@var{y} =} gammainv_gsl (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2451: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gammainv_gsl}{\folio }{\code {gammainv_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2451 ...y}, @var{err}] =} gammainv_gsl (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2453: Use of \ doesn't match its definition. l.2453 ...e reciprocal of the gamma function, 1/\\ Gamma(x) using the real La... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2457--2459 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2464: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lambert_W0}{\folio }{\code {lambert_W0}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2464 ...nction} {@var{y} =} lambert_W0 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2465: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lambert_W0}{\folio }{\code {lambert_W0}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2465 ...r{y}, @var{err}] =} lambert_W0 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2469: Use of \ doesn't match its definition. l.2469 Lambert\\ 's W functions, W(x), are defined to be solutions of the If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2470: Use of \ doesn't match its definition. l.2470 equation W(x) \\ exp(W(x)) = x. This function has multiple branches If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2477--2479 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2484: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lambert_Wm1}{\folio }{\code {lambert_Wm1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2484 ...ction} {@var{y} =} lambert_Wm1 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2485: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lambert_Wm1}{\folio }{\code {lambert_Wm1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2485 ...{y}, @var{err}] =} lambert_Wm1 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2490: Use of \ doesn't match its definition. l.2490 Lambert\\ 's W functions, W(x), are defined to be solutions of the If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2491: Use of \ doesn't match its definition. l.2491 equation W(x) \\ exp(W(x)) = x. This function has multiple branches If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2498--2500 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. [33 \entry{gammastar}{33}{\code {gammastar}} \entry{gammastar}{33}{\code {gammastar}} \entry{gammainv_gsl}{33}{\code {gammainv_gsl}} \entry{gammainv_gsl}{33}{\code {gammainv_gsl}} \entry{lambert_W0}{33}{\code {lambert_W0}} \entry{lambert_W0}{33}{\code {lambert_W0}} \entry{lambert_Wm1}{33}{\code {lambert_Wm1}} \entry{lambert_Wm1}{33}{\code {lambert_Wm1}} ] ./gsl_sf.texi:2505: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_1plusx}{\folio }{\code {log_1plusx}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2505 ...nction} {@var{y} =} log_1plusx (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2506: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_1plusx}{\folio }{\code {log_1plusx}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2506 ...r{y}, @var{err}] =} log_1plusx (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2508: Use of \ doesn't match its definition. l.2508 These routines compute \\ log(1 + x) for x > -1 using an algorithm that If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2513--2515 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2520: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_1plusx_mx}{\folio }{\code {log_1plusx_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2520 ...ion} {@var{y} =} log_1plusx_mx (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2521: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_1plusx_mx}{\folio }{\code {log_1plusx_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2521 ...}, @var{err}] =} log_1plusx_mx (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2523: Use of \ doesn't match its definition. l.2523 These routines compute \\ log(1 + x) - x for x > -1 using an algorithm If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2528--2530 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2535: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi}{\folio }{\code {psi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2535 ...able Function} {@var{y} =} psi (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2536: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi}{\folio }{\code {psi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2536 ...} {[@var{y}, @var{err}] =} psi (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2538: Use of \ doesn't match its definition. l.2538 ...routines compute the digamma function \\ psi(x) for general x, If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2539: Use of \ doesn't match its definition. l.2539 x \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2544--2546 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2551: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_1piy}{\folio }{\code {psi_1piy}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2551 ...Function} {@var{y} =} psi_1piy (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2552: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_1piy}{\folio }{\code {psi_1piy}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2552 ...var{y}, @var{err}] =} psi_1piy (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2555: Use of \ doesn't match its definition. l.2555 the line 1+i y, Re[\\ psi(1 + i y)]. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2559--2561 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2566: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{synchrotron_1}{\folio }{\code {synchrotron... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2566 ...ion} {@var{y} =} synchrotron_1 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2567: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{synchrotron_1}{\folio }{\code {synchrotron... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2567 ...}, @var{err}] =} synchrotron_1 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2570: Use of \ doesn't match its definition. l.2570 x \\ int_x^\\infty dt K_@{5/3@}(t) for x >= 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2570: Use of \ doesn't match its definition. l.2570 x \\int_x^\\ infty dt K_@{5/3@}(t) for x >= 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2574--2576 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. [34 \entry{log_1plusx}{34}{\code {log_1plusx}} \entry{log_1plusx}{34}{\code {log_1plusx}} \entry{log_1plusx_mx}{34}{\code {log_1plusx_mx}} \entry{log_1plusx_mx}{34}{\code {log_1plusx_mx}} \entry{psi}{34}{\code {psi}} \entry{psi}{34}{\code {psi}} \entry{psi_1piy}{34}{\code {psi_1piy}} \entry{psi_1piy}{34}{\code {psi_1piy}} \entry{synchrotron_1}{34}{\code {synchrotron_1}} \entry{synchrotron_1}{34}{\code {synchrotron_1}} ] ./gsl_sf.texi:2581: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{synchrotron_2}{\folio }{\code {synchrotron... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2581 ...ion} {@var{y} =} synchrotron_2 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2582: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{synchrotron_2}{\folio }{\code {synchrotron... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2582 ...}, @var{err}] =} synchrotron_2 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2589--2591 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2596: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_2}{\folio }{\code {transport_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2596 ...ction} {@var{y} =} transport_2 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2597: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_2}{\folio }{\code {transport_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2597 ...{y}, @var{err}] =} transport_2 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2602: Use of \ doesn't match its definition. l.2602 representations J(n,x) := \\ int_0^x dt t^n e^t /(e^t - 1)^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2606--2608 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2613: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_3}{\folio }{\code {transport_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2613 ...ction} {@var{y} =} transport_3 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2614: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_3}{\folio }{\code {transport_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2614 ...{y}, @var{err}] =} transport_3 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2619: Use of \ doesn't match its definition. l.2619 representations J(n,x) := \\ int_0^x dt t^n e^t /(e^t - 1)^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2623--2625 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2630: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_4}{\folio }{\code {transport_4}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2630 ...ction} {@var{y} =} transport_4 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2631: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_4}{\folio }{\code {transport_4}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2631 ...{y}, @var{err}] =} transport_4 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2636: Use of \ doesn't match its definition. l.2636 representations J(n,x) := \\ int_0^x dt t^n e^t /(e^t - 1)^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2640--2642 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2647: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_5}{\folio }{\code {transport_5}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2647 ...ction} {@var{y} =} transport_5 (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2648: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_5}{\folio }{\code {transport_5}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2648 ...{y}, @var{err}] =} transport_5 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [35 \entry{synchrotron_2}{35}{\code {synchrotron_2}} \entry{synchrotron_2}{35}{\code {synchrotron_2}} \entry{transport_2}{35}{\code {transport_2}} \entry{transport_2}{35}{\code {transport_2}} \entry{transport_3}{35}{\code {transport_3}} \entry{transport_3}{35}{\code {transport_3}} \entry{transport_4}{35}{\code {transport_4}} \entry{transport_4}{35}{\code {transport_4}} ] ./gsl_sf.texi:2653: Use of \ doesn't match its definition. l.2653 representations J(n,x) := \\ int_0^x dt t^n e^t /(e^t - 1)^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2657--2659 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2664: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{sinc_gsl}{\folio }{\code {sinc_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2664 ...Function} {@var{y} =} sinc_gsl (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2665: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{sinc_gsl}{\folio }{\code {sinc_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2665 ...var{y}, @var{err}] =} sinc_gsl (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2667: Use of \ doesn't match its definition. l.2667 These routines compute \\ sinc(x) = \\sin(\\pi x) / (\\pi x) for any v... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2667: Use of \ doesn't match its definition. l.2667 These routines compute \\sinc(x) = \\ sin(\\pi x) / (\\pi x) for any v... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2667: Use of \ doesn't match its definition. l.2667 These routines compute \\sinc(x) = \\sin(\\ pi x) / (\\pi x) for any v... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2667: Use of \ doesn't match its definition. l.2667 ... compute \\sinc(x) = \\sin(\\pi x) / (\\ pi x) for any value of x. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2671--2673 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2678: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnsinh}{\folio }{\code {lnsinh}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2678 ...e Function} {@var{y} =} lnsinh (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2679: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnsinh}{\folio }{\code {lnsinh}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2679 ...[@var{y}, @var{err}] =} lnsinh (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2681: Use of \ doesn't match its definition. l.2681 These routines compute \\ log(\\sinh(x)) for x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2681: Use of \ doesn't match its definition. l.2681 These routines compute \\log(\\ sinh(x)) for x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2685--2687 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2692: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lncosh}{\folio }{\code {lncosh}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2692 ...e Function} {@var{y} =} lncosh (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2693: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lncosh}{\folio }{\code {lncosh}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2693 ...[@var{y}, @var{err}] =} lncosh (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2695: Use of \ doesn't match its definition. l.2695 These routines compute \\ log(\\cosh(x)) for any x. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2695: Use of \ doesn't match its definition. l.2695 These routines compute \\log(\\ cosh(x)) for any x. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2699--2701 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2706: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{zeta}{\folio }{\code {zeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2706 ...ble Function} {@var{y} =} zeta (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2707: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{zeta}{\folio }{\code {zeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2707 ... {[@var{y}, @var{err}] =} zeta (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2709: Use of \ doesn't match its definition. l.2709 ...nes compute the Riemann zeta function \\ zeta(s) for If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2710: Use of \ doesn't match its definition. l.2710 arbitrary s, s \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2714: Use of \ doesn't match its definition. l.2714 \\ zeta(s) = \\sum_@{k=1@}^\\infty k^@{-s@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2714: Use of \ doesn't match its definition. l.2714 \\zeta(s) = \\ sum_@{k=1@}^\\infty k^@{-s@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2714: Use of \ doesn't match its definition. l.2714 \\zeta(s) = \\sum_@{k=1@}^\\ infty k^@{-s@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2718--2720 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2725: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{eta}{\folio }{\code {eta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2725 ...able Function} {@var{y} =} eta (@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2726: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{eta}{\folio }{\code {eta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2726 ...} {[@var{y}, @var{err}] =} eta (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2728: Use of \ doesn't match its definition. l.2728 These routines compute the eta function \\ eta(s) for arbitrary s. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [36 \entry{transport_5}{36}{\code {transport_5}} \entry{transport_5}{36}{\code {transport_5}} \entry{sinc_gsl}{36}{\code {sinc_gsl}} \entry{sinc_gsl}{36}{\code {sinc_gsl}} \entry{lnsinh}{36}{\code {lnsinh}} \entry{lnsinh}{36}{\code {lnsinh}} \entry{lncosh}{36}{\code {lncosh}} \entry{lncosh}{36}{\code {lncosh}} \entry{zeta}{36}{\code {zeta}} \entry{zeta}{36}{\code {zeta}} ] ./gsl_sf.texi:2730: Use of \ doesn't match its definition. l.2730 The eta function is defined by \\ eta(s) = (1-2^@{1-s@}) \\zeta(s). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2730: Use of \ doesn't match its definition. l.2730 ...s defined by \\eta(s) = (1-2^@{1-s@}) \\ zeta(s). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2734--2736 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2741: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Jn}{\folio }{\code {bessel_Jn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2741 ...{@var{y} =} bessel_Jn (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2742: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Jn}{\folio }{\code {bessel_Jn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2742 ...ar{y}, @var{err}] =} bessel_Jn (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2749--2751 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2756: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Yn}{\folio }{\code {bessel_Yn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2756 ...{@var{y} =} bessel_Yn (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2757: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Yn}{\folio }{\code {bessel_Yn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2757 ...ar{y}, @var{err}] =} bessel_Yn (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2764--2766 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2771: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_In}{\folio }{\code {bessel_In}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2771 ...{@var{y} =} bessel_In (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2772: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_In}{\folio }{\code {bessel_In}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2772 ...ar{y}, @var{err}] =} bessel_In (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2779--2781 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2786: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_In_scaled}{\folio }{\code {bessel_I... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2786 ...} =} bessel_In_scaled (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2787: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_In_scaled}{\folio }{\code {bessel_I... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2787 ...@var{err}] =} bessel_In_scaled (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2790: Use of \ doesn't match its definition. l.2790 function of order n, \\ exp(-|x|) I_n(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2794--2796 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2801: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Kn}{\folio }{\code {bessel_Kn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2801 ...{@var{y} =} bessel_Kn (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [37 \entry{eta}{37}{\code {eta}} \entry{eta}{37}{\code {eta}} \entry{bessel_Jn}{37}{\code {bessel_Jn}} \entry{bessel_Jn}{37}{\code {bessel_Jn}} \entry{bessel_Yn}{37}{\code {bessel_Yn}} \entry{bessel_Yn}{37}{\code {bessel_Yn}} \entry{bessel_In}{37}{\code {bessel_In}} \entry{bessel_In}{37}{\code {bessel_In}} \entry{bessel_In_scaled}{37}{\code {bessel_In_scaled}} \entry{bessel_In_scaled}{37}{\code {bessel_In_scaled}} ] ./gsl_sf.texi:2802: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Kn}{\folio }{\code {bessel_Kn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2802 ...ar{y}, @var{err}] =} bessel_Kn (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2809--2811 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2816: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Kn_scaled}{\folio }{\code {bessel_K... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2816 ...} =} bessel_Kn_scaled (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2817: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Kn_scaled}{\folio }{\code {bessel_K... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2817 ...@var{err}] =} bessel_Kn_scaled (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2823--2825 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2830: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_jl}{\folio }{\code {bessel_jl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2830 ...{@var{y} =} bessel_jl (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2831: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_jl}{\folio }{\code {bessel_jl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2831 ...ar{y}, @var{err}] =} bessel_jl (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2838--2840 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2845: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_yl}{\folio }{\code {bessel_yl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2845 ...{@var{y} =} bessel_yl (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2846: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_yl}{\folio }{\code {bessel_yl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2846 ...ar{y}, @var{err}] =} bessel_yl (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2853--2855 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2860: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_il_scaled}{\folio }{\code {bessel_i... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2860 ...} =} bessel_il_scaled (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2861: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_il_scaled}{\folio }{\code {bessel_i... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2861 ...@var{err}] =} bessel_il_scaled (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2864: Use of \ doesn't match its definition. l.2864 function of order l, \\ exp(-|x|) i_l(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2868--2870 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2875: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_kl_scaled}{\folio }{\code {bessel_k... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2875 ...} =} bessel_kl_scaled (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2876: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_kl_scaled}{\folio }{\code {bessel_k... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2876 ...@var{err}] =} bessel_kl_scaled (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2879: Use of \ doesn't match its definition. l.2879 function of order l, \\ exp(x) k_l(x), for x>0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [38 \entry{bessel_Kn}{38}{\code {bessel_Kn}} \entry{bessel_Kn}{38}{\code {bessel_Kn}} \entry{bessel_Kn_scaled}{38}{\code {bessel_Kn_scaled}} \entry{bessel_Kn_scaled}{38}{\code {bessel_Kn_scaled}} \entry{bessel_jl}{38}{\code {bessel_jl}} \entry{bessel_jl}{38}{\code {bessel_jl}} \entry{bessel_yl}{38}{\code {bessel_yl}} \entry{bessel_yl}{38}{\code {bessel_yl}} \entry{bessel_il_scaled}{38}{\code {bessel_il_scaled}} \entry{bessel_il_scaled}{38}{\code {bessel_il_scaled}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 2883--2885 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2890: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel_n}{\folio }{\code {exprel_n}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2890 ... {@var{y} =} exprel_n (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2891: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel_n}{\folio }{\code {exprel_n}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2891 ...var{y}, @var{err}] =} exprel_n (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2897: Use of \ doesn't match its definition. l.2897 exprel_N(x) = N!/x^N (\\ exp(x) - \\sum_@{k=0@}^@{N-1@} x^k/k!) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2897: Use of \ doesn't match its definition. l.2897 exprel_N(x) = N!/x^N (\\exp(x) - \\ sum_@{k=0@}^@{N-1@} x^k/k!) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2903--2905 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2910: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_int}{\folio }{\code {fermi_dir... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2910 ...y} =} fermi_dirac_int (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2911: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_int}{\folio }{\code {fermi_dir... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2911 ... @var{err}] =} fermi_dirac_int (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2914: Use of \ doesn't match its definition. l.2914 integer index of j, F_j(x) = (1/\\ Gamma(j+1)) \\int_0^\\infty dt (t^j If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2914: Use of \ doesn't match its definition. l.2914 ...index of j, F_j(x) = (1/\\Gamma(j+1)) \\ int_0^\\infty dt (t^j If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2914: Use of \ doesn't match its definition. l.2914 ... j, F_j(x) = (1/\\Gamma(j+1)) \\int_0^\\ infty dt (t^j If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:2915: Use of \ doesn't match its definition. l.2915 /(\\ exp(t-x)+1)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2919--2921 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2926: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{taylorcoeff}{\folio }{\code {taylorcoeff}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2926 ...var{y} =} taylorcoeff (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2927: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{taylorcoeff}{\folio }{\code {taylorcoeff}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2927 ...{y}, @var{err}] =} taylorcoeff (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2934--2936 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2941: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Pl}{\folio }{\code {legendre_Pl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2941 ...var{y} =} legendre_Pl (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2942: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Pl}{\folio }{\code {legendre_Pl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2942 ...{y}, @var{err}] =} legendre_Pl (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2949--2951 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. [39 \entry{bessel_kl_scaled}{39}{\code {bessel_kl_scaled}} \entry{bessel_kl_scaled}{39}{\code {bessel_kl_scaled}} \entry{exprel_n}{39}{\code {exprel_n}} \entry{exprel_n}{39}{\code {exprel_n}} \entry{fermi_dirac_int}{39}{\code {fermi_dirac_int}} \entry{fermi_dirac_int}{39}{\code {fermi_dirac_int}} \entry{taylorcoeff}{39}{\code {taylorcoeff}} \entry{taylorcoeff}{39}{\code {taylorcoeff}} \entry{legendre_Pl}{39}{\code {legendre_Pl}} \entry{legendre_Pl}{39}{\code {legendre_Pl}} ] ./gsl_sf.texi:2956: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Ql}{\folio }{\code {legendre_Ql}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2956 ...var{y} =} legendre_Ql (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2957: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Ql}{\folio }{\code {legendre_Ql}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2957 ...{y}, @var{err}] =} legendre_Ql (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2964--2966 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2971: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_n}{\folio }{\code {psi_n}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2971 ...on} {@var{y} =} psi_n (@var{n}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2972: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_n}{\folio }{\code {psi_n}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2972 ...{[@var{y}, @var{err}] =} psi_n (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2974: Use of \ doesn't match its definition. l.2974 ...utines compute the polygamma function \\ psi^@{(m)@}(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2979--2981 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:2986: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Jnu}{\folio }{\code {bessel_Jnu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2986 ...@var{z} =} bessel_Jnu (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2987: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Jnu}{\folio }{\code {bessel_Jnu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2987 ...r{z}, @var{err}] =} bessel_Jnu (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:2990: Use of \ doesn't match its definition. l.2990 fractional order nu, J_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2995--2997 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3002: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Ynu}{\folio }{\code {bessel_Ynu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3002 ...@var{z} =} bessel_Ynu (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3003: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Ynu}{\folio }{\code {bessel_Ynu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3003 ...r{z}, @var{err}] =} bessel_Ynu (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3006: Use of \ doesn't match its definition. l.3006 fractional order nu, Y_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3011--3013 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3018: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Inu}{\folio }{\code {bessel_Inu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3018 ...@var{z} =} bessel_Inu (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3019: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Inu}{\folio }{\code {bessel_Inu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3019 ...r{z}, @var{err}] =} bessel_Inu (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3022: Use of \ doesn't match its definition. l.3022 fractional order nu, I_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3023: Use of \ doesn't match its definition. l.3023 u(x) for x>0, \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3028--3030 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. [40 \entry{legendre_Ql}{40}{\code {legendre_Ql}} \entry{legendre_Ql}{40}{\code {legendre_Ql}} \entry{psi_n}{40}{\code {psi_n}} \entry{psi_n}{40}{\code {psi_n}} \entry{bessel_Jnu}{40}{\code {bessel_Jnu}} \entry{bessel_Jnu}{40}{\code {bessel_Jnu}} \entry{bessel_Ynu}{40}{\code {bessel_Ynu}} \entry{bessel_Ynu}{40}{\code {bessel_Ynu}} \entry{bessel_Inu}{40}{\code {bessel_Inu}} \entry{bessel_Inu}{40}{\code {bessel_Inu}} ] ./gsl_sf.texi:3035: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Inu_scaled}{\folio }{\code {bessel_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3035 ... =} bessel_Inu_scaled (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3036: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Inu_scaled}{\folio }{\code {bessel_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3036 ...var{err}] =} bessel_Inu_scaled (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3039: Use of \ doesn't match its definition. l.3039 fractional order nu, \\ exp(-|x|)I_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3039: Use of \ doesn't match its definition. l.3039 fractional order nu, \\exp(-|x|)I_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3040: Use of \ doesn't match its definition. l.3040 u(x) for x>0, \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3045--3047 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3052: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Knu}{\folio }{\code {bessel_Knu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3052 ...@var{z} =} bessel_Knu (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3053: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Knu}{\folio }{\code {bessel_Knu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3053 ...r{z}, @var{err}] =} bessel_Knu (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3056: Use of \ doesn't match its definition. l.3056 fractional order nu, K_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3057: Use of \ doesn't match its definition. l.3057 u(x) for x>0, \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3062--3064 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3069: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_lnKnu}{\folio }{\code {bessel_lnKnu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3069 ...ar{z} =} bessel_lnKnu (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3070: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_lnKnu}{\folio }{\code {bessel_lnKnu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3070 ...z}, @var{err}] =} bessel_lnKnu (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3073: Use of \ doesn't match its definition. l.3073 function of fractional order nu, \\ ln(K_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3073: Use of \ doesn't match its definition. l.3073 function of fractional order nu, \\ln(K_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3074: Use of \ doesn't match its definition. l.3074 u(x)) for x>0, \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3079--3081 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3086: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Knu_scaled}{\folio }{\code {bessel_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3086 ... =} bessel_Knu_scaled (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3087: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Knu_scaled}{\folio }{\code {bessel_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3087 ...var{err}] =} bessel_Knu_scaled (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3090: Use of \ doesn't match its definition. l.3090 of fractional order nu, \\ exp(+|x|) K_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3090: Use of \ doesn't match its definition. l.3090 of fractional order nu, \\exp(+|x|) K_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3091: Use of \ doesn't match its definition. l.3091 u(x) for x>0, \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3096--3098 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3103: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exp_mult}{\folio }{\code {exp_mult}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3103 ... {@var{z} =} exp_mult (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3104: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exp_mult}{\folio }{\code {exp_mult}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3104 ...var{z}, @var{err}] =} exp_mult (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3107: Use of \ doesn't match its definition. l.3107 the product y \\ exp(x). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [41 \entry{bessel_Inu_scaled}{41}{\code {bessel_Inu_scaled}} \entry{bessel_Inu_scaled}{41}{\code {bessel_Inu_scaled}} \entry{bessel_Knu}{41}{\code {bessel_Knu}} \entry{bessel_Knu}{41}{\code {bessel_Knu}} \entry{bessel_lnKnu}{41}{\code {bessel_lnKnu}} \entry{bessel_lnKnu}{41}{\code {bessel_lnKnu}} \entry{bessel_Knu_scaled}{41}{\code {bessel_Knu_scaled}} \entry{bessel_Knu_scaled}{41}{\code {bessel_Knu_scaled}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 3111--3113 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3118: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_inc_0}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3118 ... =} fermi_dirac_inc_0 (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3119: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_inc_0}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3119 ...var{err}] =} fermi_dirac_inc_0 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3122: Use of \ doesn't match its definition. l.3122 index of zero, F_0(x,b) = \\ ln(1 + e^@{b-x@}) - (b-x). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3126--3128 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3133: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{poch}{\folio }{\code {poch}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3133 ...ion} {@var{z} =} poch (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3134: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{poch}{\folio }{\code {poch}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3134 ... {[@var{z}, @var{err}] =} poch (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3138: Use of \ doesn't match its definition. l.3138 (a)_x := \\ Gamma(a + x)/\\Gamma(a), If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3138: Use of \ doesn't match its definition. l.3138 (a)_x := \\Gamma(a + x)/\\ Gamma(a), If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3145--3147 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3152: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnpoch}{\folio }{\code {lnpoch}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3152 ...n} {@var{z} =} lnpoch (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3153: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnpoch}{\folio }{\code {lnpoch}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3153 ...[@var{z}, @var{err}] =} lnpoch (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3156: Use of \ doesn't match its definition. l.3156 \\ log((a)_x) = \\log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3156: Use of \ doesn't match its definition. l.3156 \\log((a)_x) = \\ log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3156: Use of \ doesn't match its definition. l.3156 \\log((a)_x) = \\log(\\ Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3156: Use of \ doesn't match its definition. l.3156 \\log((a)_x) = \\log(\\Gamma(a + x)/\\ Gamma(a)) for a > 0, a+x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3160--3162 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3167: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{pochrel}{\folio }{\code {pochrel}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3167 ...} {@var{z} =} pochrel (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3168: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{pochrel}{\folio }{\code {pochrel}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3168 ...@var{z}, @var{err}] =} pochrel (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3171: Use of \ doesn't match its definition. l.3171 where (a,x) = (a)_x := \\ Gamma(a + x)/\\Gamma(a). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3171: Use of \ doesn't match its definition. l.3171 where (a,x) = (a)_x := \\Gamma(a + x)/\\ Gamma(a). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3175--3177 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. [42 \entry{exp_mult}{42}{\code {exp_mult}} \entry{exp_mult}{42}{\code {exp_mult}} \entry{fermi_dirac_inc_0}{42}{\code {fermi_dirac_inc_0}} \entry{fermi_dirac_inc_0}{42}{\code {fermi_dirac_inc_0}} \entry{poch}{42}{\code {poch}} \entry{poch}{42}{\code {poch}} \entry{lnpoch}{42}{\code {lnpoch}} \entry{lnpoch}{42}{\code {lnpoch}} \entry{pochrel}{42}{\code {pochrel}} \entry{pochrel}{42}{\code {pochrel}} ] ./gsl_sf.texi:3182: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc_Q}{\folio }{\code {gamma_inc_Q}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3182 ...var{z} =} gamma_inc_Q (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3183: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc_Q}{\folio }{\code {gamma_inc_Q}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3183 ...{z}, @var{err}] =} gamma_inc_Q (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3186: Use of \ doesn't match its definition. l.3186 Q(a,x) = 1/\\ Gamma(a) \\int_x\\infty dt t^@{a-1@} \\exp(-t) for a > 0... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3186: Use of \ doesn't match its definition. l.3186 Q(a,x) = 1/\\Gamma(a) \\ int_x\\infty dt t^@{a-1@} \\exp(-t) for a > 0... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3186: Use of \ doesn't match its definition. l.3186 Q(a,x) = 1/\\Gamma(a) \\int_x\\ infty dt t^@{a-1@} \\exp(-t) for a > 0... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3186: Use of \ doesn't match its definition. l.3186 ...\Gamma(a) \\int_x\\infty dt t^@{a-1@} \\ exp(-t) for a > 0, x >= 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3190--3192 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3197: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc_P}{\folio }{\code {gamma_inc_P}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3197 ...var{z} =} gamma_inc_P (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3198: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc_P}{\folio }{\code {gamma_inc_P}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3198 ...{z}, @var{err}] =} gamma_inc_P (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3201: Use of \ doesn't match its definition. l.3201 Function P(a,x) = 1/\\ Gamma(a) \\int_0^x dt t^@{a-1@} \\exp(-t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3201: Use of \ doesn't match its definition. l.3201 Function P(a,x) = 1/\\Gamma(a) \\ int_0^x dt t^@{a-1@} \\exp(-t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3201: Use of \ doesn't match its definition. l.3201 ...= 1/\\Gamma(a) \\int_0^x dt t^@{a-1@} \\ exp(-t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3206--3208 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3213: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc}{\folio }{\code {gamma_inc}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3213 ...{@var{z} =} gamma_inc (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3214: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc}{\folio }{\code {gamma_inc}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3214 ...ar{z}, @var{err}] =} gamma_inc (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3218: Use of \ doesn't match its definition. l.3218 \\ Gamma(a,x) = \\int_x\\infty dt t^@{a-1@} \\exp(-t) for a real and x... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3218: Use of \ doesn't match its definition. l.3218 \\Gamma(a,x) = \\ int_x\\infty dt t^@{a-1@} \\exp(-t) for a real and x... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3218: Use of \ doesn't match its definition. l.3218 \\Gamma(a,x) = \\int_x\\ infty dt t^@{a-1@} \\exp(-t) for a real and x... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3218: Use of \ doesn't match its definition. l.3218 ...ma(a,x) = \\int_x\\infty dt t^@{a-1@} \\ exp(-t) for a real and x >... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3222--3224 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3229: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{beta_gsl}{\folio }{\code {beta_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3229 ... {@var{z} =} beta_gsl (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3230: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{beta_gsl}{\folio }{\code {beta_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3230 ...var{z}, @var{err}] =} beta_gsl (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3233: Use of \ doesn't match its definition. l.3233 B(a,b) = \\ Gamma(a)\\Gamma(b)/\\Gamma(a+b) for a > 0, b > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3233: Use of \ doesn't match its definition. l.3233 B(a,b) = \\Gamma(a)\\ Gamma(b)/\\Gamma(a+b) for a > 0, b > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3233: Use of \ doesn't match its definition. l.3233 B(a,b) = \\Gamma(a)\\Gamma(b)/\\ Gamma(a+b) for a > 0, b > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (20.37637pt too wide) in paragraph at lines 3232--3234 []@textrm These rou-tines com-pute the Beta Func-tion, B(a,b) = Gamma(a)Gamma( b)/Gamma(a+b)| @hbox(8.2125+2.73749)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm e .etc. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3237--3239 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3244: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnbeta}{\folio }{\code {lnbeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3244 ...n} {@var{z} =} lnbeta (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3245: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnbeta}{\folio }{\code {lnbeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3245 ...[@var{z}, @var{err}] =} lnbeta (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3248: Use of \ doesn't match its definition. l.3248 \\ log(B(a,b)) for a > 0, b > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3252--3254 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. [43 \entry{gamma_inc_Q}{43}{\code {gamma_inc_Q}} \entry{gamma_inc_Q}{43}{\code {gamma_inc_Q}} \entry{gamma_inc_P}{43}{\code {gamma_inc_P}} \entry{gamma_inc_P}{43}{\code {gamma_inc_P}} \entry{gamma_inc}{43}{\code {gamma_inc}} \entry{gamma_inc}{43}{\code {gamma_inc}} \entry{beta_gsl}{43}{\code {beta_gsl}} \entry{beta_gsl}{43}{\code {beta_gsl}} \entry{lnbeta}{43}{\code {lnbeta}} \entry{lnbeta}{43}{\code {lnbeta}} ] ./gsl_sf.texi:3259: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_0F1}{\folio }{\code {hyperg_0F1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3259 ...@var{z} =} hyperg_0F1 (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3260: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_0F1}{\folio }{\code {hyperg_0F1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3260 ...r{z}, @var{err}] =} hyperg_0F1 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3266--3268 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3273: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_half}{\folio }{\code {conicalP_ha... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3273 ...r{z} =} conicalP_half (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3274: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_half}{\folio }{\code {conicalP_ha... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3274 ...}, @var{err}] =} conicalP_half (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3277: Use of \ doesn't match its definition. l.3277 P^@{1/2@}_@{-1/2 + i \\ lambda@}(x) for x > -1. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3281--3283 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3288: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_mhalf}{\folio }{\code {conicalP_m... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3288 ...{z} =} conicalP_mhalf (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3289: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_mhalf}{\folio }{\code {conicalP_m... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3289 ..., @var{err}] =} conicalP_mhalf (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3292: Use of \ doesn't match its definition. l.3292 P^@{-1/2@}_@{-1/2 + i \\ lambda@}(x) for x > -1. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3296--3298 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3303: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_0}{\folio }{\code {conicalP_0}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3303 ...@var{z} =} conicalP_0 (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3304: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_0}{\folio }{\code {conicalP_0}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3304 ...r{z}, @var{err}] =} conicalP_0 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3306: Use of \ doesn't match its definition. l.3306 ...e the conical function P^0_@{-1/2 + i \\ lambda@}(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3311--3313 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3318: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_1}{\folio }{\code {conicalP_1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3318 ...@var{z} =} conicalP_1 (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3319: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_1}{\folio }{\code {conicalP_1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3319 ...r{z}, @var{err}] =} conicalP_1 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3321: Use of \ doesn't match its definition. l.3321 ...e the conical function P^1_@{-1/2 + i \\ lambda@}(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3326--3328 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3333: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hzeta}{\folio }{\code {hzeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3333 ...on} {@var{z} =} hzeta (@var{x}, @var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3334: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hzeta}{\folio }{\code {hzeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3334 ...{[@var{z}, @var{err}] =} hzeta (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3336: Use of \ doesn't match its definition. l.3336 ...nes compute the Hurwitz zeta function \\ zeta(s,q) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [44 \entry{hyperg_0F1}{44}{\code {hyperg_0F1}} \entry{hyperg_0F1}{44}{\code {hyperg_0F1}} \entry{conicalP_half}{44}{\code {conicalP_half}} \entry{conicalP_half}{44}{\code {conicalP_half}} \entry{conicalP_mhalf}{44}{\code {conicalP_mhalf}} \entry{conicalP_mhalf}{44}{\code {conicalP_mhalf}} \entry{conicalP_0}{44}{\code {conicalP_0}} \entry{conicalP_0}{44}{\code {conicalP_0}} \entry{conicalP_1}{44}{\code {conicalP_1}} \entry{conicalP_1}{44}{\code {conicalP_1}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 3341--3343 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3348: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai}{\folio }{\code {airy_Ai}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3348 ...@var{y} =} airy_Ai (@var{x}, @var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3349: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai}{\folio }{\code {airy_Ai}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3349 ...@var{y}, @var{err}] =} airy_Ai (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3367--3369 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3374: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi}{\folio }{\code {airy_Bi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3374 ...@var{y} =} airy_Bi (@var{x}, @var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3375: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi}{\folio }{\code {airy_Bi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3375 ...@var{y}, @var{err}] =} airy_Bi (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3393--3395 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3400: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_scaled}{\folio }{\code {airy_Ai_sc... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3400 ... =} airy_Ai_scaled (@var{x}, @var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3401: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_scaled}{\folio }{\code {airy_Ai_sc... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3401 ..., @var{err}] =} airy_Ai_scaled (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3404: Use of \ doesn't match its definition. l.3404 ... For x>0 the scaling factor S_A(x) is \\ exp(+(2/3) x^(3/2)), and If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [45 \entry{hzeta}{45}{\code {hzeta}} \entry{hzeta}{45}{\code {hzeta}} \entry{airy_Ai}{45}{\code {airy_Ai}} \entry{airy_Ai}{45}{\code {airy_Ai}} \entry{airy_Bi}{45}{\code {airy_Bi}} \entry{airy_Bi}{45}{\code {airy_Bi}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 3420--3422 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3427: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_scaled}{\folio }{\code {airy_Bi_sc... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3427 ... =} airy_Bi_scaled (@var{x}, @var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3428: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_scaled}{\folio }{\code {airy_Bi_sc... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3428 ..., @var{err}] =} airy_Bi_scaled (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3447--3449 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3454: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_deriv}{\folio }{\code {airy_Ai_der... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3454 ...} =} airy_Ai_deriv (@var{x}, @var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3455: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_deriv}{\folio }{\code {airy_Ai_der... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3455 ...}, @var{err}] =} airy_Ai_deriv (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [46 \entry{airy_Ai_scaled}{46}{\code {airy_Ai_scaled}} \entry{airy_Ai_scaled}{46}{\code {airy_Ai_scaled}} \entry{airy_Bi_scaled}{46}{\code {airy_Bi_scaled}} \entry{airy_Bi_scaled}{46}{\code {airy_Bi_scaled}} \entry{airy_Ai_deriv}{46}{\code {airy_Ai_deriv}} \entry{airy_Ai_deriv}{46}{\code {airy_Ai_deriv}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 3473--3475 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3480: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_deriv}{\folio }{\code {airy_Bi_der... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3480 ...} =} airy_Bi_deriv (@var{x}, @var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3481: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_deriv}{\folio }{\code {airy_Bi_der... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3481 ...}, @var{err}] =} airy_Bi_deriv (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3499--3501 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3506: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_deriv_scaled}{\folio }{\code {airy... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3506 ...ry_Ai_deriv_scaled (@var{x}, @var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3507: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_deriv_scaled}{\folio }{\code {airy... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3507 ...{err}] =} airy_Ai_deriv_scaled (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3525--3527 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3532: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_deriv_scaled}{\folio }{\code {airy... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3532 ...ry_Bi_deriv_scaled (@var{x}, @var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3533: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_deriv_scaled}{\folio }{\code {airy... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3533 ...{err}] =} airy_Bi_deriv_scaled (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [47 \entry{airy_Bi_deriv}{47}{\code {airy_Bi_deriv}} \entry{airy_Bi_deriv}{47}{\code {airy_Bi_deriv}} \entry{airy_Ai_deriv_scaled}{47}{\code {airy_Ai_deriv_scaled}} \entry{airy_Ai_deriv_scaled}{47}{\code {airy_Ai_deriv_scaled}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 3551--3553 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3558: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{ellint_Kcomp}{\folio }{\code {ellint_Kcomp}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3558 ...y} =} ellint_Kcomp (@var{x}, @var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3559: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{ellint_Kcomp}{\folio }{\code {ellint_Kcomp}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3559 ...y}, @var{err}] =} ellint_Kcomp (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3563: Undefined control sequence. l.3563 \beforedisplay The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ./gsl_sf.texi:3569: Undefined control sequence. l.3569 \afterdisplay The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3591--3593 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3598: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{ellint_Ecomp}{\folio }{\code {ellint_Ecomp}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3598 ...y} =} ellint_Ecomp (@var{x}, @var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3599: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{ellint_Ecomp}{\folio }{\code {ellint_Ecomp}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3599 ...y}, @var{err}] =} ellint_Ecomp (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3605: Undefined control sequence. l.3605 \beforedisplay The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ./gsl_sf.texi:3611: Undefined control sequence. l.3611 \afterdisplay The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. [48 \entry{airy_Bi_deriv_scaled}{48}{\code {airy_Bi_deriv_scaled}} \entry{airy_Bi_deriv_scaled}{48}{\code {airy_Bi_deriv_scaled}} \entry{ellint_Kcomp}{48}{\code {ellint_Kcomp}} \entry{ellint_Kcomp}{48}{\code {ellint_Kcomp}} \entry{ellint_Ecomp}{48}{\code {ellint_Ecomp}} \entry{ellint_Ecomp}{48}{\code {ellint_Ecomp}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 3633--3635 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3640: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Ai}{\folio }{\code {airy_zero_Ai}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3640 ...tion} {@var{y} =} airy_zero_Ai (@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3641: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Ai}{\folio }{\code {airy_zero_Ai}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3641 ...y}, @var{err}] =} airy_zero_Ai (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3648--3650 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3655: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Bi}{\folio }{\code {airy_zero_Bi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3655 ...tion} {@var{y} =} airy_zero_Bi (@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3656: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Bi}{\folio }{\code {airy_zero_Bi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3656 ...y}, @var{err}] =} airy_zero_Bi (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3663--3665 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3670: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Ai_deriv}{\folio }{\code {airy_z... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3670 ...{@var{y} =} airy_zero_Ai_deriv (@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3671: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Ai_deriv}{\folio }{\code {airy_z... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3671 ...ar{err}] =} airy_zero_Ai_deriv (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3678--3680 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3685: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Bi_deriv}{\folio }{\code {airy_z... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3685 ...{@var{y} =} airy_zero_Bi_deriv (@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3686: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Bi_deriv}{\folio }{\code {airy_z... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3686 ...ar{err}] =} airy_zero_Bi_deriv (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [49 \entry{airy_zero_Ai}{49}{\code {airy_zero_Ai}} \entry{airy_zero_Ai}{49}{\code {airy_zero_Ai}} \entry{airy_zero_Bi}{49}{\code {airy_zero_Bi}} \entry{airy_zero_Bi}{49}{\code {airy_zero_Bi}} \entry{airy_zero_Ai_deriv}{49}{\code {airy_zero_Ai_deriv}} \entry{airy_zero_Ai_deriv}{49}{\code {airy_zero_Ai_deriv}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 3693--3695 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3700: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_zero_J0}{\folio }{\code {bessel_zer... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3700 ...on} {@var{y} =} bessel_zero_J0 (@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3701: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_zero_J0}{\folio }{\code {bessel_zer... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3701 ..., @var{err}] =} bessel_zero_J0 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3708--3710 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3715: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_zero_J1}{\folio }{\code {bessel_zer... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3715 ...on} {@var{y} =} bessel_zero_J1 (@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3716: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_zero_J1}{\folio }{\code {bessel_zer... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3716 ..., @var{err}] =} bessel_zero_J1 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3723--3725 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3730: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_1_int}{\folio }{\code {psi_1_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3730 ...unction} {@var{y} =} psi_1_int (@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3731: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_1_int}{\folio }{\code {psi_1_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3731 ...ar{y}, @var{err}] =} psi_1_int (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3733: Use of \ doesn't match its definition. l.3733 ...outines compute the Trigamma function \\ psi(n) for positive If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3738--3740 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3745: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{zeta_int}{\folio }{\code {zeta_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3745 ...Function} {@var{y} =} zeta_int (@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3746: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{zeta_int}{\folio }{\code {zeta_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3746 ...var{y}, @var{err}] =} zeta_int (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3748: Use of \ doesn't match its definition. l.3748 ...nes compute the Riemann zeta function \\ zeta(n) for If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3749: Use of \ doesn't match its definition. l.3749 integer n, n \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3754--3756 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3761: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{eta_int}{\folio }{\code {eta_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3761 ... Function} {@var{y} =} eta_int (@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3762: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{eta_int}{\folio }{\code {eta_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3762 ...@var{y}, @var{err}] =} eta_int (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3764: Use of \ doesn't match its definition. l.3764 These routines compute the eta function \\ eta(n) for integer n. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [50 \entry{airy_zero_Bi_deriv}{50}{\code {airy_zero_Bi_deriv}} \entry{airy_zero_Bi_deriv}{50}{\code {airy_zero_Bi_deriv}} \entry{bessel_zero_J0}{50}{\code {bessel_zero_J0}} \entry{bessel_zero_J0}{50}{\code {bessel_zero_J0}} \entry{bessel_zero_J1}{50}{\code {bessel_zero_J1}} \entry{bessel_zero_J1}{50}{\code {bessel_zero_J1}} \entry{psi_1_int}{50}{\code {psi_1_int}} \entry{psi_1_int}{50}{\code {psi_1_int}} \entry{zeta_int}{50}{\code {zeta_int}} \entry{zeta_int}{50}{\code {zeta_int}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 3768--3770 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3775: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Plm}{\folio }{\code {legendre_Plm}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3775 ...legendre_Plm (@var{n}, @var{m}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3776: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Plm}{\folio }{\code {legendre_Plm}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3776 ...y}, @var{err}] =} legendre_Plm (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3783--3785 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3790: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_sphPlm}{\folio }{\code {legendre_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3790 ...endre_sphPlm (@var{n}, @var{m}, @var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3791: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_sphPlm}{\folio }{\code {legendre_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3791 ... @var{err}] =} legendre_sphPlm (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3794: Use of \ doesn't match its definition. l.3794 $\\ sqrt@{(2l+1)/(4\\pi)@} \\sqrt@{(l-m)!/(l+m)!@} P_l^m(x)$ suitable ... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3794: Use of \ doesn't match its definition. l.3794 $\\sqrt@{(2l+1)/(4\\ pi)@} \\sqrt@{(l-m)!/(l+m)!@} P_l^m(x)$ suitable ... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl_sf.texi:3794: Use of \ doesn't match its definition. l.3794 $\\sqrt@{(2l+1)/(4\\pi)@} \\ sqrt@{(l-m)!/(l+m)!@} P_l^m(x)$ suitable ... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Underfull \hbox (badness 10000) in paragraph at lines 3793--3798 []@textrm These rou-tines com-pute the nor-mal-ized as-so-ci-ated Leg-en-dre p oly-no-mial @hbox(7.60416+2.12917)x433.62, glue set 4.66573 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm e .etc. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3801--3803 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3808: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_U}{\folio }{\code {hyperg_U}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3808 ... hyperg_U (@var{x0}, @var{x1}, @var{x2}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3809: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_U}{\folio }{\code {hyperg_U}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3809 ...r{out}, @var{err}] =} hyperg_U (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3816--3818 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. ./gsl_sf.texi:3823: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_1F1}{\folio }{\code {hyperg_1F1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3823 ...yperg_1F1 (@var{x0}, @var{x1}, @var{x2}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl_sf.texi:3824: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_1F1}{\folio }{\code {hyperg_1F1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3824 ...out}, @var{err}] =} hyperg_1F1 (@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3831--3833 []@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@textt t http://www.gnu.org/software/gsl/[][][]| @hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@glue(@leftskip) 28.90755 .@hbox(0.0+0.0)x0.0 .@textrm T .@textrm h .@textrm i .etc. [51 \entry{eta_int}{51}{\code {eta_int}} \entry{eta_int}{51}{\code {eta_int}} \entry{legendre_Plm}{51}{\code {legendre_Plm}} \entry{legendre_Plm}{51}{\code {legendre_Plm}} \entry{legendre_sphPlm}{51}{\code {legendre_sphPlm}} \entry{legendre_sphPlm}{51}{\code {legendre_sphPlm}} \entry{hyperg_U}{51}{\code {hyperg_U}} \entry{hyperg_U}{51}{\code {hyperg_U}} \entry{hyperg_1F1}{51}{\code {hyperg_1F1}} \entry{hyperg_1F1}{51}{\code {hyperg_1F1}} ] ) Here is how much of TeX's memory you used: 1576 strings out of 97341 16810 string characters out of 1211892 39971 words of memory out of 1000000 2682 multiletter control sequences out of 10000+50000 32127 words of font info for 112 fonts, out of 500000 for 2000 51 hyphenation exceptions out of 1000 12i,9n,16p,238b,419s stack positions out of 1500i,500n,5000p,200000b,5000s PDF statistics: 412 PDF objects out of 300000 0 named destinations out of 131072 1 words of extra memory for PDF output out of 65536 Output written on gsl_sf.pdf (51 pages, 207615 bytes). gsl-1.0.8/doc/DOSCSTRINGS.old0000755000175000017500000016534711201030403013165 0ustar shshgsl_sf -*- texinfo -*- @deftypefn {Loadable Function} {} gsl_sf () Octave bindings to the GNU Scientific Library. All GSL functions can be called with by the GSL names within octave. @end deftypefn clausen -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} clausen (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} clausen (@dots{}) The Clausen function is defined by the following integral, Cl_2(x) = - \\int_0^x dt \\log(2 \\sin(t/2)) It is related to the dilogarithm by Cl_2(\\theta) = \\Im Li_2(\\exp(i \\theta)). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn dawson -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} dawson (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} dawson (@dots{}) The Dawson integral is defined by \\exp(-x^2) \\int_0^x dt \\exp(t^2). A table of Dawson integral can be found in Abramowitz & Stegun, Table 7.5. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn debye_1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} debye_1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_1 (@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn debye_2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} debye_2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_2 (@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn debye_3 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} debye_3 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_3 (@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn debye_4 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} debye_4 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_4 (@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn erf_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} erf_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erf_gsl (@dots{}) These routines compute the error function erf(x) = (2/\\sqrt(\\pi)) \\int_0^x dt \\exp(-t^2). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn erfc_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} erfc_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erfc_gsl (@dots{}) These routines compute the complementary error function erfc(x) = 1 - erf(x) = (2/\\sqrt(\\pi)) \\int_x^\\infty \\exp(-t^2). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn log_erfc -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} log_erfc (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} log_erfc (@dots{}) These routines compute the logarithm of the complementary error function \\log(\\erfc(x)). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn erf_Z -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} erf_Z (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erf_Z (@dots{}) These routines compute the Gaussian probability function Z(x) = (1/(2\\pi)) \\exp(-x^2/2). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn erf_Q -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} erf_Q (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erf_Q (@dots{}) These routines compute the upper tail of the Gaussian probability function Q(x) = (1/(2\\pi)) \\int_x^\\infty dt \\exp(-t^2/2). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hazard -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} hazard (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} hazard (@dots{}) The hazard function for the normal distrbution, also known as the inverse Mill\\'s ratio, is defined as h(x) = Z(x)/Q(x) = \\sqrt@{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2)@}. It decreases rapidly as x approaches -\\infty and asymptotes to h(x) \\sim x as x approaches +\\infty. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn expm1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} expm1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expm1 (@dots{}) These routines compute the quantity \\exp(x)-1 using an algorithm that is accurate for small x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn exprel -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} exprel (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} exprel (@dots{}) These routines compute the quantity (\\exp(x)-1)/x using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion (\\exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\dots. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn exprel_2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} exprel_2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} exprel_2 (@dots{}) These routines compute the quantity 2(\\exp(x)-1-x)/x^2 using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion 2(\\exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\dots. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn expint_E1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} expint_E1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_E1 (@dots{}) These routines compute the exponential integral E_1(x), E_1(x) := Re \\int_1^\\infty dt \\exp(-xt)/t. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn expint_E2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} expint_E2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_E2 (@dots{}) These routines compute the second-order exponential integral E_2(x), E_2(x) := \\Re \\int_1^\\infty dt \\exp(-xt)/t^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn expint_Ei -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} expint_Ei (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_Ei (@dots{}) These routines compute the exponential integral E_i(x), Ei(x) := - PV(\\int_@{-x@}^\\infty dt \\exp(-t)/t) where PV denotes the principal value of the integral. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn Shi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} Shi (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Shi (@dots{}) These routines compute the integral Shi(x) = \\int_0^x dt \\sinh(t)/t. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn Chi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} Chi (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Chi (@dots{}) These routines compute the integral Chi(x) := Re[ \\gamma_E + \\log(x) + \\int_0^x dt (\\cosh[t]-1)/t] , where \\gamma_E is the Euler constant. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn expint_3 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} expint_3 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_3 (@dots{}) These routines compute the exponential integral Ei_3(x) = \\int_0^x dt \\exp(-t^3) for x >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn Si -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} Si (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Si (@dots{}) These routines compute the Sine integral Si(x) = \\int_0^x dt \\sin(t)/t. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn Ci -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} Ci (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Ci (@dots{}) These routines compute the Cosine integral Ci(x) = -\\int_x^\\infty dt \\cos(t)/t for x > 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn atanint -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} atanint (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} atanint (@dots{}) These routines compute the Arctangent integral AtanInt(x) = \\int_0^x dt \\arctan(t)/t. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_mhalf -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_mhalf (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_mhalf (@dots{}) These routines compute the complete Fermi-Dirac integral F_@{-1/2@}(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_half -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_half (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_half (@dots{}) These routines compute the complete Fermi-Dirac integral F_@{1/2@}(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_3half -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_3half (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_3half (@dots{}) These routines compute the complete Fermi-Dirac integral F_@{3/2@}(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gamma_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} gamma_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} gamma_gsl (@dots{}) These routines compute the Gamma function \\Gamma(x), subject to x not being a negative integer. The function is computed using the real Lanczos method. The maximum value of x such that \\Gamma(x) is not considered an overflow is given by the macro GSL_SF_GAMMA_XMAX and is 171.0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lngamma_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lngamma_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lngamma_gsl (@dots{}) These routines compute the logarithm of the Gamma function, \\log(\\Gamma(x)), subject to x not a being negative integer. For x<0 the real part of \\log(\\Gamma(x)) is returned, which is equivalent to \\log(|\\Gamma(x)|). The function is computed using the real Lanczos method. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gammastar -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} gammastar (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} gammastar (@dots{}) These routines compute the regulated Gamma Function \\Gamma^*(x) for x > 0. The regulated gamma function is given by, \\Gamma^*(x) = \\Gamma(x)/(\\sqrt@{2\\pi@} x^@{(x-1/2)@} \\exp(-x)) = (1 + (1/12x) + ...) for x \\to \\infty and is a useful suggestion of Temme. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gammainv_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} gammainv_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} gammainv_gsl (@dots{}) These routines compute the reciprocal of the gamma function, 1/\\Gamma(x) using the real Lanczos method. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lambert_W0 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lambert_W0 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lambert_W0 (@dots{}) These compute the principal branch of the Lambert W function, W_0(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@{-1@}(x) to be the other real branch, where W < -1 for x < 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lambert_Wm1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lambert_Wm1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lambert_Wm1 (@dots{}) These compute the secondary real-valued branch of the Lambert W function, W_@{-1@}(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@{-1@}(x) to be the other real branch, where W < -1 for x < 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn log_1plusx -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} log_1plusx (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} log_1plusx (@dots{}) These routines compute \\log(1 + x) for x > -1 using an algorithm that is accurate for small x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn log_1plusx_mx -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} log_1plusx_mx (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} log_1plusx_mx (@dots{}) These routines compute \\log(1 + x) - x for x > -1 using an algorithm that is accurate for small x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn psi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} psi (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi (@dots{}) These routines compute the digamma function \\psi(x) for general x, x \ e 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn psi_1piy -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} psi_1piy (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi_1piy (@dots{}) These routines compute the real part of the digamma function on the line 1+i y, Re[\\psi(1 + i y)]. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn synchrotron_1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} synchrotron_1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} synchrotron_1 (@dots{}) These routines compute the first synchrotron function x \\int_x^\\infty dt K_@{5/3@}(t) for x >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn synchrotron_2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} synchrotron_2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} synchrotron_2 (@dots{}) These routines compute the second synchrotron function x K_@{2/3@}(x) for x >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn transport_2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} transport_2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_2 (@dots{}) These routines compute the transport function J(2,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn transport_3 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} transport_3 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_3 (@dots{}) These routines compute the transport function J(3,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn transport_4 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} transport_4 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_4 (@dots{}) These routines compute the transport function J(4,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn transport_5 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} transport_5 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_5 (@dots{}) These routines compute the transport function J(5,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn sinc_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} sinc_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} sinc_gsl (@dots{}) These routines compute \\sinc(x) = \\sin(\\pi x) / (\\pi x) for any value of x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lnsinh -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lnsinh (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lnsinh (@dots{}) These routines compute \\log(\\sinh(x)) for x > 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lncosh -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lncosh (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lncosh (@dots{}) These routines compute \\log(\\cosh(x)) for any x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn zeta -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} zeta (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} zeta (@dots{}) These routines compute the Riemann zeta function \\zeta(s) for arbitrary s, s \ e 1. The Riemann zeta function is defined by the infinite sum \\zeta(s) = \\sum_@{k=1@}^\\infty k^@{-s@}. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn eta -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} eta (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} eta (@dots{}) These routines compute the eta function \\eta(s) for arbitrary s. The eta function is defined by \\eta(s) = (1-2^@{1-s@}) \\zeta(s). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Jn -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_Jn (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Jn (@dots{}) These routines compute the regular cylindrical Bessel function of order n, J_n(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Yn -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_Yn (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Yn (@dots{}) These routines compute the irregular cylindrical Bessel function of order n, Y_n(x), for x>0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_In -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_In (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_In (@dots{}) These routines compute the regular modified cylindrical Bessel function of order n, I_n(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_In_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_In_scaled (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_In_scaled (@dots{}) These routines compute the scaled regular modified cylindrical Bessel function of order n, \\exp(-|x|) I_n(x) @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Kn -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_Kn (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Kn (@dots{}) These routines compute the irregular modified cylindrical Bessel function of order n, K_n(x), for x > 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Kn_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_Kn_scaled (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Kn_scaled (@dots{}) @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_jl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_jl (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_jl (@dots{}) These routines compute the regular spherical Bessel function of order l, j_l(x), for l >= 0 and x >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_yl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_yl (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_yl (@dots{}) These routines compute the irregular spherical Bessel function of order l, y_l(x), for l >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_il_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_il_scaled (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_il_scaled (@dots{}) These routines compute the scaled regular modified spherical Bessel function of order l, \\exp(-|x|) i_l(x) @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_kl_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_kl_scaled (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_kl_scaled (@dots{}) These routines compute the scaled irregular modified spherical Bessel function of order l, \\exp(x) k_l(x), for x>0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn exprel_n -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} exprel_n (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} exprel_n (@dots{}) These routines compute the N-relative exponential, which is the n-th generalization of the functions gsl_sf_exprel and gsl_sf_exprel2. The N-relative exponential is given by, exprel_N(x) = N!/x^N (\\exp(x) - \\sum_@{k=0@}^@{N-1@} x^k/k!) = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ... = 1F1 (1,1+N,x) @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_int -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_int (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_int (@dots{}) These routines compute the complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/\\Gamma(j+1)) \\int_0^\\infty dt (t^j /(\\exp(t-x)+1)). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn taylorcoeff -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} taylorcoeff (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} taylorcoeff (@dots{}) These routines compute the Taylor coefficient x^n / n! for x >= 0, n >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn legendre_Pl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} legendre_Pl (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_Pl (@dots{}) These functions evaluate the Legendre polynomial P_l(x) for a specific value of l, x subject to l >= 0, |x| <= 1 @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn legendre_Ql -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} legendre_Ql (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_Ql (@dots{}) These routines compute the Legendre function Q_l(x) for x > -1, x != 1 and l >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn psi_n -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} psi_n (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi_n (@dots{}) These routines compute the polygamma function \\psi^@{(m)@}(x) for m >= 0, x > 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Jnu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Jnu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Jnu (@dots{}) These routines compute the regular cylindrical Bessel function of fractional order nu, J_\ u(x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Ynu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Ynu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Ynu (@dots{}) These routines compute the irregular cylindrical Bessel function of fractional order nu, Y_\ u(x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Inu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Inu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Inu (@dots{}) These routines compute the regular modified Bessel function of fractional order nu, I_\ u(x) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Inu_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Inu_scaled (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Inu_scaled (@dots{}) These routines compute the scaled regular modified Bessel function of fractional order nu, \\exp(-|x|)I_\ u(x) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Knu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Knu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Knu (@dots{}) These routines compute the irregular modified Bessel function of fractional order nu, K_\ u(x) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_lnKnu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_lnKnu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_lnKnu (@dots{}) These routines compute the logarithm of the irregular modified Bessel function of fractional order nu, \\ln(K_\ u(x)) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Knu_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Knu_scaled (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Knu_scaled (@dots{}) These routines compute the scaled irregular modified Bessel function of fractional order nu, \\exp(+|x|) K_\ u(x) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn exp_mult -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} exp_mult (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} exp_mult (@dots{}) These routines exponentiate x and multiply by the factor y to return the product y \\exp(x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_inc_0 -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} fermi_dirac_inc_0 (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} fermi_dirac_inc_0 (@dots{}) These routines compute the incomplete Fermi-Dirac integral with an index of zero, F_0(x,b) = \\ln(1 + e^@{b-x@}) - (b-x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn poch -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} poch (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} poch (@dots{}) These routines compute the Pochhammer symbol (a)_x := \\Gamma(a + x)/\\Gamma(a), subject to a and a+x not being negative integers. The Pochhammer symbol is also known as the Apell symbol. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lnpoch -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} lnpoch (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} lnpoch (@dots{}) These routines compute the logarithm of the Pochhammer symbol, \\log((a)_x) = \\log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn pochrel -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} pochrel (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} pochrel (@dots{}) These routines compute the relative Pochhammer symbol ((a,x) - 1)/x where (a,x) = (a)_x := \\Gamma(a + x)/\\Gamma(a). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gamma_inc_Q -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} gamma_inc_Q (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} gamma_inc_Q (@dots{}) These routines compute the normalized incomplete Gamma Function Q(a,x) = 1/\\Gamma(a) \\int_x\\infty dt t^@{a-1@} \\exp(-t) for a > 0, x >= 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gamma_inc_P -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} gamma_inc_P (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} gamma_inc_P (@dots{}) These routines compute the complementary normalized incomplete Gamma Function P(a,x) = 1/\\Gamma(a) \\int_0^x dt t^@{a-1@} \\exp(-t) for a > 0, x >= 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gamma_inc -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} gamma_inc (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} gamma_inc (@dots{}) These functions compute the incomplete Gamma Function the normalization factor included in the previously defined functions: \\Gamma(a,x) = \\int_x\\infty dt t^@{a-1@} \\exp(-t) for a real and x >= 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn beta_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} beta_gsl (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} beta_gsl (@dots{}) These routines compute the Beta Function, B(a,b) = \\Gamma(a)\\Gamma(b)/\\Gamma(a+b) for a > 0, b > 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lnbeta -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} lnbeta (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} lnbeta (@dots{}) These routines compute the logarithm of the Beta Function, \\log(B(a,b)) for a > 0, b > 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hyperg_0F1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} hyperg_0F1 (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} hyperg_0F1 (@dots{}) These routines compute the hypergeometric function 0F1(c,x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn conicalP_half -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} conicalP_half (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_half (@dots{}) These routines compute the irregular Spherical Conical Function P^@{1/2@}_@{-1/2 + i \\lambda@}(x) for x > -1. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn conicalP_mhalf -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} conicalP_mhalf (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_mhalf (@dots{}) These routines compute the regular Spherical Conical Function P^@{-1/2@}_@{-1/2 + i \\lambda@}(x) for x > -1. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn conicalP_0 -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} conicalP_0 (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_0 (@dots{}) These routines compute the conical function P^0_@{-1/2 + i \\lambda@}(x) for x > -1. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn conicalP_1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} conicalP_1 (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_1 (@dots{}) These routines compute the conical function P^1_@{-1/2 + i \\lambda@}(x) for x > -1. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hzeta -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} hzeta (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} hzeta (@dots{}) These routines compute the Hurwitz zeta function \\zeta(s,q) for s > 1, q > 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Ai -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Ai (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai (@dots{}) These routines compute the Airy function Ai(x) with an accuracy specified by mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Bi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Bi (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi (@dots{}) These routines compute the Airy function Bi(x) with an accuracy specified by mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Ai_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Ai_scaled (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai_scaled (@dots{}) These routines compute a scaled version of the Airy function S_A(x) Ai(x). For x>0 the scaling factor S_A(x) is \\exp(+(2/3) x^(3/2)), and is 1 for x<0. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Bi_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Bi_scaled (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi_scaled (@dots{}) These routines compute a scaled version of the Airy function S_B(x) Bi(x). For x>0 the scaling factor S_B(x) is exp(-(2/3) x^(3/2)), and is 1 for x<0. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Ai_deriv -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Ai_deriv (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai_deriv (@dots{}) These routines compute the Airy function derivative Ai'(x) with an accuracy specified by mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Bi_deriv -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Bi_deriv (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi_deriv (@dots{}) These routines compute the Airy function derivative Bi'(x) with an accuracy specified by mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Ai_deriv_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Ai_deriv_scaled (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai_deriv_scaled (@dots{}) These routines compute the derivative of the scaled Airy function S_A(x) Ai(x). The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Bi_deriv_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Bi_deriv_scaled (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi_deriv_scaled (@dots{}) These routines compute the derivative of the scaled Airy function S_B(x) Bi(x). The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn ellint_Kcomp -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} ellint_Kcomp (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} ellint_Kcomp (@dots{}) These routines compute the complete elliptic integral K(k) to the accuracy specified by the mode variable mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn ellint_Ecomp -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} ellint_Ecomp (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} ellint_Ecomp (@dots{}) These routines compute the complete elliptic integral E(k) to the accuracy specified by the mode variable mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_zero_Ai -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_zero_Ai (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Ai (@dots{}) These routines compute the location of the s-th zero of the Airy function Ai(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_zero_Bi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_zero_Bi (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Bi (@dots{}) These routines compute the location of the s-th zero of the Airy function Bi(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_zero_Ai_deriv -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_zero_Ai_deriv (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Ai_deriv (@dots{}) These routines compute the location of the s-th zero of the Airy function derivative Ai(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_zero_Bi_deriv -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_zero_Bi_deriv (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Bi_deriv (@dots{}) These routines compute the location of the s-th zero of the Airy function derivative Bi(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_zero_J0 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_zero_J0 (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_zero_J0 (@dots{}) These routines compute the location of the s-th positive zero of the Bessel function J_0(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_zero_J1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_zero_J1 (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_zero_J1 (@dots{}) These routines compute the location of the s-th positive zero of the Bessel function J_1(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn psi_1_int -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} psi_1_int (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi_1_int (@dots{}) These routines compute the Trigamma function \\psi(n) for positive integer n. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn zeta_int -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} zeta_int (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} zeta_int (@dots{}) These routines compute the Riemann zeta function \\zeta(n) for integer n, n \ e 1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn eta_int -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} eta_int (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} eta_int (@dots{}) These routines compute the eta function \\eta(n) for integer n. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn legendre_Plm -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} legendre_Plm (@var{n}, @var{m}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_Plm (@dots{}) These routines compute the associated Legendre polynomial P_l^m(x) for m >= 0, l >= m, |x| <= 1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn legendre_sphPlm -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} legendre_sphPlm (@var{n}, @var{m}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_sphPlm (@dots{}) These routines compute the normalized associated Legendre polynomial $\\sqrt@{(2l+1)/(4\\pi)@} \\sqrt@{(l-m)!/(l+m)!@} P_l^m(x)$ suitable for use in spherical harmonics. The parameters must satisfy m >= 0, l >= m, |x| <= 1. Theses routines avoid the overflows that occur for the standard normalization of P_l^m(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hyperg_U -*- texinfo -*- @deftypefn {Loadable Function} {@var{out} =} hyperg_U (@var{x0}, @var{x1}, @var{x2}) @deftypefnx {Loadable Function} {[@var{out}, @var{err}] =} hyperg_U (@dots{}) @var{err} contains an estimate of the absolute error in the value @var{out}.a. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hyperg_1F1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{out} =} hyperg_1F1 (@var{x0}, @var{x1}, @var{x2}) @deftypefnx {Loadable Function} {[@var{out}, @var{err}] =} hyperg_1F1 (@dots{}) @var{err} contains an estimate of the absolute error in the value @var{out}.a. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gsl-1.0.8/doc/mk_pdf_dvi0000755000175000017500000000024711201030403012673 0ustar shsh #!/bin/bash cp ../src/$1.cc ./$1.cc ./mkdoc >$1.doc ./mktexi_inc $1.doc >$1.texi tex -interaction batchmode $1.texi texi2pdf -b $1.texi dvips -o $1.ps $1.dvi gsl-1.0.8/doc/make.lst0000644000175000017500000011334311201030403012306 0ustar shshGNU Make 3.81 Copyright (C) 2006 Free Software Foundation, Inc. This is free software; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. This program built for i386-redhat-linux-gnu Reading makefiles... Reading makefile `Makefile'... Reading makefile `../../../Makeconf' (search path) (don't care) (no ~ expansion)... Updating makefiles.... Considering target file `../../../Makeconf'. Looking for an implicit rule for `../../../Makeconf'. 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Trying implicit prerequisite `../../../Makeconf.y,v'. Trying pattern rule with stem `Makeconf.y'. Trying implicit prerequisite `../../../RCS/Makeconf.y,v'. Trying pattern rule with stem `Makeconf.y'. Trying implicit prerequisite `../../../RCS/Makeconf.y'. Trying pattern rule with stem `Makeconf.y'. Trying implicit prerequisite `../../../s.Makeconf.y'. Trying pattern rule with stem `Makeconf.y'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.y'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.l'. Looking for a rule with intermediate file `../../../Makeconf.l'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makeconf.l'. Trying implicit prerequisite `../../../Makeconf.l,v'. Trying pattern rule with stem `Makeconf.l'. Trying implicit prerequisite `../../../RCS/Makeconf.l,v'. Trying pattern rule with stem `Makeconf.l'. Trying implicit prerequisite `../../../RCS/Makeconf.l'. Trying pattern rule with stem `Makeconf.l'. Trying implicit prerequisite `../../../s.Makeconf.l'. Trying pattern rule with stem `Makeconf.l'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.l'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.w'. Looking for a rule with intermediate file `../../../Makeconf.w'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makeconf.w'. Trying implicit prerequisite `../../../Makeconf.w,v'. Trying pattern rule with stem `Makeconf.w'. Trying implicit prerequisite `../../../RCS/Makeconf.w,v'. Trying pattern rule with stem `Makeconf.w'. Trying implicit prerequisite `../../../RCS/Makeconf.w'. Trying pattern rule with stem `Makeconf.w'. Trying implicit prerequisite `../../../s.Makeconf.w'. Trying pattern rule with stem `Makeconf.w'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.w'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.w'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.f'. Looking for a rule with intermediate file `../../../Makeconf.f'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.F'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.r'. Trying pattern rule with stem `Makeconf.f'. Trying implicit prerequisite `../../../Makeconf.f,v'. Trying pattern rule with stem `Makeconf.f'. Trying implicit prerequisite `../../../RCS/Makeconf.f,v'. Trying pattern rule with stem `Makeconf.f'. Trying implicit prerequisite `../../../RCS/Makeconf.f'. Trying pattern rule with stem `Makeconf.f'. Trying implicit prerequisite `../../../s.Makeconf.f'. Trying pattern rule with stem `Makeconf.f'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.f'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.F'. Looking for a rule with intermediate file `../../../Makeconf.F'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makeconf.F'. Trying implicit prerequisite `../../../Makeconf.F,v'. Trying pattern rule with stem `Makeconf.F'. Trying implicit prerequisite `../../../RCS/Makeconf.F,v'. Trying pattern rule with stem `Makeconf.F'. Trying implicit prerequisite `../../../RCS/Makeconf.F'. Trying pattern rule with stem `Makeconf.F'. Trying implicit prerequisite `../../../s.Makeconf.F'. Trying pattern rule with stem `Makeconf.F'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.F'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.r'. Looking for a rule with intermediate file `../../../Makeconf.r'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.l'. Trying pattern rule with stem `Makeconf.r'. Trying implicit prerequisite `../../../Makeconf.r,v'. Trying pattern rule with stem `Makeconf.r'. Trying implicit prerequisite `../../../RCS/Makeconf.r,v'. Trying pattern rule with stem `Makeconf.r'. Trying implicit prerequisite `../../../RCS/Makeconf.r'. Trying pattern rule with stem `Makeconf.r'. Trying implicit prerequisite `../../../s.Makeconf.r'. Trying pattern rule with stem `Makeconf.r'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.r'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.cc'. Looking for a rule with intermediate file `../../../Makeconf.cc'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makeconf.cc'. Trying implicit prerequisite `../../../Makeconf.cc,v'. Trying pattern rule with stem `Makeconf.cc'. Trying implicit prerequisite `../../../RCS/Makeconf.cc,v'. Trying pattern rule with stem `Makeconf.cc'. Trying implicit prerequisite `../../../RCS/Makeconf.cc'. Trying pattern rule with stem `Makeconf.cc'. Trying implicit prerequisite `../../../s.Makeconf.cc'. Trying pattern rule with stem `Makeconf.cc'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.cc'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.C'. Looking for a rule with intermediate file `../../../Makeconf.C'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makeconf.C'. Trying implicit prerequisite `../../../Makeconf.C,v'. Trying pattern rule with stem `Makeconf.C'. Trying implicit prerequisite `../../../RCS/Makeconf.C,v'. Trying pattern rule with stem `Makeconf.C'. Trying implicit prerequisite `../../../RCS/Makeconf.C'. Trying pattern rule with stem `Makeconf.C'. Trying implicit prerequisite `../../../s.Makeconf.C'. Trying pattern rule with stem `Makeconf.C'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.C'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.cpp'. Looking for a rule with intermediate file `../../../Makeconf.cpp'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makeconf.cpp'. Trying implicit prerequisite `../../../Makeconf.cpp,v'. Trying pattern rule with stem `Makeconf.cpp'. Trying implicit prerequisite `../../../RCS/Makeconf.cpp,v'. Trying pattern rule with stem `Makeconf.cpp'. Trying implicit prerequisite `../../../RCS/Makeconf.cpp'. Trying pattern rule with stem `Makeconf.cpp'. Trying implicit prerequisite `../../../s.Makeconf.cpp'. Trying pattern rule with stem `Makeconf.cpp'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.cpp'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.p'. Looking for a rule with intermediate file `../../../Makeconf.p'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.web'. Trying pattern rule with stem `Makeconf.p'. Trying implicit prerequisite `../../../Makeconf.p,v'. Trying pattern rule with stem `Makeconf.p'. Trying implicit prerequisite `../../../RCS/Makeconf.p,v'. Trying pattern rule with stem `Makeconf.p'. Trying implicit prerequisite `../../../RCS/Makeconf.p'. Trying pattern rule with stem `Makeconf.p'. Trying implicit prerequisite `../../../s.Makeconf.p'. Trying pattern rule with stem `Makeconf.p'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.p'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.web'. Looking for a rule with intermediate file `../../../Makeconf.web'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makeconf.web'. Trying implicit prerequisite `../../../Makeconf.web,v'. Trying pattern rule with stem `Makeconf.web'. Trying implicit prerequisite `../../../RCS/Makeconf.web,v'. Trying pattern rule with stem `Makeconf.web'. Trying implicit prerequisite `../../../RCS/Makeconf.web'. Trying pattern rule with stem `Makeconf.web'. Trying implicit prerequisite `../../../s.Makeconf.web'. Trying pattern rule with stem `Makeconf.web'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.web'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.F'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.r'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.s'. Looking for a rule with intermediate file `../../../Makeconf.s'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.S'. Trying pattern rule with stem `Makeconf.s'. Trying implicit prerequisite `../../../Makeconf.s,v'. Trying pattern rule with stem `Makeconf.s'. Trying implicit prerequisite `../../../RCS/Makeconf.s,v'. Trying pattern rule with stem `Makeconf.s'. Trying implicit prerequisite `../../../RCS/Makeconf.s'. Trying pattern rule with stem `Makeconf.s'. Trying implicit prerequisite `../../../s.Makeconf.s'. Trying pattern rule with stem `Makeconf.s'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.s'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.S'. Looking for a rule with intermediate file `../../../Makeconf.S'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makeconf.S'. Trying implicit prerequisite `../../../Makeconf.S,v'. Trying pattern rule with stem `Makeconf.S'. Trying implicit prerequisite `../../../RCS/Makeconf.S,v'. Trying pattern rule with stem `Makeconf.S'. Trying implicit prerequisite `../../../RCS/Makeconf.S'. Trying pattern rule with stem `Makeconf.S'. Trying implicit prerequisite `../../../s.Makeconf.S'. Trying pattern rule with stem `Makeconf.S'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.S'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.S'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.mod'. Looking for a rule with intermediate file `../../../Makeconf.mod'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makeconf.mod'. Trying implicit prerequisite `../../../Makeconf.mod,v'. Trying pattern rule with stem `Makeconf.mod'. Trying implicit prerequisite `../../../RCS/Makeconf.mod,v'. Trying pattern rule with stem `Makeconf.mod'. Trying implicit prerequisite `../../../RCS/Makeconf.mod'. Trying pattern rule with stem `Makeconf.mod'. Trying implicit prerequisite `../../../s.Makeconf.mod'. Trying pattern rule with stem `Makeconf.mod'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.mod'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.c'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.cc'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.C'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.cpp'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.p'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.f'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.F'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.r'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.s'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.S'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.mod'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.sh'. Looking for a rule with intermediate file `../../../Makeconf.sh'. Avoiding implicit rule recursion. Trying pattern rule with stem `Makeconf.sh'. Trying implicit prerequisite `../../../Makeconf.sh,v'. Trying pattern rule with stem `Makeconf.sh'. Trying implicit prerequisite `../../../RCS/Makeconf.sh,v'. Trying pattern rule with stem `Makeconf.sh'. Trying implicit prerequisite `../../../RCS/Makeconf.sh'. Trying pattern rule with stem `Makeconf.sh'. Trying implicit prerequisite `../../../s.Makeconf.sh'. Trying pattern rule with stem `Makeconf.sh'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.sh'. No implicit rule found for `../../../Makeconf'. Finished prerequisites of target file `../../../Makeconf'. No need to remake target `../../../Makeconf'. Considering target file `Makefile'. Looking for an implicit rule for `Makefile'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.o'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.c'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.cc'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.C'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.cpp'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.p'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.f'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.F'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.r'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.s'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.S'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.mod'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.sh'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile,v'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `RCS/Makefile,v'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `RCS/Makefile'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `s.Makefile'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `SCCS/s.Makefile'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.o'. Looking for a rule with intermediate file `Makefile.o'. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.c'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.f'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.cc'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.C'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.cpp'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.p'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.F'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.r'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.s'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.S'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.mod'. Trying pattern rule with stem `Makefile.o'. Trying implicit prerequisite `Makefile.o,v'. Trying pattern rule with stem `Makefile.o'. Trying implicit prerequisite `RCS/Makefile.o,v'. Trying pattern rule with stem `Makefile.o'. Trying implicit prerequisite `RCS/Makefile.o'. Trying pattern rule with stem `Makefile.o'. Trying implicit prerequisite `s.Makefile.o'. Trying pattern rule with stem `Makefile.o'. Trying implicit prerequisite `SCCS/s.Makefile.o'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.c'. Looking for a rule with intermediate file `Makefile.c'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.y'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.l'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.w'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.w'. Trying pattern rule with stem `Makefile.c'. Trying implicit prerequisite `Makefile.c,v'. Trying pattern rule with stem `Makefile.c'. Trying implicit prerequisite `RCS/Makefile.c,v'. Trying pattern rule with stem `Makefile.c'. Trying implicit prerequisite `RCS/Makefile.c'. Trying pattern rule with stem `Makefile.c'. Trying implicit prerequisite `s.Makefile.c'. Trying pattern rule with stem `Makefile.c'. Trying implicit prerequisite `SCCS/s.Makefile.c'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.y'. Looking for a rule with intermediate file `Makefile.y'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.y'. Trying implicit prerequisite `Makefile.y,v'. Trying pattern rule with stem `Makefile.y'. Trying implicit prerequisite `RCS/Makefile.y,v'. Trying pattern rule with stem `Makefile.y'. Trying implicit prerequisite `RCS/Makefile.y'. Trying pattern rule with stem `Makefile.y'. Trying implicit prerequisite `s.Makefile.y'. Trying pattern rule with stem `Makefile.y'. Trying implicit prerequisite `SCCS/s.Makefile.y'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.l'. Looking for a rule with intermediate file `Makefile.l'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.l'. Trying implicit prerequisite `Makefile.l,v'. Trying pattern rule with stem `Makefile.l'. Trying implicit prerequisite `RCS/Makefile.l,v'. Trying pattern rule with stem `Makefile.l'. Trying implicit prerequisite `RCS/Makefile.l'. Trying pattern rule with stem `Makefile.l'. Trying implicit prerequisite `s.Makefile.l'. Trying pattern rule with stem `Makefile.l'. Trying implicit prerequisite `SCCS/s.Makefile.l'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.w'. Looking for a rule with intermediate file `Makefile.w'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.w'. Trying implicit prerequisite `Makefile.w,v'. Trying pattern rule with stem `Makefile.w'. Trying implicit prerequisite `RCS/Makefile.w,v'. Trying pattern rule with stem `Makefile.w'. Trying implicit prerequisite `RCS/Makefile.w'. Trying pattern rule with stem `Makefile.w'. Trying implicit prerequisite `s.Makefile.w'. Trying pattern rule with stem `Makefile.w'. Trying implicit prerequisite `SCCS/s.Makefile.w'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.w'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.f'. Looking for a rule with intermediate file `Makefile.f'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.F'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.r'. Trying pattern rule with stem `Makefile.f'. Trying implicit prerequisite `Makefile.f,v'. Trying pattern rule with stem `Makefile.f'. Trying implicit prerequisite `RCS/Makefile.f,v'. Trying pattern rule with stem `Makefile.f'. Trying implicit prerequisite `RCS/Makefile.f'. Trying pattern rule with stem `Makefile.f'. Trying implicit prerequisite `s.Makefile.f'. Trying pattern rule with stem `Makefile.f'. Trying implicit prerequisite `SCCS/s.Makefile.f'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.F'. Looking for a rule with intermediate file `Makefile.F'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.F'. Trying implicit prerequisite `Makefile.F,v'. Trying pattern rule with stem `Makefile.F'. Trying implicit prerequisite `RCS/Makefile.F,v'. Trying pattern rule with stem `Makefile.F'. Trying implicit prerequisite `RCS/Makefile.F'. Trying pattern rule with stem `Makefile.F'. Trying implicit prerequisite `s.Makefile.F'. Trying pattern rule with stem `Makefile.F'. Trying implicit prerequisite `SCCS/s.Makefile.F'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.r'. Looking for a rule with intermediate file `Makefile.r'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.l'. Trying pattern rule with stem `Makefile.r'. Trying implicit prerequisite `Makefile.r,v'. Trying pattern rule with stem `Makefile.r'. Trying implicit prerequisite `RCS/Makefile.r,v'. Trying pattern rule with stem `Makefile.r'. Trying implicit prerequisite `RCS/Makefile.r'. Trying pattern rule with stem `Makefile.r'. Trying implicit prerequisite `s.Makefile.r'. Trying pattern rule with stem `Makefile.r'. Trying implicit prerequisite `SCCS/s.Makefile.r'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.cc'. Looking for a rule with intermediate file `Makefile.cc'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.cc'. Trying implicit prerequisite `Makefile.cc,v'. Trying pattern rule with stem `Makefile.cc'. Trying implicit prerequisite `RCS/Makefile.cc,v'. Trying pattern rule with stem `Makefile.cc'. Trying implicit prerequisite `RCS/Makefile.cc'. Trying pattern rule with stem `Makefile.cc'. Trying implicit prerequisite `s.Makefile.cc'. Trying pattern rule with stem `Makefile.cc'. Trying implicit prerequisite `SCCS/s.Makefile.cc'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.C'. Looking for a rule with intermediate file `Makefile.C'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.C'. Trying implicit prerequisite `Makefile.C,v'. Trying pattern rule with stem `Makefile.C'. Trying implicit prerequisite `RCS/Makefile.C,v'. Trying pattern rule with stem `Makefile.C'. Trying implicit prerequisite `RCS/Makefile.C'. Trying pattern rule with stem `Makefile.C'. Trying implicit prerequisite `s.Makefile.C'. Trying pattern rule with stem `Makefile.C'. Trying implicit prerequisite `SCCS/s.Makefile.C'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.cpp'. Looking for a rule with intermediate file `Makefile.cpp'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.cpp'. Trying implicit prerequisite `Makefile.cpp,v'. Trying pattern rule with stem `Makefile.cpp'. Trying implicit prerequisite `RCS/Makefile.cpp,v'. Trying pattern rule with stem `Makefile.cpp'. Trying implicit prerequisite `RCS/Makefile.cpp'. Trying pattern rule with stem `Makefile.cpp'. Trying implicit prerequisite `s.Makefile.cpp'. Trying pattern rule with stem `Makefile.cpp'. Trying implicit prerequisite `SCCS/s.Makefile.cpp'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.p'. Looking for a rule with intermediate file `Makefile.p'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.web'. Trying pattern rule with stem `Makefile.p'. Trying implicit prerequisite `Makefile.p,v'. Trying pattern rule with stem `Makefile.p'. Trying implicit prerequisite `RCS/Makefile.p,v'. Trying pattern rule with stem `Makefile.p'. Trying implicit prerequisite `RCS/Makefile.p'. Trying pattern rule with stem `Makefile.p'. Trying implicit prerequisite `s.Makefile.p'. Trying pattern rule with stem `Makefile.p'. Trying implicit prerequisite `SCCS/s.Makefile.p'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.web'. Looking for a rule with intermediate file `Makefile.web'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.web'. Trying implicit prerequisite `Makefile.web,v'. Trying pattern rule with stem `Makefile.web'. Trying implicit prerequisite `RCS/Makefile.web,v'. Trying pattern rule with stem `Makefile.web'. Trying implicit prerequisite `RCS/Makefile.web'. Trying pattern rule with stem `Makefile.web'. Trying implicit prerequisite `s.Makefile.web'. Trying pattern rule with stem `Makefile.web'. Trying implicit prerequisite `SCCS/s.Makefile.web'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.F'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.r'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.s'. Looking for a rule with intermediate file `Makefile.s'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.S'. Trying pattern rule with stem `Makefile.s'. Trying implicit prerequisite `Makefile.s,v'. Trying pattern rule with stem `Makefile.s'. Trying implicit prerequisite `RCS/Makefile.s,v'. Trying pattern rule with stem `Makefile.s'. Trying implicit prerequisite `RCS/Makefile.s'. Trying pattern rule with stem `Makefile.s'. Trying implicit prerequisite `s.Makefile.s'. Trying pattern rule with stem `Makefile.s'. Trying implicit prerequisite `SCCS/s.Makefile.s'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.S'. Looking for a rule with intermediate file `Makefile.S'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.S'. Trying implicit prerequisite `Makefile.S,v'. Trying pattern rule with stem `Makefile.S'. Trying implicit prerequisite `RCS/Makefile.S,v'. Trying pattern rule with stem `Makefile.S'. Trying implicit prerequisite `RCS/Makefile.S'. Trying pattern rule with stem `Makefile.S'. Trying implicit prerequisite `s.Makefile.S'. Trying pattern rule with stem `Makefile.S'. Trying implicit prerequisite `SCCS/s.Makefile.S'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.S'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.mod'. Looking for a rule with intermediate file `Makefile.mod'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.mod'. Trying implicit prerequisite `Makefile.mod,v'. Trying pattern rule with stem `Makefile.mod'. Trying implicit prerequisite `RCS/Makefile.mod,v'. Trying pattern rule with stem `Makefile.mod'. Trying implicit prerequisite `RCS/Makefile.mod'. Trying pattern rule with stem `Makefile.mod'. Trying implicit prerequisite `s.Makefile.mod'. Trying pattern rule with stem `Makefile.mod'. Trying implicit prerequisite `SCCS/s.Makefile.mod'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.c'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.cc'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.C'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.cpp'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.p'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.f'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.F'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.r'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.s'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.S'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.mod'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.sh'. Looking for a rule with intermediate file `Makefile.sh'. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.sh'. Trying implicit prerequisite `Makefile.sh,v'. Trying pattern rule with stem `Makefile.sh'. Trying implicit prerequisite `RCS/Makefile.sh,v'. Trying pattern rule with stem `Makefile.sh'. Trying implicit prerequisite `RCS/Makefile.sh'. Trying pattern rule with stem `Makefile.sh'. Trying implicit prerequisite `s.Makefile.sh'. Trying pattern rule with stem `Makefile.sh'. Trying implicit prerequisite `SCCS/s.Makefile.sh'. No implicit rule found for `Makefile'. Finished prerequisites of target file `Makefile'. No need to remake target `Makefile'. Updating goal targets.... Considering target file `../src/gsl_sf.cc'. Looking for an implicit rule for `../src/gsl_sf.cc'. Trying pattern rule with stem `gsl_sf.cc'. Trying implicit prerequisite `../src/gsl_sf.cc,v'. Trying pattern rule with stem `gsl_sf.cc'. Trying implicit prerequisite `../src/RCS/gsl_sf.cc,v'. Trying pattern rule with stem `gsl_sf.cc'. Trying implicit prerequisite `../src/RCS/gsl_sf.cc'. Trying pattern rule with stem `gsl_sf.cc'. Trying implicit prerequisite `../src/s.gsl_sf.cc'. Trying pattern rule with stem `gsl_sf.cc'. Trying implicit prerequisite `../src/SCCS/s.gsl_sf.cc'. No implicit rule found for `../src/gsl_sf.cc'. Finished prerequisites of target file `../src/gsl_sf.cc'. No need to remake target `../src/gsl_sf.cc'. make: Nothing to be done for `../src/gsl_sf.cc'. gsl-1.0.8/doc/mktexi0000644000175000017500000003044711201030403012074 0ustar shsh#!/usr/bin/env perl # # David Bateman Feb 02 2003 # # Extracts the help in texinfo format for particular function for use # in documentation. Based on make_index script from octave_forge. use strict; use File::Find; use File::Basename; use Text::Wrap; use FileHandle; use IPC::Open3; use POSIX ":sys_wait_h"; my $file = shift @ARGV; my $docfile = shift @ARGV; my $indexfile = shift @ARGV; my $line; print("\\input texinfo \n"); print("\@ifnottex \n"); print("\@node Top \n"); print("print("\@top Octave gsl \n"); @end ifnottex if ( open(IN,$file) ) { $line = ; my $tex = 0; while ($line) { if ($line =~ /^\@DOCSTRING/) { my $found = 0; my $func = $line; $func =~ s/\@DOCSTRING\(//; $func =~ s/\)[\n\r]+//; my $func0 = $func; my $func1 = $func; $func0 =~ s/,.*$//; $func1 =~ s/^.*,//; if ( open(DOC,$docfile) ) { while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func0$/) { my $desc = ""; my $docline; my $doctex = 0; while (($docline = ) && ($docline !~ /^\037/)) { $docline =~ s/^\s*-[*]- texinfo -[*]-\s*//; if ($docline =~ /\@tex/) { $doctex = 1; } if ($doctex) { $docline =~ s/\\\\/\\/g; } if ($docline =~ /\@end tex/) { $doctex = 0; } $desc .= $docline; } $desc =~ s/$func0/$func1/g; $desc =~ s/\@seealso\{(.*[^}])\}/See also: \1/g; print "$desc", "\n"; $found = 1; last; } } close (DOC); if (! $found) { print "\@emph{Not implemented}\n"; } } else { print STDERR "Could not open file $docfile\n"; exit 1; } } elsif ($line =~ /^\@REFERENCE_SECTION/) { my $secfound = 0; my $sec = $line; $sec =~ s/\@REFERENCE_SECTION\(//; $sec =~ s/\)[\n\r]+//; my @listfunc = (); my $nfunc = 0; my $seccat = 0; if ( open(IND,$indexfile) ) { while () { next unless /^[^ ]/; my $section = $_; $section =~ s/[\n\r]+//; if ($section =~ /^(.*?)\s*>>\s*(.*?)$/) { $section =~ s/.*>>(.*)/\1/; $seccat = 1; } $section =~ s/^ *//; $section =~ s/ *$//; if ($section =~ /^$sec$/) { if ($seccat) { print "\@iftex\n"; print "\@section Functions by Category\n"; # Get the list of categories to index my $firstcat = 1; my $category; while () { last if />>/; if (/^[^ ]/) { if (! $firstcat) { print "\@end table\n"; } else { $firstcat = 0; } $category = $_; $category =~ s/[\n\r]+//; print "\@subsection $category\n"; print "\@table \@asis\n"; } elsif (/^\s+(\S.*\S)\s*=\s*(\S.*\S)\s*$/) { my $func = $1; my $desc = $2; print "\@item $func\n"; print "$desc\n"; print "\n"; } else { if ($firstcat) { print STDERR "Error parsing index file\n"; exit 1; } s/^\s+//; my @funcs = split /\s+/; while ($#funcs >= 0) { my $func = shift @funcs; $func =~ s/^ *//; $func =~ s/[\n\r]+//; push @listfunc, $func; $nfunc = $nfunc + 1; print "\@item $func\n"; print func_summary($func, $docfile); print "\n"; } } } if (! $firstcat) { print "\@end table\n"; } print "\n\@section Functions Alphabetically\n"; print "\@end iftex\n\n"; } else { # Get the list of functions to index my $indline; while (($indline = ) && ($indline =~ /^ /)) { if ($indline =~ /^\s+(\S.*\S)\s*=\s*(\S.*\S)\s*$/) { next; } $indline =~ s/^\s+//; my @funcs = split(/\s+/,$indline); while ($#funcs >= 0) { my $func = shift @funcs; $func =~ s/^ *//; $func =~ s/[\n\r]+//; push @listfunc, $func; $nfunc = $nfunc + 1; } } } $secfound = 1; last; } } close (IND); if (! $secfound) { print STDERR "Did not find section $sec\n"; } } else { print STDERR "Could not open file $indexfile\n"; exit 1; } @listfunc = sort(@listfunc); my @listfunc2 = (); my $indent = 16 - 3; print "\@menu\n"; foreach my $func (@listfunc) { if ( open(DOC,$docfile) ) { my $found = 0; while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func$/) { $found = 1; last; } } close (DOC); if ($found) { push @listfunc2, $func; my $func0 = "${func}::"; my $entry = sprintf("* %-*s %s",$indent,$func0,func_summary($func,$docfile)); print wrap("","\t\t","$entry"), "\n"; } } else { print STDERR "Could not open file $indexfile\n"; exit 1; } } print "\@end menu\n"; my $up = "Function Reference"; my $next; my $prev; my $mfunc = 1; foreach my $func (@listfunc2) { if ($mfunc == $nfunc) { $next = ""; } else { $next = @listfunc2[$mfunc]; $mfunc = $mfunc + 1; } print "\n\@node $func, $next, $prev, $up\n"; if ($seccat) { print "\@subsection $func\n\n"; } else { print "\@section $func\n\n"; } $prev = $func; my $found = 0; my $desc = ""; if ( open(DOC,$docfile) ) { while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func$/) { my $docline; my $doctex = 0; while (($docline = ) && ($docline !~ /^\037/)) { $docline =~ s/^\s*-[*]- texinfo -[*]-\s*//; if ($docline =~ /\@tex/) { $doctex = 1; } if ($doctex) { $docline =~ s/\\\\/\\/g; } if ($docline =~ /\@end tex/) { $doctex = 0; } $desc .= $docline; } $desc =~ s/\@seealso\{(.*[^}])\}/See also: \1/g; print "$desc", "\n"; $found = 1; last; } } close (DOC); if (! $found) { print "\@emph{Not implemented}\n"; } } else { print STDERR "Could not open file $docfile\n"; exit 1; } } } else { if ($line =~ /\@tex/) { $tex = 1; } if ($tex) { $line =~ s/\\\\/\\/g; } print "$line"; if ($line =~ /\@end tex/) { $tex = 0; } } $line = ; } } else { print STDERR "Could not open file $file\n"; exit 1; }; print("\@bye"); sub func_summary { # {{{1 my ($func, # in function name $docfile # in DOCSTRINGS ) = @_; my $desc = ""; my $found = 0; if ( open(DOC,$docfile) ) { while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func$/) { my $docline; my $doctex = 0; while (($docline = ) && ($docline !~ /^\037/)) { if ($docline =~ /\@tex/) { $doctex = 1; } if ($doctex) { $docline =~ s/\\\\/\\/g; } if ($docline =~ /\@end tex/) { $doctex = 0; } $desc .= $docline; } $desc =~ s/\@seealso\{(.*[^}])\}/See also: \1/g; $found = 1; last; } } close (DOC); if (! $found) { $desc = "\@emph{Not implemented}"; } } else { print STDERR "Could not open file $docfile\n"; exit 1; } return first_sentence($desc); } # 1}}} sub first_sentence { # {{{1 # grab the first real sentence from the function documentation my ($desc) = @_; my $retval = ''; my $line; my $next; my @lines; my $trace = 0; # $trace = 1 if $desc =~ /Levenberg/; return "" unless defined $desc; if ($desc =~ /^\s*-[*]- texinfo -[*]-/) { # help text contains texinfo. Strip the indicator and run it # through makeinfo. (XXX FIXME XXX this needs to be a function) $desc =~ s/^\s*-[*]- texinfo -[*]-\s*//; my $cmd = "makeinfo --fill-column 1600 --no-warn --no-validate --no-headers --force --ifinfo"; open3(*Writer, *Reader, *Errer, $cmd) or die "Could not run info"; print Writer "\@macro seealso {args}\n\n\@noindent\nSee also: \\args\\.\n\@end macro\n"; print Writer "$desc"; close(Writer); @lines = ; close(Reader); my @err = ; close(Errer); waitpid(-1,&WNOHANG); # Display source and errors, if any if (@err) { my $n = 1; foreach $line ( split(/\n/,$desc) ) { printf "%2d: %s\n",$n++,$line; } print ">>> @err"; } # Print trace showing formatted output # print "\n"; # Skip prototype and blank lines while (1) { return "" unless @lines; $line = shift @lines; next if $line =~ /^\s*-/; next if $line =~ /^\s*$/; last; } } else { # print "\n"; # Skip prototype and blank lines @lines = split(/\n/,$desc); while (1) { return "" if ($#lines < 0); $line = shift @lines; next if $line =~ /^\s*[Uu][Ss][Aa][Gg][Ee]/; # skip " usage " $line =~ s/^\s*\w+\s*://; # chop " blah : " print "strip blah: $line\n" if $trace; $line =~ s/^\s*[Ff]unction\s+//; # chop " function " print "strip function $line\n" if $trace; $line =~ s/^\s*\[.*\]\s*=\s*//; # chop " [a,b] = " print "strip []= $line\n" if $trace; $line =~ s/^\s*\w+\s*=\s*//; # chop " a = " print "strip a= $line\n" if $trace; $line =~ s/^\s*\w+\s*\([^\)]*\)\s*//; # chop " f(x) " print "strip f(x) $line\n" if $trace; $line =~ s/^\s*[;:]\s*//; # chop " ; " print "strip ; $line\n" if $trace; $line =~ s/^\s*[[:upper:]][[:upper:]0-9_]+//; # chop " BLAH" print "strip BLAH $line\n" if $trace; $line =~ s/^\s*\w*\s*[-]+\s+//; # chop " blah --- " print "strip blah --- $line\n" if $trace; $line =~ s/^\s*\w+ *\t\s*//; # chop " blah " print "strip blah $line\n" if $trace; $line =~ s/^\s*\w+\s\s+//; # chop " blah " print "strip blah $line\n" if $trace; # next if $line =~ /^\s*\[/; # skip [a,b] = f(x) # next if $line =~ /^\s*\w+\s*(=|\()/; # skip a = f(x) OR f(x) next if $line =~ /^\s*or\s*$/; # skip blah \n or \n blah next if $line =~ /^\s*$/; # skip blank line next if $line =~ /^\s?!\//; # skip # !/usr/bin/octave # XXX FIXME XXX should be testing for unmatched () in proto # before going to the next line! last; } } # Try to make a complete sentence, including the '.' if ( "$line " !~ /[^.][.]\s/ && $#lines >= 0) { my $next = $lines[0]; $line =~ s/\s*$//; # trim trailing blanks on last $next =~ s/^\s*//; # trim leading blanks on next $line .= " $next" if "$next " =~ /[^.][.]\s/; # ends the sentence } # Tidy up the sentence. chomp $line; # trim trailing newline, if there is one $line =~ s/^\s*//; # trim leading blanks on line $line =~ s/([^.][.])\s.*$/$1/; # trim everything after the sentence print "Skipping:\n$desc---\n" if $line eq ""; # And return it. return $line; } # 1}}} __END__ This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, see . This program is granted to the public domain. THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. gsl-1.0.8/doc/mkdoc0000755000175000017500000001236311201030403011670 0ustar shsh#!/usr/bin/env perl # # David Bateman Feb 02 2003 # # Extracts the help in texinfo format from *.cc and *.m files for use # in documentation. Based on make_index script from octave_forge. use strict; use File::Find; use File::Basename; use FileHandle; my $docdir = "."; if (@ARGV) { $docdir = @ARGV[0]; } # locate all C++ and m-files in current directory my @m_files = (); my @C_files = (); find(\&cc_and_m_files, $docdir); sub cc_and_m_files { # {{{1 populates global array @files return unless -f and /\.(m|cc)$/; # .m and .cc files my $path = "$File::Find::dir/$_"; $path =~ s|^[.]/||; if (/\.m$/) { push @m_files, $path; } else { push @C_files, $path; } } # 1}}} # grab help from C++ files foreach my $f ( @C_files ) { # XXX FIXME XXX. Should run the preprocessor over the file first, since # the help might include defines that are compile dependent. if ( open(IN,$f) ) { while () { # skip to the next function next unless /^DEFUN_DLD/; # extract function name to pattern space /\((\w*)\s*,/; # remember function name my $function = $1; # skip to next line if comment doesn't start on this line # XXX FIXME XXX maybe we want a loop here? $_ = unless /\"/; # skip to the beginning of the comment string by # chopping everything up to opening " my $desc = $_; $desc =~ s/^[^\"]*\"//; # join lines until you get the end of the comment string # plus a bit more. You need the "plus a bit more" because # C compilers allow implicitly concatenated string constants # "A" "B" ==> "AB". while ($desc !~ /[^\\]\"\s*\S/ && $desc !~ /^\"/) { # if line ends in '\', chop it and the following '\n' $desc =~ s/\\\s*\n//; # join with the next line $desc .= ; # eliminate consecutive quotes, being careful to ignore # preceding slashes. XXX FIXME XXX what about \\" ? $desc =~ s/([^\\])\"\s*\"/$1/; } $desc = "" if $desc =~ /^\"/; # chop everything if it was "" $desc =~ s/\\n/\n/g; # insert fake line ends $desc =~ s/([^\"])\".*$/$1/; # chop everything after final '"' $desc =~ s/\\\"/\"/; # convert \"; XXX FIXME XXX \\" $desc =~ s/$//g; # chop trailing ... if (!($desc =~ /^\s*-[*]- texinfo -[*]-/)) { my $err = sprintf("Function %s, does not contain texinfo help\n", $function); print STDERR "$err"; } my $entry = sprintf("\037%s\n%s", $function, $desc); print "$entry", "\n"; } close (IN); } else { print STDERR "Could not open file ($f): $!\n"; } } # grab help from m-files foreach my $f ( @m_files ) { my $desc = extract_description($f); my $function = basename($f, ('.m')); die "Null function?? [$f]\n" unless $function; if (!($desc =~ /^\s*-[*]- texinfo -[*]-/)) { my $err = sprintf("Function %s, does not contain texinfo help\n", $function); print STDERR "$err"; } my $entry = sprintf("\037%s\n%s", $function, $desc); print "$entry", "\n"; } sub extract_description { # {{{1 # grab the entire documentation comment from an m-file my ($file) = @_; my $retval = ''; if( open( IN, "$file")) { # skip leading blank lines while () { last if /\S/; } if( m/\s*[%\#][\s\#%]* Copyright/) { # next block is copyright statement, skip it while () { last unless /^\s*[%\#]/; } } # Skip everything until the next comment block while ( !/^\s*[\#%]/ ) { $_ = ; last if not defined $_; } # Return the next comment block as the documentation while (/^\s*[\#%]/) { s/^[\s%\#]*//; # strip leading comment characters s/[\cM\s]*$//; # strip trailing spaces. s/[\.*]$//; $retval .= "$_\n"; $_ = ; last if not defined $_; } close(IN); return $retval; } else { print STDERR "Could not open file ($file): $!\n"; } } # 1}}} __END__ This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, see . This program is granted to the public domain. THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. 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# # txt2latex -- by Tristan Miller (psychonaut@nothingisreal.com) # This program is in the public domain. It comes with absolutely NO # WARRANTY -- use at your own risk. # # Revision history # ---------------- # 1.0 -- 2002/02/20 -- initial release # # Description # ----------- # txt2latex assists in translation from ASCII text to LaTeX by escaping # special characters and "fixing" quote marks (using English conventions). # Reads from standard input and writes to standard output. # Any "unfixed" double quotes are reported on standard error. # # If there is a demand, I will add command-line options allowing # customization or suppression of the document header/footer, and use of # non-English quotation marks (e.g., "` and "'). $count = 0; # Header print STDOUT "\\documentclass{article}\n\\begin{document}\n"; foreach $line (<>) { $count++; # Escape special characters $line =~ s/\\/{\\textbackslash}/g; $line =~ s/{/\\{/g; $line =~ s/}/\\}/g; $line =~ s/\\{\\textbackslash\\}/{\\textbackslash}/g; $line =~ s/\$/\\\$/g; $line =~ s/%/\\%/g; $line =~ s/_/\\_/g; $line =~ s/&/\\&/g; $line =~ s/\#/\\\#/g; # Ellipses $line =~ s/(^|[^.])\.\.\.([^.])/\1\\ldots\2/g; # Fix double quotes $line =~ s/(^|\s)\"/\1``/g; $line =~ s/\"(\W|$)/''\1/g; # Fix single quotes $line =~ s/(^|\s)'/\1`/g; if ($line =~ /\"/) { print STDERR "txt2latex: unfixed quote mark on line $count\n"; } print STDOUT $line; } # Footer print STDOUT "\\end{document}\n"; gsl-1.0.8/doc/README0000644000175000017500000000150311201030403011517 0ustar shsh README for gsl/doc .dvi, .ps,.pdf documentation generation This generation has only been brought up to a usable form. It still generates erros along the way. use ./mk_pdf_dvi gsl to update the pdf/dvi/ps documents. The gsl argument merely determines the prefixs; gsl.dvi, etc... It should probably do more. Look at the script above and make them; it simple. special files in this directory. mktexi_inc : added some headers and footers to the output .texi file. This allows more program to operate on it as an individual file. testinfo.tex: copied form the gnu gsl source file. The octave-forge original ended up replacing "_" in function names and such with a overhead period. makeinfo gsl.texi doesn't work now in this directory; but I will let the octave-forge gang continue to build it out of the src directory. gsl-1.0.8/doc/texinfo.tex.max0000755000175000017500000060667711201030403013653 0ustar shsh% texinfo.tex -- TeX macros to handle Texinfo files. % % Load plain if necessary, i.e., if running under initex. \expandafter\ifx\csname fmtname\endcsname\relax\input plain\fi % \def\texinfoversion{1999-09-25.10} % % Copyright (C) 1985, 86, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99 % Free Software Foundation, Inc. % % This texinfo.tex file is free software; you can redistribute it and/or % modify it under the terms of the GNU General Public License as % published by the Free Software Foundation; either version 2, or (at % your option) any later version. % % This texinfo.tex file is distributed in the hope that it will be % useful, but WITHOUT ANY WARRANTY; without even the implied warranty % of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU % General Public License for more details. % % You should have received a copy of the GNU General Public License % along with this texinfo.tex file; see the file COPYING. If not, see % . % % In other words, you are welcome to use, share and improve this program. % You are forbidden to forbid anyone else to use, share and improve % what you give them. Help stamp out software-hoarding! % % Please try the latest version of texinfo.tex before submitting bug % reports; you can get the latest version from: % ftp://ftp.gnu.org/gnu/texinfo.tex % (and all GNU mirrors, see http://www.gnu.org/order/ftp.html) % ftp://texinfo.org/tex/texinfo.tex % ftp://us.ctan.org/macros/texinfo/texinfo.tex % (and all CTAN mirrors, finger ctan@us.ctan.org for a list). % /home/gd/gnu/doc/texinfo.tex on the GNU machines. % The texinfo.tex in any given Texinfo distribution could well be out % of date, so if that's what you're using, please check. % Texinfo has a small home page at http://texinfo.org/. % % Send bug reports to bug-texinfo@gnu.org. Please include including a % complete document in each bug report with which we can reproduce the % problem. Patches are, of course, greatly appreciated. % % To process a Texinfo manual with TeX, it's most reliable to use the % texi2dvi shell script that comes with the distribution. For a simple % manual foo.texi, however, you can get away with this: % tex foo.texi % texindex foo.?? % tex foo.texi % tex foo.texi % dvips foo.dvi -o # or whatever, to process the dvi file; this makes foo.ps. % The extra runs of TeX get the cross-reference information correct. % Sometimes one run after texindex suffices, and sometimes you need more % than two; texi2dvi does it as many times as necessary. % % It is possible to adapt texinfo.tex for other languages. You can get % the existing language-specific files from ftp://ftp.gnu.org/gnu/texinfo/. \message{Loading texinfo [version \texinfoversion]:} % If in a .fmt file, print the version number % and turn on active characters that we couldn't do earlier because % they might have appeared in the input file name. \everyjob{\message{[Texinfo version \texinfoversion]}% \catcode`+=\active \catcode`\_=\active} % Save some parts of plain tex whose names we will redefine. \let\ptexb=\b \let\ptexbullet=\bullet \let\ptexc=\c \let\ptexcomma=\, \let\ptexdot=\. \let\ptexdots=\dots \let\ptexend=\end \let\ptexequiv=\equiv \let\ptexexclam=\! \let\ptexi=\i \let\ptexlbrace=\{ \let\ptexrbrace=\} \let\ptexstar=\* \let\ptext=\t % We never want plain's outer \+ definition in Texinfo. % For @tex, we can use \tabalign. \let\+ = \relax \message{Basics,} \chardef\other=12 % If this character appears in an error message or help string, it % starts a new line in the output. \newlinechar = `^^J % Set up fixed words for English if not already set. \ifx\putwordAppendix\undefined \gdef\putwordAppendix{Appendix}\fi \ifx\putwordChapter\undefined \gdef\putwordChapter{Chapter}\fi \ifx\putwordfile\undefined \gdef\putwordfile{file}\fi \ifx\putwordin\undefined \gdef\putwordin{in}\fi \ifx\putwordIndexIsEmpty\undefined \gdef\putwordIndexIsEmpty{(Index is empty)}\fi \ifx\putwordIndexNonexistent\undefined \gdef\putwordIndexNonexistent{(Index is nonexistent)}\fi \ifx\putwordInfo\undefined \gdef\putwordInfo{Info}\fi \ifx\putwordInstanceVariableof\undefined \gdef\putwordInstanceVariableof{Instance Variable of}\fi \ifx\putwordMethodon\undefined \gdef\putwordMethodon{Method on}\fi \ifx\putwordNoTitle\undefined \gdef\putwordNoTitle{No Title}\fi \ifx\putwordof\undefined \gdef\putwordof{of}\fi \ifx\putwordon\undefined \gdef\putwordon{on}\fi \ifx\putwordpage\undefined \gdef\putwordpage{page}\fi \ifx\putwordsection\undefined \gdef\putwordsection{section}\fi \ifx\putwordSection\undefined \gdef\putwordSection{Section}\fi \ifx\putwordsee\undefined \gdef\putwordsee{see}\fi \ifx\putwordSee\undefined \gdef\putwordSee{See}\fi \ifx\putwordShortTOC\undefined \gdef\putwordShortTOC{Short Contents}\fi \ifx\putwordTOC\undefined \gdef\putwordTOC{Table of Contents}\fi % \ifx\putwordMJan\undefined \gdef\putwordMJan{January}\fi \ifx\putwordMFeb\undefined \gdef\putwordMFeb{February}\fi \ifx\putwordMMar\undefined \gdef\putwordMMar{March}\fi \ifx\putwordMApr\undefined \gdef\putwordMApr{April}\fi \ifx\putwordMMay\undefined \gdef\putwordMMay{May}\fi \ifx\putwordMJun\undefined \gdef\putwordMJun{June}\fi \ifx\putwordMJul\undefined \gdef\putwordMJul{July}\fi \ifx\putwordMAug\undefined \gdef\putwordMAug{August}\fi \ifx\putwordMSep\undefined \gdef\putwordMSep{September}\fi \ifx\putwordMOct\undefined \gdef\putwordMOct{October}\fi \ifx\putwordMNov\undefined \gdef\putwordMNov{November}\fi \ifx\putwordMDec\undefined \gdef\putwordMDec{December}\fi % \ifx\putwordDefmac\undefined \gdef\putwordDefmac{Macro}\fi \ifx\putwordDefspec\undefined \gdef\putwordDefspec{Special Form}\fi \ifx\putwordDefvar\undefined \gdef\putwordDefvar{Variable}\fi \ifx\putwordDefopt\undefined \gdef\putwordDefopt{User Option}\fi \ifx\putwordDeftypevar\undefined\gdef\putwordDeftypevar{Variable}\fi \ifx\putwordDeffunc\undefined \gdef\putwordDeffunc{Function}\fi \ifx\putwordDeftypefun\undefined\gdef\putwordDeftypefun{Function}\fi % Ignore a token. % \def\gobble#1{} \hyphenation{ap-pen-dix} \hyphenation{mini-buf-fer mini-buf-fers} \hyphenation{eshell} \hyphenation{white-space} % Margin to add to right of even pages, to left of odd pages. \newdimen \bindingoffset \newdimen \normaloffset \newdimen\pagewidth \newdimen\pageheight % Sometimes it is convenient to have everything in the transcript file % and nothing on the terminal. We don't just call \tracingall here, % since that produces some useless output on the terminal. % \def\gloggingall{\begingroup \globaldefs = 1 \loggingall \endgroup}% \ifx\eTeXversion\undefined \def\loggingall{\tracingcommands2 \tracingstats2 \tracingpages1 \tracingoutput1 \tracinglostchars1 \tracingmacros2 \tracingparagraphs1 \tracingrestores1 \showboxbreadth\maxdimen\showboxdepth\maxdimen }% \else \def\loggingall{\tracingcommands3 \tracingstats2 \tracingpages1 \tracingoutput1 \tracinglostchars1 \tracingmacros2 \tracingparagraphs1 \tracingrestores1 \tracingscantokens1 \tracingassigns1 \tracingifs1 \tracinggroups1 \tracingnesting2 \showboxbreadth\maxdimen\showboxdepth\maxdimen }% \fi % For @cropmarks command. % Do @cropmarks to get crop marks. % \newif\ifcropmarks \let\cropmarks = \cropmarkstrue % % Dimensions to add cropmarks at corners. % Added by P. A. MacKay, 12 Nov. 1986 % \newdimen\outerhsize \newdimen\outervsize % set by the paper size routines \newdimen\cornerlong \cornerlong=1pc \newdimen\cornerthick \cornerthick=.3pt \newdimen\topandbottommargin \topandbottommargin=.75in % Main output routine. \chardef\PAGE = 255 \output = {\onepageout{\pagecontents\PAGE}} \newbox\headlinebox \newbox\footlinebox % \onepageout takes a vbox as an argument. Note that \pagecontents % does insertions, but you have to call it yourself. \def\onepageout#1{% \ifcropmarks \hoffset=0pt \else \hoffset=\normaloffset \fi % \ifodd\pageno \advance\hoffset by \bindingoffset \else \advance\hoffset by -\bindingoffset\fi % % Do this outside of the \shipout so @code etc. will be expanded in % the headline as they should be, not taken literally (outputting ''code). \setbox\headlinebox = \vbox{\let\hsize=\pagewidth \makeheadline}% \setbox\footlinebox = \vbox{\let\hsize=\pagewidth \makefootline}% % {% % Have to do this stuff outside the \shipout because we want it to % take effect in \write's, yet the group defined by the \vbox ends % before the \shipout runs. % \escapechar = `\\ % use backslash in output files. \indexdummies % don't expand commands in the output. \normalturnoffactive % \ in index entries must not stay \, e.g., if % the page break happens to be in the middle of an example. \shipout\vbox{% \ifcropmarks \vbox to \outervsize\bgroup \hsize = \outerhsize \vskip-\topandbottommargin \vtop to0pt{% \line{\ewtop\hfil\ewtop}% \nointerlineskip \line{% \vbox{\moveleft\cornerthick\nstop}% \hfill \vbox{\moveright\cornerthick\nstop}% }% \vss}% \vskip\topandbottommargin \line\bgroup \hfil % center the page within the outer (page) hsize. \ifodd\pageno\hskip\bindingoffset\fi \vbox\bgroup \fi % \unvbox\headlinebox \pagebody{#1}% \ifdim\ht\footlinebox > 0pt % Only leave this space if the footline is nonempty. % (We lessened \vsize for it in \oddfootingxxx.) % The \baselineskip=24pt in plain's \makefootline has no effect. \vskip 2\baselineskip \unvbox\footlinebox \fi % \ifpdfmakepagedest \pdfmkdest{\the\pageno} \fi % \ifcropmarks \egroup % end of \vbox\bgroup \hfil\egroup % end of (centering) \line\bgroup \vskip\topandbottommargin plus1fill minus1fill \boxmaxdepth = \cornerthick \vbox to0pt{\vss \line{% \vbox{\moveleft\cornerthick\nsbot}% \hfill \vbox{\moveright\cornerthick\nsbot}% }% \nointerlineskip \line{\ewbot\hfil\ewbot}% }% \egroup % \vbox from first cropmarks clause \fi }% end of \shipout\vbox }% end of group with \turnoffactive \advancepageno \ifnum\outputpenalty>-20000 \else\dosupereject\fi } \newinsert\margin \dimen\margin=\maxdimen \def\pagebody#1{\vbox to\pageheight{\boxmaxdepth=\maxdepth #1}} {\catcode`\@ =11 \gdef\pagecontents#1{\ifvoid\topins\else\unvbox\topins\fi % marginal hacks, juha@viisa.uucp (Juha Takala) \ifvoid\margin\else % marginal info is present \rlap{\kern\hsize\vbox to\z@{\kern1pt\box\margin \vss}}\fi \dimen@=\dp#1 \unvbox#1 \ifvoid\footins\else\vskip\skip\footins\footnoterule \unvbox\footins\fi \ifr@ggedbottom \kern-\dimen@ \vfil \fi} } % Here are the rules for the cropmarks. Note that they are % offset so that the space between them is truly \outerhsize or \outervsize % (P. A. MacKay, 12 November, 1986) % \def\ewtop{\vrule height\cornerthick depth0pt width\cornerlong} \def\nstop{\vbox {\hrule height\cornerthick depth\cornerlong width\cornerthick}} \def\ewbot{\vrule height0pt depth\cornerthick width\cornerlong} \def\nsbot{\vbox {\hrule height\cornerlong depth\cornerthick width\cornerthick}} % Parse an argument, then pass it to #1. The argument is the rest of % the input line (except we remove a trailing comment). #1 should be a % macro which expects an ordinary undelimited TeX argument. % \def\parsearg#1{% \let\next = #1% \begingroup \obeylines \futurelet\temp\parseargx } % If the next token is an obeyed space (from an @example environment or % the like), remove it and recurse. Otherwise, we're done. \def\parseargx{% % \obeyedspace is defined far below, after the definition of \sepspaces. \ifx\obeyedspace\temp \expandafter\parseargdiscardspace \else \expandafter\parseargline \fi } % Remove a single space (as the delimiter token to the macro call). {\obeyspaces % \gdef\parseargdiscardspace {\futurelet\temp\parseargx}} {\obeylines % \gdef\parseargline#1^^M{% \endgroup % End of the group started in \parsearg. % % First remove any @c comment, then any @comment. % Result of each macro is put in \toks0. \argremovec #1\c\relax % \expandafter\argremovecomment \the\toks0 \comment\relax % % % Call the caller's macro, saved as \next in \parsearg. \expandafter\next\expandafter{\the\toks0}% }% } % Since all \c{,omment} does is throw away the argument, we can let TeX % do that for us. The \relax here is matched by the \relax in the call % in \parseargline; it could be more or less anything, its purpose is % just to delimit the argument to the \c. \def\argremovec#1\c#2\relax{\toks0 = {#1}} \def\argremovecomment#1\comment#2\relax{\toks0 = {#1}} % \argremovec{,omment} might leave us with trailing spaces, though; e.g., % @end itemize @c foo % will have two active spaces as part of the argument with the % `itemize'. Here we remove all active spaces from #1, and assign the % result to \toks0. % % This loses if there are any *other* active characters besides spaces % in the argument -- _ ^ +, for example -- since they get expanded. % Fortunately, Texinfo does not define any such commands. (If it ever % does, the catcode of the characters in questionwill have to be changed % here.) But this means we cannot call \removeactivespaces as part of % \argremovec{,omment}, since @c uses \parsearg, and thus the argument % that \parsearg gets might well have any character at all in it. % \def\removeactivespaces#1{% \begingroup \ignoreactivespaces \edef\temp{#1}% \global\toks0 = \expandafter{\temp}% \endgroup } % Change the active space to expand to nothing. % \begingroup \obeyspaces \gdef\ignoreactivespaces{\obeyspaces\let =\empty} \endgroup \def\flushcr{\ifx\par\lisppar \def\next##1{}\else \let\next=\relax \fi \next} %% These are used to keep @begin/@end levels from running away %% Call \inENV within environments (after a \begingroup) \newif\ifENV \ENVfalse \def\inENV{\ifENV\relax\else\ENVtrue\fi} \def\ENVcheck{% \ifENV\errmessage{Still within an environment; press RETURN to continue} \endgroup\fi} % This is not perfect, but it should reduce lossage % @begin foo is the same as @foo, for now. \newhelp\EMsimple{Press RETURN to continue.} \outer\def\begin{\parsearg\beginxxx} \def\beginxxx #1{% \expandafter\ifx\csname #1\endcsname\relax {\errhelp=\EMsimple \errmessage{Undefined command @begin #1}}\else \csname #1\endcsname\fi} % @end foo executes the definition of \Efoo. % \def\end{\parsearg\endxxx} \def\endxxx #1{% \removeactivespaces{#1}% \edef\endthing{\the\toks0}% % \expandafter\ifx\csname E\endthing\endcsname\relax \expandafter\ifx\csname \endthing\endcsname\relax % There's no \foo, i.e., no ``environment'' foo. \errhelp = \EMsimple \errmessage{Undefined command `@end \endthing'}% \else \unmatchedenderror\endthing \fi \else % Everything's ok; the right environment has been started. \csname E\endthing\endcsname \fi } % There is an environment #1, but it hasn't been started. Give an error. % \def\unmatchedenderror#1{% \errhelp = \EMsimple \errmessage{This `@end #1' doesn't have a matching `@#1'}% } % Define the control sequence \E#1 to give an unmatched @end error. % \def\defineunmatchedend#1{% \expandafter\def\csname E#1\endcsname{\unmatchedenderror{#1}}% } % Single-spacing is done by various environments (specifically, in % \nonfillstart and \quotations). \newskip\singlespaceskip \singlespaceskip = 12.5pt \def\singlespace{% % Why was this kern here? It messes up equalizing space above and below % environments. --karl, 6may93 %{\advance \baselineskip by -\singlespaceskip %\kern \baselineskip}% \setleading \singlespaceskip } %% Simple single-character @ commands % @@ prints an @ % Kludge this until the fonts are right (grr). \def\@{{\tt\char64}} % This is turned off because it was never documented % and you can use @w{...} around a quote to suppress ligatures. %% Define @` and @' to be the same as ` and ' %% but suppressing ligatures. %\def\`{{`}} %\def\'{{'}} % Used to generate quoted braces. \def\mylbrace {{\tt\char123}} \def\myrbrace {{\tt\char125}} \let\{=\mylbrace \let\}=\myrbrace \begingroup % Definitions to produce actual \{ & \} command in an index. \catcode`\{ = 12 \catcode`\} = 12 \catcode`\[ = 1 \catcode`\] = 2 \catcode`\@ = 0 \catcode`\\ = 12 @gdef@lbracecmd[\{]% @gdef@rbracecmd[\}]% @endgroup % Accents: @, @dotaccent @ringaccent @ubaraccent @udotaccent % Others are defined by plain TeX: @` @' @" @^ @~ @= @v @H. \let\, = \c \let\dotaccent = \. \def\ringaccent#1{{\accent23 #1}} \let\tieaccent = \t \let\ubaraccent = \b \let\udotaccent = \d % Other special characters: @questiondown @exclamdown % Plain TeX defines: @AA @AE @O @OE @L (and lowercase versions) @ss. \def\questiondown{?`} \def\exclamdown{!`} % Dotless i and dotless j, used for accents. \def\imacro{i} \def\jmacro{j} \def\dotless#1{% \def\temp{#1}% \ifx\temp\imacro \ptexi \else\ifx\temp\jmacro \j \else \errmessage{@dotless can be used only with i or j}% \fi\fi } % Be sure we're in horizontal mode when doing a tie, since we make space % equivalent to this in @example-like environments. Otherwise, a space % at the beginning of a line will start with \penalty -- and % since \penalty is valid in vertical mode, we'd end up putting the % penalty on the vertical list instead of in the new paragraph. {\catcode`@ = 11 % Avoid using \@M directly, because that causes trouble % if the definition is written into an index file. \global\let\tiepenalty = \@M \gdef\tie{\leavevmode\penalty\tiepenalty\ } } % @: forces normal size whitespace following. \def\:{\spacefactor=1000 } % @* forces a line break. \def\*{\hfil\break\hbox{}\ignorespaces} % @. is an end-of-sentence period. \def\.{.\spacefactor=3000 } % @! is an end-of-sentence bang. \def\!{!\spacefactor=3000 } % @? is an end-of-sentence query. \def\?{?\spacefactor=3000 } % @w prevents a word break. Without the \leavevmode, @w at the % beginning of a paragraph, when TeX is still in vertical mode, would % produce a whole line of output instead of starting the paragraph. \def\w#1{\leavevmode\hbox{#1}} % @group ... @end group forces ... to be all on one page, by enclosing % it in a TeX vbox. We use \vtop instead of \vbox to construct the box % to keep its height that of a normal line. According to the rules for % \topskip (p.114 of the TeXbook), the glue inserted is % max (\topskip - \ht (first item), 0). If that height is large, % therefore, no glue is inserted, and the space between the headline and % the text is small, which looks bad. % \def\group{\begingroup \ifnum\catcode13=\active \else \errhelp = \groupinvalidhelp \errmessage{@group invalid in context where filling is enabled}% \fi % % The \vtop we start below produces a box with normal height and large % depth; thus, TeX puts \baselineskip glue before it, and (when the % next line of text is done) \lineskip glue after it. (See p.82 of % the TeXbook.) Thus, space below is not quite equal to space % above. But it's pretty close. \def\Egroup{% \egroup % End the \vtop. \endgroup % End the \group. }% % \vtop\bgroup % We have to put a strut on the last line in case the @group is in % the midst of an example, rather than completely enclosing it. % Otherwise, the interline space between the last line of the group % and the first line afterwards is too small. But we can't put the % strut in \Egroup, since there it would be on a line by itself. % Hence this just inserts a strut at the beginning of each line. \everypar = {\strut}% % % Since we have a strut on every line, we don't need any of TeX's % normal interline spacing. \offinterlineskip % % OK, but now we have to do something about blank % lines in the input in @example-like environments, which normally % just turn into \lisppar, which will insert no space now that we've % turned off the interline space. Simplest is to make them be an % empty paragraph. \ifx\par\lisppar \edef\par{\leavevmode \par}% % % Reset ^^M's definition to new definition of \par. \obeylines \fi % % Do @comment since we are called inside an environment such as % @example, where each end-of-line in the input causes an % end-of-line in the output. We don't want the end-of-line after % the `@group' to put extra space in the output. Since @group % should appear on a line by itself (according to the Texinfo % manual), we don't worry about eating any user text. \comment } % % TeX puts in an \escapechar (i.e., `@') at the beginning of the help % message, so this ends up printing `@group can only ...'. % \newhelp\groupinvalidhelp{% group can only be used in environments such as @example,^^J% where each line of input produces a line of output.} % @need space-in-mils % forces a page break if there is not space-in-mils remaining. \newdimen\mil \mil=0.001in \def\need{\parsearg\needx} % Old definition--didn't work. %\def\needx #1{\par % %% This method tries to make TeX break the page naturally %% if the depth of the box does not fit. %{\baselineskip=0pt% %\vtop to #1\mil{\vfil}\kern -#1\mil\nobreak %\prevdepth=-1000pt %}} \def\needx#1{% % Ensure vertical mode, so we don't make a big box in the middle of a % paragraph. \par % % If the @need value is less than one line space, it's useless. \dimen0 = #1\mil \dimen2 = \ht\strutbox \advance\dimen2 by \dp\strutbox \ifdim\dimen0 > \dimen2 % % Do a \strut just to make the height of this box be normal, so the % normal leading is inserted relative to the preceding line. % And a page break here is fine. \vtop to #1\mil{\strut\vfil}% % % TeX does not even consider page breaks if a penalty added to the % main vertical list is 10000 or more. But in order to see if the % empty box we just added fits on the page, we must make it consider % page breaks. On the other hand, we don't want to actually break the % page after the empty box. So we use a penalty of 9999. % % There is an extremely small chance that TeX will actually break the % page at this \penalty, if there are no other feasible breakpoints in % sight. (If the user is using lots of big @group commands, which % almost-but-not-quite fill up a page, TeX will have a hard time doing % good page breaking, for example.) However, I could not construct an % example where a page broke at this \penalty; if it happens in a real % document, then we can reconsider our strategy. \penalty9999 % % Back up by the size of the box, whether we did a page break or not. \kern -#1\mil % % Do not allow a page break right after this kern. \nobreak \fi } % @br forces paragraph break \let\br = \par % @dots{} output an ellipsis using the current font. % We do .5em per period so that it has the same spacing in a typewriter % font as three actual period characters. % \def\dots{% \leavevmode \hbox to 1.5em{% \hskip 0pt plus 0.25fil minus 0.25fil .\hss.\hss.% \hskip 0pt plus 0.5fil minus 0.5fil }% } % @enddots{} is an end-of-sentence ellipsis. % \def\enddots{% \leavevmode \hbox to 2em{% \hskip 0pt plus 0.25fil minus 0.25fil .\hss.\hss.\hss.% \hskip 0pt plus 0.5fil minus 0.5fil }% \spacefactor=3000 } % @page forces the start of a new page % \def\page{\par\vfill\supereject} % @exdent text.... % outputs text on separate line in roman font, starting at standard page margin % This records the amount of indent in the innermost environment. % That's how much \exdent should take out. \newskip\exdentamount % This defn is used inside fill environments such as @defun. \def\exdent{\parsearg\exdentyyy} \def\exdentyyy #1{{\hfil\break\hbox{\kern -\exdentamount{\rm#1}}\hfil\break}} % This defn is used inside nofill environments such as @example. \def\nofillexdent{\parsearg\nofillexdentyyy} \def\nofillexdentyyy #1{{\advance \leftskip by -\exdentamount \leftline{\hskip\leftskip{\rm#1}}}} % @inmargin{TEXT} puts TEXT in the margin next to the current paragraph. \def\inmargin#1{% \strut\vadjust{\nobreak\kern-\strutdepth \vtop to \strutdepth{\baselineskip\strutdepth\vss \llap{\rightskip=\inmarginspacing \vbox{\noindent #1}}\null}}} \newskip\inmarginspacing \inmarginspacing=1cm \def\strutdepth{\dp\strutbox} %\hbox{{\rm#1}}\hfil\break}} % @include file insert text of that file as input. % Allow normal characters that we make active in the argument (a file name). \def\include{\begingroup \catcode`\\=12 \catcode`~=12 \catcode`^=12 \catcode`_=12 \catcode`|=12 \catcode`<=12 \catcode`>=12 \catcode`+=12 \parsearg\includezzz} % Restore active chars for included file. \def\includezzz#1{\endgroup\begingroup % Read the included file in a group so nested @include's work. \def\thisfile{#1}% \input\thisfile \endgroup} \def\thisfile{} % @center line outputs that line, centered \def\center{\parsearg\centerzzz} \def\centerzzz #1{{\advance\hsize by -\leftskip \advance\hsize by -\rightskip \centerline{#1}}} % @sp n outputs n lines of vertical space \def\sp{\parsearg\spxxx} \def\spxxx #1{\vskip #1\baselineskip} % @comment ...line which is ignored... % @c is the same as @comment % @ignore ... @end ignore is another way to write a comment \def\comment{\begingroup \catcode`\^^M=\other% \catcode`\@=\other \catcode`\{=\other \catcode`\}=\other% \commentxxx} {\catcode`\^^M=\other \gdef\commentxxx#1^^M{\endgroup}} \let\c=\comment % @paragraphindent NCHARS % We'll use ems for NCHARS, close enough. % We cannot implement @paragraphindent asis, though. % \def\asisword{asis} % no translation, these are keywords \def\noneword{none} % \def\paragraphindent{\parsearg\doparagraphindent} \def\doparagraphindent#1{% \def\temp{#1}% \ifx\temp\asisword \else \ifx\temp\noneword \defaultparindent = 0pt \else \defaultparindent = #1em \fi \fi \parindent = \defaultparindent } % @exampleindent NCHARS % We'll use ems for NCHARS like @paragraphindent. % It seems @exampleindent asis isn't necessary, but % I preserve it to make it similar to @paragraphindent. \def\exampleindent{\parsearg\doexampleindent} \def\doexampleindent#1{% \def\temp{#1}% \ifx\temp\asisword \else \ifx\temp\noneword \lispnarrowing = 0pt \else \lispnarrowing = #1em \fi \fi } % @asis just yields its argument. Used with @table, for example. % \def\asis#1{#1} % @math means output in math mode. % We don't use $'s directly in the definition of \math because control % sequences like \math are expanded when the toc file is written. Then, % we read the toc file back, the $'s will be normal characters (as they % should be, according to the definition of Texinfo). So we must use a % control sequence to switch into and out of math mode. % % This isn't quite enough for @math to work properly in indices, but it % seems unlikely it will ever be needed there. % \let\implicitmath = $ \def\math#1{\implicitmath #1\implicitmath} % @bullet and @minus need the same treatment as @math, just above. \def\bullet{\implicitmath\ptexbullet\implicitmath} \def\minus{\implicitmath-\implicitmath} % @refill is a no-op. \let\refill=\relax % If working on a large document in chapters, it is convenient to % be able to disable indexing, cross-referencing, and contents, for test runs. % This is done with @novalidate (before @setfilename). % \newif\iflinks \linkstrue % by default we want the aux files. \let\novalidate = \linksfalse % @setfilename is done at the beginning of every texinfo file. % So open here the files we need to have open while reading the input. % This makes it possible to make a .fmt file for texinfo. \def\setfilename{% \iflinks \readauxfile \fi % \openindices needs to do some work in any case. \openindices \fixbackslash % Turn off hack to swallow `\input texinfo'. \global\let\setfilename=\comment % Ignore extra @setfilename cmds. % % If texinfo.cnf is present on the system, read it. % Useful for site-wide @afourpaper, etc. % Just to be on the safe side, close the input stream before the \input. \openin 1 texinfo.cnf \ifeof1 \let\temp=\relax \else \def\temp{\input texinfo.cnf }\fi \closein1 \temp % \comment % Ignore the actual filename. } % Called from \setfilename. % \def\openindices{% \newindex{cp}% \newcodeindex{fn}% \newcodeindex{vr}% \newcodeindex{tp}% \newcodeindex{ky}% \newcodeindex{pg}% } % @bye. \outer\def\bye{\pagealignmacro\tracingstats=1\ptexend} \message{pdf,} % adobe `portable' document format \newcount\tempnum \newcount\lnkcount \newtoks\filename \newcount\filenamelength \newcount\pgn \newtoks\toksA \newtoks\toksB \newtoks\toksC \newtoks\toksD \newbox\boxA \newcount\countA \newif\ifpdf \newif\ifpdfmakepagedest \ifx\pdfoutput\undefined \pdffalse \let\pdfmkdest = \gobble \let\pdfurl = \gobble \let\endlink = \relax \let\linkcolor = \relax \let\pdfmakeoutlines = \relax \else \pdftrue \pdfoutput = 1 \input pdfcolor \def\dopdfimage#1#2#3{% \def\imagewidth{#2}% \def\imageheight{#3}% \ifnum\pdftexversion < 14 \pdfimage \else \pdfximage \fi \ifx\empty\imagewidth\else width \imagewidth \fi \ifx\empty\imageheight\else height \imageheight \fi {#1.pdf}% \ifnum\pdftexversion < 14 \else \pdfrefximage \pdflastximage \fi} \def\pdfmkdest#1{\pdfdest name{#1@} xyz} \def\pdfmkpgn#1{#1@} \let\linkcolor = \Cyan \def\endlink{\Black\pdfendlink} % Adding outlines to PDF; macros for calculating structure of outlines % come from Petr Olsak \def\expnumber#1{\expandafter\ifx\csname#1\endcsname\relax 0% \else \csname#1\endcsname \fi} \def\advancenumber#1{\tempnum=\expnumber{#1}\relax \advance\tempnum by1 \expandafter\xdef\csname#1\endcsname{\the\tempnum}} \def\pdfmakeoutlines{{% \openin 1 \jobname.toc \ifeof 1\else\bgroup \closein 1 \indexnofonts \def\tt{} % thanh's hack / proper braces in bookmarks \edef\mylbrace{\iftrue \string{\else}\fi}\let\{=\mylbrace \edef\myrbrace{\iffalse{\else\string}\fi}\let\}=\myrbrace % \def\chapentry ##1##2##3{} \def\unnumbchapentry ##1##2{} \def\secentry ##1##2##3##4{\advancenumber{chap##2}} \def\unnumbsecentry ##1##2{} \def\subsecentry ##1##2##3##4##5{\advancenumber{sec##2.##3}} \def\unnumbsubsecentry ##1##2{} \def\subsubsecentry ##1##2##3##4##5##6{\advancenumber{subsec##2.##3.##4}} \def\unnumbsubsubsecentry ##1##2{} \input \jobname.toc \def\chapentry ##1##2##3{% \pdfoutline goto name{\pdfmkpgn{##3}}count-\expnumber{chap##2}{##1}} \def\unnumbchapentry ##1##2{% \pdfoutline goto name{\pdfmkpgn{##2}}{##1}} \def\secentry ##1##2##3##4{% \pdfoutline goto name{\pdfmkpgn{##4}}count-\expnumber{sec##2.##3}{##1}} \def\unnumbsecentry ##1##2{% \pdfoutline goto name{\pdfmkpgn{##2}}{##1}} \def\subsecentry ##1##2##3##4##5{% \pdfoutline goto name{\pdfmkpgn{##5}}count-\expnumber{subsec##2.##3.##4}{##1}} \def\unnumbsubsecentry ##1##2{% \pdfoutline goto name{\pdfmkpgn{##2}}{##1}} \def\subsubsecentry ##1##2##3##4##5##6{% \pdfoutline goto name{\pdfmkpgn{##6}}{##1}} \def\unnumbsubsubsecentry ##1##2{% \pdfoutline goto name{\pdfmkpgn{##2}}{##1}} \input \jobname.toc \egroup\fi }} \def\makelinks #1,{% \def\params{#1}\def\E{END}% \ifx\params\E \let\nextmakelinks=\relax \else \let\nextmakelinks=\makelinks \ifnum\lnkcount>0,\fi \picknum{#1}% \startlink attr{/Border [0 0 0]} goto name{\pdfmkpgn{\the\pgn}}% \linkcolor #1% \advance\lnkcount by 1% \endlink \fi \nextmakelinks } \def\picknum#1{\expandafter\pn#1} \def\pn#1{% \def\p{#1}% \ifx\p\lbrace \let\nextpn=\ppn \else \let\nextpn=\ppnn \def\first{#1} \fi \nextpn } \def\ppn#1{\pgn=#1\gobble} \def\ppnn{\pgn=\first} \def\pdfmklnk#1{\lnkcount=0\makelinks #1,END,} \def\addtokens#1#2{\edef\addtoks{\noexpand#1={\the#1#2}}\addtoks} \def\skipspaces#1{\def\PP{#1}\def\D{|}% \ifx\PP\D\let\nextsp\relax \else\let\nextsp\skipspaces \ifx\p\space\else\addtokens{\filename}{\PP}% \advance\filenamelength by 1 \fi \fi \nextsp} \def\getfilename#1{\filenamelength=0\expandafter\skipspaces#1|\relax} \ifnum\pdftexversion < 14 \let \startlink \pdfannotlink \else \let \startlink \pdfstartlink \fi \def\pdfurl#1{% \begingroup \normalturnoffactive\def\@{@}% \leavevmode\Red \startlink attr{/Border [0 0 0]}% user{/Subtype /Link /A << /S /URI /URI (#1) >>}% % #1 \endgroup} \def\pdfgettoks#1.{\setbox\boxA=\hbox{\toksA={#1.}\toksB={}\maketoks}} \def\addtokens#1#2{\edef\addtoks{\noexpand#1={\the#1#2}}\addtoks} \def\adn#1{\addtokens{\toksC}{#1}\global\countA=1\let\next=\maketoks} \def\poptoks#1#2|ENDTOKS|{\let\first=#1\toksD={#1}\toksA={#2}} \def\maketoks{% \expandafter\poptoks\the\toksA|ENDTOKS| \ifx\first0\adn0 \else\ifx\first1\adn1 \else\ifx\first2\adn2 \else\ifx\first3\adn3 \else\ifx\first4\adn4 \else\ifx\first5\adn5 \else\ifx\first6\adn6 \else\ifx\first7\adn7 \else\ifx\first8\adn8 \else\ifx\first9\adn9 \else \ifnum0=\countA\else\makelink\fi \ifx\first.\let\next=\done\else \let\next=\maketoks \addtokens{\toksB}{\the\toksD} \ifx\first,\addtokens{\toksB}{\space}\fi \fi \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi \next} \def\makelink{\addtokens{\toksB}% {\noexpand\pdflink{\the\toksC}}\toksC={}\global\countA=0} \def\pdflink#1{% \startlink attr{/Border [0 0 0]} goto name{\mkpgn{#1}} \linkcolor #1\endlink} \def\mkpgn#1{#1@} \def\done{\edef\st{\global\noexpand\toksA={\the\toksB}}\st} \fi % \ifx\pdfoutput \message{fonts,} % Font-change commands. % Texinfo sort of supports the sans serif font style, which plain TeX does not. % So we set up a \sf analogous to plain's \rm, etc. \newfam\sffam \def\sf{\fam=\sffam \tensf} \let\li = \sf % Sometimes we call it \li, not \sf. % We don't need math for this one. \def\ttsl{\tenttsl} % Use Computer Modern fonts at \magstephalf (11pt). \newcount\mainmagstep \mainmagstep=\magstephalf % Set the font macro #1 to the font named #2, adding on the % specified font prefix (normally `cm'). % #3 is the font's design size, #4 is a scale factor \def\setfont#1#2#3#4{\font#1=\fontprefix#2#3 scaled #4} % Use cm as the default font prefix. % To specify the font prefix, you must define \fontprefix % before you read in texinfo.tex. \ifx\fontprefix\undefined \def\fontprefix{cm} \fi % Support font families that don't use the same naming scheme as CM. \def\rmshape{r} \def\rmbshape{bx} %where the normal face is bold \def\bfshape{b} \def\bxshape{bx} \def\ttshape{tt} \def\ttbshape{tt} \def\ttslshape{sltt} \def\itshape{ti} \def\itbshape{bxti} \def\slshape{sl} \def\slbshape{bxsl} \def\sfshape{ss} \def\sfbshape{ss} \def\scshape{csc} \def\scbshape{csc} \ifx\bigger\relax \let\mainmagstep=\magstep1 \setfont\textrm\rmshape{12}{1000} \setfont\texttt\ttshape{12}{1000} \else \setfont\textrm\rmshape{10}{\mainmagstep} \setfont\texttt\ttshape{10}{\mainmagstep} \fi % Instead of cmb10, you many want to use cmbx10. % cmbx10 is a prettier font on its own, but cmb10 % looks better when embedded in a line with cmr10. \setfont\textbf\bfshape{10}{\mainmagstep} \setfont\textit\itshape{10}{\mainmagstep} \setfont\textsl\slshape{10}{\mainmagstep} \setfont\textsf\sfshape{10}{\mainmagstep} \setfont\textsc\scshape{10}{\mainmagstep} \setfont\textttsl\ttslshape{10}{\mainmagstep} \font\texti=cmmi10 scaled \mainmagstep \font\textsy=cmsy10 scaled \mainmagstep % A few fonts for @defun, etc. \setfont\defbf\bxshape{10}{\magstep1} %was 1314 \setfont\deftt\ttshape{10}{\magstep1} \def\df{\let\tentt=\deftt \let\tenbf = \defbf \bf} % Fonts for indices, footnotes, small examples (9pt). \setfont\smallrm\rmshape{9}{1000} \setfont\smalltt\ttshape{9}{1000} \setfont\smallbf\bfshape{10}{900} \setfont\smallit\itshape{9}{1000} \setfont\smallsl\slshape{9}{1000} \setfont\smallsf\sfshape{9}{1000} \setfont\smallsc\scshape{10}{900} \setfont\smallttsl\ttslshape{10}{900} \font\smalli=cmmi9 \font\smallsy=cmsy9 % Fonts for title page: \setfont\titlerm\rmbshape{12}{\magstep3} \setfont\titleit\itbshape{10}{\magstep4} \setfont\titlesl\slbshape{10}{\magstep4} \setfont\titlett\ttbshape{12}{\magstep3} \setfont\titlettsl\ttslshape{10}{\magstep4} \setfont\titlesf\sfbshape{17}{\magstep1} \let\titlebf=\titlerm \setfont\titlesc\scbshape{10}{\magstep4} \font\titlei=cmmi12 scaled \magstep3 \font\titlesy=cmsy10 scaled \magstep4 \def\authorrm{\secrm} % Chapter (and unnumbered) fonts (17.28pt). \setfont\chaprm\rmbshape{12}{\magstep2} \setfont\chapit\itbshape{10}{\magstep3} \setfont\chapsl\slbshape{10}{\magstep3} \setfont\chaptt\ttbshape{12}{\magstep2} \setfont\chapttsl\ttslshape{10}{\magstep3} \setfont\chapsf\sfbshape{17}{1000} \let\chapbf=\chaprm \setfont\chapsc\scbshape{10}{\magstep3} \font\chapi=cmmi12 scaled \magstep2 \font\chapsy=cmsy10 scaled \magstep3 % Section fonts (14.4pt). \setfont\secrm\rmbshape{12}{\magstep1} \setfont\secit\itbshape{10}{\magstep2} \setfont\secsl\slbshape{10}{\magstep2} \setfont\sectt\ttbshape{12}{\magstep1} \setfont\secttsl\ttslshape{10}{\magstep2} \setfont\secsf\sfbshape{12}{\magstep1} \let\secbf\secrm \setfont\secsc\scbshape{10}{\magstep2} \font\seci=cmmi12 scaled \magstep1 \font\secsy=cmsy10 scaled \magstep2 % \setfont\ssecrm\bxshape{10}{\magstep1} % This size an font looked bad. % \setfont\ssecit\itshape{10}{\magstep1} % The letters were too crowded. % \setfont\ssecsl\slshape{10}{\magstep1} % \setfont\ssectt\ttshape{10}{\magstep1} % \setfont\ssecsf\sfshape{10}{\magstep1} %\setfont\ssecrm\bfshape{10}{1315} % Note the use of cmb rather than cmbx. %\setfont\ssecit\itshape{10}{1315} % Also, the size is a little larger than %\setfont\ssecsl\slshape{10}{1315} % being scaled magstep1. %\setfont\ssectt\ttshape{10}{1315} %\setfont\ssecsf\sfshape{10}{1315} %\let\ssecbf=\ssecrm % Subsection fonts (13.15pt). \setfont\ssecrm\rmbshape{12}{\magstephalf} \setfont\ssecit\itbshape{10}{1315} \setfont\ssecsl\slbshape{10}{1315} \setfont\ssectt\ttbshape{12}{\magstephalf} \setfont\ssecttsl\ttslshape{10}{1315} \setfont\ssecsf\sfbshape{12}{\magstephalf} \let\ssecbf\ssecrm \setfont\ssecsc\scbshape{10}{\magstep1} \font\sseci=cmmi12 scaled \magstephalf \font\ssecsy=cmsy10 scaled 1315 % The smallcaps and symbol fonts should actually be scaled \magstep1.5, % but that is not a standard magnification. % In order for the font changes to affect most math symbols and letters, % we have to define the \textfont of the standard families. Since % texinfo doesn't allow for producing subscripts and superscripts, we % don't bother to reset \scriptfont and \scriptscriptfont (which would % also require loading a lot more fonts). % \def\resetmathfonts{% \textfont0 = \tenrm \textfont1 = \teni \textfont2 = \tensy \textfont\itfam = \tenit \textfont\slfam = \tensl \textfont\bffam = \tenbf \textfont\ttfam = \tentt \textfont\sffam = \tensf } % The font-changing commands redefine the meanings of \tenSTYLE, instead % of just \STYLE. We do this so that font changes will continue to work % in math mode, where it is the current \fam that is relevant in most % cases, not the current font. Plain TeX does \def\bf{\fam=\bffam % \tenbf}, for example. By redefining \tenbf, we obviate the need to % redefine \bf itself. \def\textfonts{% \let\tenrm=\textrm \let\tenit=\textit \let\tensl=\textsl \let\tenbf=\textbf \let\tentt=\texttt \let\smallcaps=\textsc \let\tensf=\textsf \let\teni=\texti \let\tensy=\textsy \let\tenttsl=\textttsl \resetmathfonts} \def\titlefonts{% \let\tenrm=\titlerm \let\tenit=\titleit \let\tensl=\titlesl \let\tenbf=\titlebf \let\tentt=\titlett \let\smallcaps=\titlesc \let\tensf=\titlesf \let\teni=\titlei \let\tensy=\titlesy \let\tenttsl=\titlettsl \resetmathfonts \setleading{25pt}} \def\titlefont#1{{\titlefonts\rm #1}} \def\chapfonts{% \let\tenrm=\chaprm \let\tenit=\chapit \let\tensl=\chapsl \let\tenbf=\chapbf \let\tentt=\chaptt \let\smallcaps=\chapsc \let\tensf=\chapsf \let\teni=\chapi \let\tensy=\chapsy \let\tenttsl=\chapttsl \resetmathfonts \setleading{19pt}} \def\secfonts{% \let\tenrm=\secrm \let\tenit=\secit \let\tensl=\secsl \let\tenbf=\secbf \let\tentt=\sectt \let\smallcaps=\secsc \let\tensf=\secsf \let\teni=\seci \let\tensy=\secsy \let\tenttsl=\secttsl \resetmathfonts \setleading{16pt}} \def\subsecfonts{% \let\tenrm=\ssecrm \let\tenit=\ssecit \let\tensl=\ssecsl \let\tenbf=\ssecbf \let\tentt=\ssectt \let\smallcaps=\ssecsc \let\tensf=\ssecsf \let\teni=\sseci \let\tensy=\ssecsy \let\tenttsl=\ssecttsl \resetmathfonts \setleading{15pt}} \let\subsubsecfonts = \subsecfonts % Maybe make sssec fonts scaled magstephalf? \def\smallfonts{% \let\tenrm=\smallrm \let\tenit=\smallit \let\tensl=\smallsl \let\tenbf=\smallbf \let\tentt=\smalltt \let\smallcaps=\smallsc \let\tensf=\smallsf \let\teni=\smalli \let\tensy=\smallsy \let\tenttsl=\smallttsl \resetmathfonts \setleading{11pt}} % Set up the default fonts, so we can use them for creating boxes. % \textfonts % Define these so they can be easily changed for other fonts. \def\angleleft{$\langle$} \def\angleright{$\rangle$} % Count depth in font-changes, for error checks \newcount\fontdepth \fontdepth=0 % Fonts for short table of contents. \setfont\shortcontrm\rmshape{12}{1000} \setfont\shortcontbf\bxshape{12}{1000} \setfont\shortcontsl\slshape{12}{1000} %% Add scribe-like font environments, plus @l for inline lisp (usually sans %% serif) and @ii for TeX italic % \smartitalic{ARG} outputs arg in italics, followed by an italic correction % unless the following character is such as not to need one. \def\smartitalicx{\ifx\next,\else\ifx\next-\else\ifx\next.\else\/\fi\fi\fi} \def\smartslanted#1{{\sl #1}\futurelet\next\smartitalicx} \def\smartitalic#1{{\it #1}\futurelet\next\smartitalicx} \let\i=\smartitalic \let\var=\smartslanted \let\dfn=\smartslanted \let\emph=\smartitalic \let\cite=\smartslanted \def\b#1{{\bf #1}} \let\strong=\b % We can't just use \exhyphenpenalty, because that only has effect at % the end of a paragraph. Restore normal hyphenation at the end of the % group within which \nohyphenation is presumably called. % \def\nohyphenation{\hyphenchar\font = -1 \aftergroup\restorehyphenation} \def\restorehyphenation{\hyphenchar\font = `- } \def\t#1{% {\tt \rawbackslash \frenchspacing #1}% \null } \let\ttfont=\t \def\samp#1{`\tclose{#1}'\null} \setfont\keyrm\rmshape{8}{1000} \font\keysy=cmsy9 \def\key#1{{\keyrm\textfont2=\keysy \leavevmode\hbox{% \raise0.4pt\hbox{\angleleft}\kern-.08em\vtop{% \vbox{\hrule\kern-0.4pt \hbox{\raise0.4pt\hbox{\vphantom{\angleleft}}#1}}% \kern-0.4pt\hrule}% \kern-.06em\raise0.4pt\hbox{\angleright}}}} % The old definition, with no lozenge: %\def\key #1{{\ttsl \nohyphenation \uppercase{#1}}\null} \def\ctrl #1{{\tt \rawbackslash \hat}#1} % @file, @option are the same as @samp. \let\file=\samp \let\option=\samp % @code is a modification of @t, % which makes spaces the same size as normal in the surrounding text. \def\tclose#1{% {% % Change normal interword space to be same as for the current font. \spaceskip = \fontdimen2\font % % Switch to typewriter. \tt % % But `\ ' produces the large typewriter interword space. \def\ {{\spaceskip = 0pt{} }}% % % Turn off hyphenation. \nohyphenation % \rawbackslash \frenchspacing #1% }% \null } % We *must* turn on hyphenation at `-' and `_' in \code. % Otherwise, it is too hard to avoid overfull hboxes % in the Emacs manual, the Library manual, etc. % Unfortunately, TeX uses one parameter (\hyphenchar) to control % both hyphenation at - and hyphenation within words. % We must therefore turn them both off (\tclose does that) % and arrange explicitly to hyphenate at a dash. % -- rms. { \catcode`\-=\active \catcode`\_=\active % \global\def\code{\begingroup \catcode`\-=\active \let-\codedash \catcode`\_=\active \let_\codeunder \codex } % % If we end up with any active - characters when handling the index, % just treat them as a normal -. \global\def\indexbreaks{\catcode`\-=\active \let-\realdash} } \def\realdash{-} \def\codedash{-\discretionary{}{}{}} \def\codeunder{\ifusingtt{\normalunderscore\discretionary{}{}{}}{\_}} \def\codex #1{\tclose{#1}\endgroup} %\let\exp=\tclose %Was temporary % @kbd is like @code, except that if the argument is just one @key command, % then @kbd has no effect. % @kbdinputstyle -- arg is `distinct' (@kbd uses slanted tty font always), % `example' (@kbd uses ttsl only inside of @example and friends), % or `code' (@kbd uses normal tty font always). \def\kbdinputstyle{\parsearg\kbdinputstylexxx} \def\kbdinputstylexxx#1{% \def\arg{#1}% \ifx\arg\worddistinct \gdef\kbdexamplefont{\ttsl}\gdef\kbdfont{\ttsl}% \else\ifx\arg\wordexample \gdef\kbdexamplefont{\ttsl}\gdef\kbdfont{\tt}% \else\ifx\arg\wordcode \gdef\kbdexamplefont{\tt}\gdef\kbdfont{\tt}% \fi\fi\fi } \def\worddistinct{distinct} \def\wordexample{example} \def\wordcode{code} % Default is kbdinputdistinct. (Too much of a hassle to call the macro, % the catcodes are wrong for parsearg to work.) \gdef\kbdexamplefont{\ttsl}\gdef\kbdfont{\ttsl} \def\xkey{\key} \def\kbdfoo#1#2#3\par{\def\one{#1}\def\three{#3}\def\threex{??}% \ifx\one\xkey\ifx\threex\three \key{#2}% \else{\tclose{\kbdfont\look}}\fi \else{\tclose{\kbdfont\look}}\fi} % For @url, @env, @command quotes seem unnecessary, so use \code. \let\url=\code \let\env=\code \let\command=\code % @uref (abbreviation for `urlref') takes an optional (comma-separated) % second argument specifying the text to display and an optional third % arg as text to display instead of (rather than in addition to) the url % itself. First (mandatory) arg is the url. Perhaps eventually put in % a hypertex \special here. % \def\uref#1{\douref #1,,,\finish} \def\douref#1,#2,#3,#4\finish{\begingroup \unsepspaces \pdfurl{#1}% \setbox0 = \hbox{\ignorespaces #3}% \ifdim\wd0 > 0pt \unhbox0 % third arg given, show only that \else \setbox0 = \hbox{\ignorespaces #2}% \ifdim\wd0 > 0pt \ifpdf \unhbox0 % PDF: 2nd arg given, show only it \else \unhbox0\ (\code{#1})% DVI: 2nd arg given, show both it and url \fi \else \code{#1}% only url given, so show it \fi \fi \endlink \endgroup} % rms does not like angle brackets --karl, 17may97. % So now @email is just like @uref, unless we are pdf. % %\def\email#1{\angleleft{\tt #1}\angleright} \ifpdf \def\email#1{\doemail#1,,\finish} \def\doemail#1,#2,#3\finish{\begingroup \unsepspaces \pdfurl{mailto:#1}% \setbox0 = \hbox{\ignorespaces #2}% \ifdim\wd0>0pt\unhbox0\else\code{#1}\fi \endlink \endgroup} \else \let\email=\uref \fi % Check if we are currently using a typewriter font. Since all the % Computer Modern typewriter fonts have zero interword stretch (and % shrink), and it is reasonable to expect all typewriter fonts to have % this property, we can check that font parameter. % \def\ifmonospace{\ifdim\fontdimen3\font=0pt } % Typeset a dimension, e.g., `in' or `pt'. The only reason for the % argument is to make the input look right: @dmn{pt} instead of @dmn{}pt. % \def\dmn#1{\thinspace #1} \def\kbd#1{\def\look{#1}\expandafter\kbdfoo\look??\par} % @l was never documented to mean ``switch to the Lisp font'', % and it is not used as such in any manual I can find. We need it for % Polish suppressed-l. --karl, 22sep96. %\def\l#1{{\li #1}\null} % Explicit font changes: @r, @sc, undocumented @ii. \def\r#1{{\rm #1}} % roman font \def\sc#1{{\smallcaps#1}} % smallcaps font \def\ii#1{{\it #1}} % italic font % @acronym downcases the argument and prints in smallcaps. \def\acronym#1{{\smallcaps \lowercase{#1}}} % @pounds{} is a sterling sign. \def\pounds{{\it\$}} \message{page headings,} \newskip\titlepagetopglue \titlepagetopglue = 1.5in \newskip\titlepagebottomglue \titlepagebottomglue = 2pc % First the title page. Must do @settitle before @titlepage. \newif\ifseenauthor \newif\iffinishedtitlepage % Do an implicit @contents or @shortcontents after @end titlepage if the % user says @setcontentsaftertitlepage or @setshortcontentsaftertitlepage. % \newif\ifsetcontentsaftertitlepage \let\setcontentsaftertitlepage = \setcontentsaftertitlepagetrue \newif\ifsetshortcontentsaftertitlepage \let\setshortcontentsaftertitlepage = \setshortcontentsaftertitlepagetrue \def\shorttitlepage{\parsearg\shorttitlepagezzz} \def\shorttitlepagezzz #1{\begingroup\hbox{}\vskip 1.5in \chaprm \centerline{#1}% \endgroup\page\hbox{}\page} \def\titlepage{\begingroup \parindent=0pt \textfonts \let\subtitlerm=\tenrm \def\subtitlefont{\subtitlerm \normalbaselineskip = 13pt \normalbaselines}% % \def\authorfont{\authorrm \normalbaselineskip = 16pt \normalbaselines}% % % Leave some space at the very top of the page. \vglue\titlepagetopglue % % Now you can print the title using @title. \def\title{\parsearg\titlezzz}% \def\titlezzz##1{\leftline{\titlefonts\rm ##1} % print a rule at the page bottom also. \finishedtitlepagefalse \vskip4pt \hrule height 4pt width \hsize \vskip4pt}% % No rule at page bottom unless we print one at the top with @title. \finishedtitlepagetrue % % Now you can put text using @subtitle. \def\subtitle{\parsearg\subtitlezzz}% \def\subtitlezzz##1{{\subtitlefont \rightline{##1}}}% % % @author should come last, but may come many times. \def\author{\parsearg\authorzzz}% \def\authorzzz##1{\ifseenauthor\else\vskip 0pt plus 1filll\seenauthortrue\fi {\authorfont \leftline{##1}}}% % % Most title ``pages'' are actually two pages long, with space % at the top of the second. We don't want the ragged left on the second. \let\oldpage = \page \def\page{% \iffinishedtitlepage\else \finishtitlepage \fi \oldpage \let\page = \oldpage \hbox{}}% % \def\page{\oldpage \hbox{}} } \def\Etitlepage{% \iffinishedtitlepage\else \finishtitlepage \fi % It is important to do the page break before ending the group, % because the headline and footline are only empty inside the group. % If we use the new definition of \page, we always get a blank page % after the title page, which we certainly don't want. \oldpage \endgroup % % If they want short, they certainly want long too. \ifsetshortcontentsaftertitlepage \shortcontents \contents \global\let\shortcontents = \relax \global\let\contents = \relax \fi % \ifsetcontentsaftertitlepage \contents \global\let\contents = \relax \global\let\shortcontents = \relax \fi % \ifpdf \pdfmakepagedesttrue \fi % \HEADINGSon } \def\finishtitlepage{% \vskip4pt \hrule height 2pt width \hsize \vskip\titlepagebottomglue \finishedtitlepagetrue } %%% Set up page headings and footings. \let\thispage=\folio \newtoks\evenheadline % headline on even pages \newtoks\oddheadline % headline on odd pages \newtoks\evenfootline % footline on even pages \newtoks\oddfootline % footline on odd pages % Now make Tex use those variables \headline={{\textfonts\rm \ifodd\pageno \the\oddheadline \else \the\evenheadline \fi}} \footline={{\textfonts\rm \ifodd\pageno \the\oddfootline \else \the\evenfootline \fi}\HEADINGShook} \let\HEADINGShook=\relax % Commands to set those variables. % For example, this is what @headings on does % @evenheading @thistitle|@thispage|@thischapter % @oddheading @thischapter|@thispage|@thistitle % @evenfooting @thisfile|| % @oddfooting ||@thisfile \def\evenheading{\parsearg\evenheadingxxx} \def\oddheading{\parsearg\oddheadingxxx} \def\everyheading{\parsearg\everyheadingxxx} \def\evenfooting{\parsearg\evenfootingxxx} \def\oddfooting{\parsearg\oddfootingxxx} \def\everyfooting{\parsearg\everyfootingxxx} {\catcode`\@=0 % \gdef\evenheadingxxx #1{\evenheadingyyy #1@|@|@|@|\finish} \gdef\evenheadingyyy #1@|#2@|#3@|#4\finish{% \global\evenheadline={\rlap{\centerline{#2}}\line{#1\hfil#3}}} \gdef\oddheadingxxx #1{\oddheadingyyy #1@|@|@|@|\finish} \gdef\oddheadingyyy #1@|#2@|#3@|#4\finish{% \global\oddheadline={\rlap{\centerline{#2}}\line{#1\hfil#3}}} \gdef\everyheadingxxx#1{\oddheadingxxx{#1}\evenheadingxxx{#1}}% \gdef\evenfootingxxx #1{\evenfootingyyy #1@|@|@|@|\finish} \gdef\evenfootingyyy #1@|#2@|#3@|#4\finish{% \global\evenfootline={\rlap{\centerline{#2}}\line{#1\hfil#3}}} \gdef\oddfootingxxx #1{\oddfootingyyy #1@|@|@|@|\finish} \gdef\oddfootingyyy #1@|#2@|#3@|#4\finish{% \global\oddfootline = {\rlap{\centerline{#2}}\line{#1\hfil#3}}% % % Leave some space for the footline. Hopefully ok to assume % @evenfooting will not be used by itself. \global\advance\pageheight by -\baselineskip \global\advance\vsize by -\baselineskip } \gdef\everyfootingxxx#1{\oddfootingxxx{#1}\evenfootingxxx{#1}} % }% unbind the catcode of @. % @headings double turns headings on for double-sided printing. % @headings single turns headings on for single-sided printing. % @headings off turns them off. % @headings on same as @headings double, retained for compatibility. % @headings after turns on double-sided headings after this page. % @headings doubleafter turns on double-sided headings after this page. % @headings singleafter turns on single-sided headings after this page. % By default, they are off at the start of a document, % and turned `on' after @end titlepage. \def\headings #1 {\csname HEADINGS#1\endcsname} \def\HEADINGSoff{ \global\evenheadline={\hfil} \global\evenfootline={\hfil} \global\oddheadline={\hfil} \global\oddfootline={\hfil}} \HEADINGSoff % When we turn headings on, set the page number to 1. % For double-sided printing, put current file name in lower left corner, % chapter name on inside top of right hand pages, document % title on inside top of left hand pages, and page numbers on outside top % edge of all pages. \def\HEADINGSdouble{ \global\pageno=1 \global\evenfootline={\hfil} \global\oddfootline={\hfil} \global\evenheadline={\line{\folio\hfil\thistitle}} \global\oddheadline={\line{\thischapter\hfil\folio}} \global\let\contentsalignmacro = \chapoddpage } \let\contentsalignmacro = \chappager % For single-sided printing, chapter title goes across top left of page, % page number on top right. \def\HEADINGSsingle{ \global\pageno=1 \global\evenfootline={\hfil} \global\oddfootline={\hfil} \global\evenheadline={\line{\thischapter\hfil\folio}} \global\oddheadline={\line{\thischapter\hfil\folio}} \global\let\contentsalignmacro = \chappager } \def\HEADINGSon{\HEADINGSdouble} \def\HEADINGSafter{\let\HEADINGShook=\HEADINGSdoublex} \let\HEADINGSdoubleafter=\HEADINGSafter \def\HEADINGSdoublex{% \global\evenfootline={\hfil} \global\oddfootline={\hfil} \global\evenheadline={\line{\folio\hfil\thistitle}} \global\oddheadline={\line{\thischapter\hfil\folio}} \global\let\contentsalignmacro = \chapoddpage } \def\HEADINGSsingleafter{\let\HEADINGShook=\HEADINGSsinglex} \def\HEADINGSsinglex{% \global\evenfootline={\hfil} \global\oddfootline={\hfil} \global\evenheadline={\line{\thischapter\hfil\folio}} \global\oddheadline={\line{\thischapter\hfil\folio}} \global\let\contentsalignmacro = \chappager } % Subroutines used in generating headings % Produces Day Month Year style of output. \def\today{% \number\day\space \ifcase\month \or\putwordMJan\or\putwordMFeb\or\putwordMMar\or\putwordMApr \or\putwordMMay\or\putwordMJun\or\putwordMJul\or\putwordMAug \or\putwordMSep\or\putwordMOct\or\putwordMNov\or\putwordMDec \fi \space\number\year} % @settitle line... specifies the title of the document, for headings. % It generates no output of its own. \def\thistitle{\putwordNoTitle} \def\settitle{\parsearg\settitlezzz} \def\settitlezzz #1{\gdef\thistitle{#1}} \message{tables,} % Tables -- @table, @ftable, @vtable, @item(x), @kitem(x), @xitem(x). % default indentation of table text \newdimen\tableindent \tableindent=.8in % default indentation of @itemize and @enumerate text \newdimen\itemindent \itemindent=.3in % margin between end of table item and start of table text. \newdimen\itemmargin \itemmargin=.1in % used internally for \itemindent minus \itemmargin \newdimen\itemmax % Note @table, @vtable, and @vtable define @item, @itemx, etc., with % these defs. % They also define \itemindex % to index the item name in whatever manner is desired (perhaps none). \newif\ifitemxneedsnegativevskip \def\itemxpar{\par\ifitemxneedsnegativevskip\nobreak\vskip-\parskip\nobreak\fi} \def\internalBitem{\smallbreak \parsearg\itemzzz} \def\internalBitemx{\itemxpar \parsearg\itemzzz} \def\internalBxitem "#1"{\def\xitemsubtopix{#1} \smallbreak \parsearg\xitemzzz} \def\internalBxitemx "#1"{\def\xitemsubtopix{#1} \itemxpar \parsearg\xitemzzz} \def\internalBkitem{\smallbreak \parsearg\kitemzzz} \def\internalBkitemx{\itemxpar \parsearg\kitemzzz} \def\kitemzzz #1{\dosubind {kw}{\code{#1}}{for {\bf \lastfunction}}% \itemzzz {#1}} \def\xitemzzz #1{\dosubind {kw}{\code{#1}}{for {\bf \xitemsubtopic}}% \itemzzz {#1}} \def\itemzzz #1{\begingroup % \advance\hsize by -\rightskip \advance\hsize by -\tableindent \setbox0=\hbox{\itemfont{#1}}% \itemindex{#1}% \nobreak % This prevents a break before @itemx. % % If the item text does not fit in the space we have, put it on a line % by itself, and do not allow a page break either before or after that % line. We do not start a paragraph here because then if the next % command is, e.g., @kindex, the whatsit would get put into the % horizontal list on a line by itself, resulting in extra blank space. \ifdim \wd0>\itemmax % % Make this a paragraph so we get the \parskip glue and wrapping, % but leave it ragged-right. \begingroup \advance\leftskip by-\tableindent \advance\hsize by\tableindent \advance\rightskip by0pt plus1fil \leavevmode\unhbox0\par \endgroup % % We're going to be starting a paragraph, but we don't want the % \parskip glue -- logically it's part of the @item we just started. \nobreak \vskip-\parskip % % Stop a page break at the \parskip glue coming up. Unfortunately % we can't prevent a possible page break at the following % \baselineskip glue. \nobreak \endgroup \itemxneedsnegativevskipfalse \else % The item text fits into the space. Start a paragraph, so that the % following text (if any) will end up on the same line. \noindent % Do this with kerns and \unhbox so that if there is a footnote in % the item text, it can migrate to the main vertical list and % eventually be printed. \nobreak\kern-\tableindent \dimen0 = \itemmax \advance\dimen0 by \itemmargin \advance\dimen0 by -\wd0 \unhbox0 \nobreak\kern\dimen0 \endgroup \itemxneedsnegativevskiptrue \fi } \def\item{\errmessage{@item while not in a table}} \def\itemx{\errmessage{@itemx while not in a table}} \def\kitem{\errmessage{@kitem while not in a table}} \def\kitemx{\errmessage{@kitemx while not in a table}} \def\xitem{\errmessage{@xitem while not in a table}} \def\xitemx{\errmessage{@xitemx while not in a table}} % Contains a kludge to get @end[description] to work. \def\description{\tablez{\dontindex}{1}{}{}{}{}} % @table, @ftable, @vtable. \def\table{\begingroup\inENV\obeylines\obeyspaces\tablex} {\obeylines\obeyspaces% \gdef\tablex #1^^M{% \tabley\dontindex#1 \endtabley}} \def\ftable{\begingroup\inENV\obeylines\obeyspaces\ftablex} {\obeylines\obeyspaces% \gdef\ftablex #1^^M{% \tabley\fnitemindex#1 \endtabley \def\Eftable{\endgraf\afterenvbreak\endgroup}% \let\Etable=\relax}} \def\vtable{\begingroup\inENV\obeylines\obeyspaces\vtablex} {\obeylines\obeyspaces% \gdef\vtablex #1^^M{% \tabley\vritemindex#1 \endtabley \def\Evtable{\endgraf\afterenvbreak\endgroup}% \let\Etable=\relax}} \def\dontindex #1{} \def\fnitemindex #1{\doind {fn}{\code{#1}}}% \def\vritemindex #1{\doind {vr}{\code{#1}}}% {\obeyspaces % \gdef\tabley#1#2 #3 #4 #5 #6 #7\endtabley{\endgroup% \tablez{#1}{#2}{#3}{#4}{#5}{#6}}} \def\tablez #1#2#3#4#5#6{% \aboveenvbreak % \begingroup % \def\Edescription{\Etable}% Necessary kludge. \let\itemindex=#1% \ifnum 0#3>0 \advance \leftskip by #3\mil \fi % \ifnum 0#4>0 \tableindent=#4\mil \fi % \ifnum 0#5>0 \advance \rightskip by #5\mil \fi % \def\itemfont{#2}% \itemmax=\tableindent % \advance \itemmax by -\itemmargin % \advance \leftskip by \tableindent % \exdentamount=\tableindent \parindent = 0pt \parskip = \smallskipamount \ifdim \parskip=0pt \parskip=2pt \fi% \def\Etable{\endgraf\afterenvbreak\endgroup}% \let\item = \internalBitem % \let\itemx = \internalBitemx % \let\kitem = \internalBkitem % \let\kitemx = \internalBkitemx % \let\xitem = \internalBxitem % \let\xitemx = \internalBxitemx % } % This is the counter used by @enumerate, which is really @itemize \newcount \itemno \def\itemize{\parsearg\itemizezzz} \def\itemizezzz #1{% \begingroup % ended by the @end itemize \itemizey {#1}{\Eitemize} } \def\itemizey #1#2{% \aboveenvbreak % \itemmax=\itemindent % \advance \itemmax by -\itemmargin % \advance \leftskip by \itemindent % \exdentamount=\itemindent \parindent = 0pt % \parskip = \smallskipamount % \ifdim \parskip=0pt \parskip=2pt \fi% \def#2{\endgraf\afterenvbreak\endgroup}% \def\itemcontents{#1}% \let\item=\itemizeitem} % Set sfcode to normal for the chars that usually have another value. % These are `.?!:;,' \def\frenchspacing{\sfcode46=1000 \sfcode63=1000 \sfcode33=1000 \sfcode58=1000 \sfcode59=1000 \sfcode44=1000 } % \splitoff TOKENS\endmark defines \first to be the first token in % TOKENS, and \rest to be the remainder. % \def\splitoff#1#2\endmark{\def\first{#1}\def\rest{#2}}% % Allow an optional argument of an uppercase letter, lowercase letter, % or number, to specify the first label in the enumerated list. No % argument is the same as `1'. % \def\enumerate{\parsearg\enumeratezzz} \def\enumeratezzz #1{\enumeratey #1 \endenumeratey} \def\enumeratey #1 #2\endenumeratey{% \begingroup % ended by the @end enumerate % % If we were given no argument, pretend we were given `1'. \def\thearg{#1}% \ifx\thearg\empty \def\thearg{1}\fi % % Detect if the argument is a single token. If so, it might be a % letter. Otherwise, the only valid thing it can be is a number. % (We will always have one token, because of the test we just made. % This is a good thing, since \splitoff doesn't work given nothing at % all -- the first parameter is undelimited.) \expandafter\splitoff\thearg\endmark \ifx\rest\empty % Only one token in the argument. It could still be anything. % A ``lowercase letter'' is one whose \lccode is nonzero. % An ``uppercase letter'' is one whose \lccode is both nonzero, and % not equal to itself. % Otherwise, we assume it's a number. % % We need the \relax at the end of the \ifnum lines to stop TeX from % continuing to look for a . % \ifnum\lccode\expandafter`\thearg=0\relax \numericenumerate % a number (we hope) \else % It's a letter. \ifnum\lccode\expandafter`\thearg=\expandafter`\thearg\relax \lowercaseenumerate % lowercase letter \else \uppercaseenumerate % uppercase letter \fi \fi \else % Multiple tokens in the argument. We hope it's a number. \numericenumerate \fi } % An @enumerate whose labels are integers. The starting integer is % given in \thearg. % \def\numericenumerate{% \itemno = \thearg \startenumeration{\the\itemno}% } % The starting (lowercase) letter is in \thearg. \def\lowercaseenumerate{% \itemno = \expandafter`\thearg \startenumeration{% % Be sure we're not beyond the end of the alphabet. \ifnum\itemno=0 \errmessage{No more lowercase letters in @enumerate; get a bigger alphabet}% \fi \char\lccode\itemno }% } % The starting (uppercase) letter is in \thearg. \def\uppercaseenumerate{% \itemno = \expandafter`\thearg \startenumeration{% % Be sure we're not beyond the end of the alphabet. \ifnum\itemno=0 \errmessage{No more uppercase letters in @enumerate; get a bigger alphabet} \fi \char\uccode\itemno }% } % Call itemizey, adding a period to the first argument and supplying the % common last two arguments. Also subtract one from the initial value in % \itemno, since @item increments \itemno. % \def\startenumeration#1{% \advance\itemno by -1 \itemizey{#1.}\Eenumerate\flushcr } % @alphaenumerate and @capsenumerate are abbreviations for giving an arg % to @enumerate. % \def\alphaenumerate{\enumerate{a}} \def\capsenumerate{\enumerate{A}} \def\Ealphaenumerate{\Eenumerate} \def\Ecapsenumerate{\Eenumerate} % Definition of @item while inside @itemize. \def\itemizeitem{% \advance\itemno by 1 {\let\par=\endgraf \smallbreak}% \ifhmode \errmessage{In hmode at itemizeitem}\fi {\parskip=0in \hskip 0pt \hbox to 0pt{\hss \itemcontents\hskip \itemmargin}% \vadjust{\penalty 1200}}% \flushcr} % @multitable macros % Amy Hendrickson, 8/18/94, 3/6/96 % % @multitable ... @end multitable will make as many columns as desired. % Contents of each column will wrap at width given in preamble. Width % can be specified either with sample text given in a template line, % or in percent of \hsize, the current width of text on page. % Table can continue over pages but will only break between lines. % To make preamble: % % Either define widths of columns in terms of percent of \hsize: % @multitable @columnfractions .25 .3 .45 % @item ... % % Numbers following @columnfractions are the percent of the total % current hsize to be used for each column. You may use as many % columns as desired. % Or use a template: % @multitable {Column 1 template} {Column 2 template} {Column 3 template} % @item ... % using the widest term desired in each column. % % For those who want to use more than one line's worth of words in % the preamble, break the line within one argument and it % will parse correctly, i.e., % % @multitable {Column 1 template} {Column 2 template} {Column 3 % template} % Not: % @multitable {Column 1 template} {Column 2 template} % {Column 3 template} % Each new table line starts with @item, each subsequent new column % starts with @tab. Empty columns may be produced by supplying @tab's % with nothing between them for as many times as empty columns are needed, % ie, @tab@tab@tab will produce two empty columns. % @item, @tab, @multitable or @end multitable do not need to be on their % own lines, but it will not hurt if they are. % Sample multitable: % @multitable {Column 1 template} {Column 2 template} {Column 3 template} % @item first col stuff @tab second col stuff @tab third col % @item % first col stuff % @tab % second col stuff % @tab % third col % @item first col stuff @tab second col stuff % @tab Many paragraphs of text may be used in any column. % % They will wrap at the width determined by the template. % @item@tab@tab This will be in third column. % @end multitable % Default dimensions may be reset by user. % @multitableparskip is vertical space between paragraphs in table. % @multitableparindent is paragraph indent in table. % @multitablecolmargin is horizontal space to be left between columns. % @multitablelinespace is space to leave between table items, baseline % to baseline. % 0pt means it depends on current normal line spacing. % \newskip\multitableparskip \newskip\multitableparindent \newdimen\multitablecolspace \newskip\multitablelinespace \multitableparskip=0pt \multitableparindent=6pt \multitablecolspace=12pt \multitablelinespace=0pt % Macros used to set up halign preamble: % \let\endsetuptable\relax \def\xendsetuptable{\endsetuptable} \let\columnfractions\relax \def\xcolumnfractions{\columnfractions} \newif\ifsetpercent % #1 is the part of the @columnfraction before the decimal point, which % is presumably either 0 or the empty string (but we don't check, we % just throw it away). #2 is the decimal part, which we use as the % percent of \hsize for this column. \def\pickupwholefraction#1.#2 {% \global\advance\colcount by 1 \expandafter\xdef\csname col\the\colcount\endcsname{.#2\hsize}% \setuptable } \newcount\colcount \def\setuptable#1{% \def\firstarg{#1}% \ifx\firstarg\xendsetuptable \let\go = \relax \else \ifx\firstarg\xcolumnfractions \global\setpercenttrue \else \ifsetpercent \let\go\pickupwholefraction \else \global\advance\colcount by 1 \setbox0=\hbox{#1\unskip }% Add a normal word space as a separator; % typically that is always in the input, anyway. \expandafter\xdef\csname col\the\colcount\endcsname{\the\wd0}% \fi \fi \ifx\go\pickupwholefraction % Put the argument back for the \pickupwholefraction call, so % we'll always have a period there to be parsed. \def\go{\pickupwholefraction#1}% \else \let\go = \setuptable \fi% \fi \go } % This used to have \hskip1sp. But then the space in a template line is % not enough. That is bad. So let's go back to just & until we % encounter the problem it was intended to solve again. % --karl, nathan@acm.org, 20apr99. \def\tab{&} % @multitable ... @end multitable definitions: % \def\multitable{\parsearg\dotable} \def\dotable#1{\bgroup \vskip\parskip \let\item\crcr \tolerance=9500 \hbadness=9500 \setmultitablespacing \parskip=\multitableparskip \parindent=\multitableparindent \overfullrule=0pt \global\colcount=0 \def\Emultitable{\global\setpercentfalse\cr\egroup\egroup}% % % To parse everything between @multitable and @item: \setuptable#1 \endsetuptable % % \everycr will reset column counter, \colcount, at the end of % each line. Every column entry will cause \colcount to advance by one. % The table preamble % looks at the current \colcount to find the correct column width. \everycr{\noalign{% % % \filbreak%% keeps underfull box messages off when table breaks over pages. % Maybe so, but it also creates really weird page breaks when the table % breaks over pages. Wouldn't \vfil be better? Wait until the problem % manifests itself, so it can be fixed for real --karl. \global\colcount=0\relax}}% % % This preamble sets up a generic column definition, which will % be used as many times as user calls for columns. % \vtop will set a single line and will also let text wrap and % continue for many paragraphs if desired. \halign\bgroup&\global\advance\colcount by 1\relax \multistrut\vtop{\hsize=\expandafter\csname col\the\colcount\endcsname % % In order to keep entries from bumping into each other % we will add a \leftskip of \multitablecolspace to all columns after % the first one. % % If a template has been used, we will add \multitablecolspace % to the width of each template entry. % % If the user has set preamble in terms of percent of \hsize we will % use that dimension as the width of the column, and the \leftskip % will keep entries from bumping into each other. Table will start at % left margin and final column will justify at right margin. % % Make sure we don't inherit \rightskip from the outer environment. \rightskip=0pt \ifnum\colcount=1 % The first column will be indented with the surrounding text. \advance\hsize by\leftskip \else \ifsetpercent \else % If user has not set preamble in terms of percent of \hsize % we will advance \hsize by \multitablecolspace. \advance\hsize by \multitablecolspace \fi % In either case we will make \leftskip=\multitablecolspace: \leftskip=\multitablecolspace \fi % Ignoring space at the beginning and end avoids an occasional spurious % blank line, when TeX decides to break the line at the space before the % box from the multistrut, so the strut ends up on a line by itself. % For example: % @multitable @columnfractions .11 .89 % @item @code{#} % @tab Legal holiday which is valid in major parts of the whole country. % Is automatically provided with highlighting sequences respectively marking % characters. \noindent\ignorespaces##\unskip\multistrut}\cr } \def\setmultitablespacing{% test to see if user has set \multitablelinespace. % If so, do nothing. If not, give it an appropriate dimension based on % current baselineskip. \ifdim\multitablelinespace=0pt \setbox0=\vbox{X}\global\multitablelinespace=\the\baselineskip \global\advance\multitablelinespace by-\ht0 %% strut to put in table in case some entry doesn't have descenders, %% to keep lines equally spaced \let\multistrut = \strut \else %% FIXME: what is \box0 supposed to be? \gdef\multistrut{\vrule height\multitablelinespace depth\dp0 width0pt\relax} \fi %% Test to see if parskip is larger than space between lines of %% table. If not, do nothing. %% If so, set to same dimension as multitablelinespace. \ifdim\multitableparskip>\multitablelinespace \global\multitableparskip=\multitablelinespace \global\advance\multitableparskip-7pt %% to keep parskip somewhat smaller %% than skip between lines in the table. \fi% \ifdim\multitableparskip=0pt \global\multitableparskip=\multitablelinespace \global\advance\multitableparskip-7pt %% to keep parskip somewhat smaller %% than skip between lines in the table. \fi} \message{conditionals,} % Prevent errors for section commands. % Used in @ignore and in failing conditionals. \def\ignoresections{% \let\chapter=\relax \let\unnumbered=\relax \let\top=\relax \let\unnumberedsec=\relax \let\unnumberedsection=\relax \let\unnumberedsubsec=\relax \let\unnumberedsubsection=\relax \let\unnumberedsubsubsec=\relax \let\unnumberedsubsubsection=\relax \let\section=\relax \let\subsec=\relax \let\subsubsec=\relax \let\subsection=\relax \let\subsubsection=\relax \let\appendix=\relax \let\appendixsec=\relax \let\appendixsection=\relax \let\appendixsubsec=\relax \let\appendixsubsection=\relax \let\appendixsubsubsec=\relax \let\appendixsubsubsection=\relax \let\contents=\relax \let\smallbook=\relax \let\titlepage=\relax } % Used in nested conditionals, where we have to parse the Texinfo source % and so want to turn off most commands, in case they are used % incorrectly. % \def\ignoremorecommands{% \let\defcodeindex = \relax \let\defcv = \relax \let\deffn = \relax \let\deffnx = \relax \let\defindex = \relax \let\defivar = \relax \let\defmac = \relax \let\defmethod = \relax \let\defop = \relax \let\defopt = \relax \let\defspec = \relax \let\deftp = \relax \let\deftypefn = \relax \let\deftypefun = \relax \let\deftypeivar = \relax \let\deftypeop = \relax \let\deftypevar = \relax \let\deftypevr = \relax \let\defun = \relax \let\defvar = \relax \let\defvr = \relax \let\ref = \relax \let\xref = \relax \let\printindex = \relax \let\pxref = \relax \let\settitle = \relax \let\setchapternewpage = \relax \let\setchapterstyle = \relax \let\everyheading = \relax \let\evenheading = \relax \let\oddheading = \relax \let\everyfooting = \relax \let\evenfooting = \relax \let\oddfooting = \relax \let\headings = \relax \let\include = \relax \let\lowersections = \relax \let\down = \relax \let\raisesections = \relax \let\up = \relax \let\set = \relax \let\clear = \relax \let\item = \relax } % Ignore @ignore ... @end ignore. % \def\ignore{\doignore{ignore}} % Ignore @ifinfo, @ifhtml, @ifnottex, @html, @menu, and @direntry text. % \def\ifinfo{\doignore{ifinfo}} \def\ifhtml{\doignore{ifhtml}} \def\ifnottex{\doignore{ifnottex}} \def\html{\doignore{html}} \def\menu{\doignore{menu}} \def\direntry{\doignore{direntry}} % @dircategory CATEGORY -- specify a category of the dir file % which this file should belong to. Ignore this in TeX. \let\dircategory = \comment % Ignore text until a line `@end #1'. % \def\doignore#1{\begingroup % Don't complain about control sequences we have declared \outer. \ignoresections % % Define a command to swallow text until we reach `@end #1'. % This @ is a catcode 12 token (that is the normal catcode of @ in % this texinfo.tex file). We change the catcode of @ below to match. \long\def\doignoretext##1@end #1{\enddoignore}% % % Make sure that spaces turn into tokens that match what \doignoretext wants. \catcode32 = 10 % % Ignore braces, too, so mismatched braces don't cause trouble. \catcode`\{ = 9 \catcode`\} = 9 % % We must not have @c interpreted as a control sequence. \catcode`\@ = 12 % % Make the letter c a comment character so that the rest of the line % will be ignored. This way, the document can have (for example) % @c @end ifinfo % and the @end ifinfo will be properly ignored. % (We've just changed @ to catcode 12.) \catcode`\c = 14 % % And now expand that command. \doignoretext } % What we do to finish off ignored text. % \def\enddoignore{\endgroup\ignorespaces}% \newif\ifwarnedobs\warnedobsfalse \def\obstexwarn{% \ifwarnedobs\relax\else % We need to warn folks that they may have trouble with TeX 3.0. % This uses \immediate\write16 rather than \message to get newlines. \immediate\write16{} \immediate\write16{WARNING: for users of Unix TeX 3.0!} \immediate\write16{This manual trips a bug in TeX version 3.0 (tex hangs).} \immediate\write16{If you are running another version of TeX, relax.} \immediate\write16{If you are running Unix TeX 3.0, kill this TeX process.} \immediate\write16{ Then upgrade your TeX installation if you can.} \immediate\write16{ (See ftp://ftp.gnu.org/pub/gnu/TeX.README.)} \immediate\write16{If you are stuck with version 3.0, run the} \immediate\write16{ script ``tex3patch'' from the Texinfo distribution} \immediate\write16{ to use a workaround.} \immediate\write16{} \global\warnedobstrue \fi } % **In TeX 3.0, setting text in \nullfont hangs tex. For a % workaround (which requires the file ``dummy.tfm'' to be installed), % uncomment the following line: %%%%%\font\nullfont=dummy\let\obstexwarn=\relax % Ignore text, except that we keep track of conditional commands for % purposes of nesting, up to an `@end #1' command. % \def\nestedignore#1{% \obstexwarn % We must actually expand the ignored text to look for the @end % command, so that nested ignore constructs work. Thus, we put the % text into a \vbox and then do nothing with the result. To minimize % the change of memory overflow, we follow the approach outlined on % page 401 of the TeXbook: make the current font be a dummy font. % \setbox0 = \vbox\bgroup % Don't complain about control sequences we have declared \outer. \ignoresections % % Define `@end #1' to end the box, which will in turn undefine the % @end command again. \expandafter\def\csname E#1\endcsname{\egroup\ignorespaces}% % % We are going to be parsing Texinfo commands. Most cause no % trouble when they are used incorrectly, but some commands do % complicated argument parsing or otherwise get confused, so we % undefine them. % % We can't do anything about stray @-signs, unfortunately; % they'll produce `undefined control sequence' errors. \ignoremorecommands % % Set the current font to be \nullfont, a TeX primitive, and define % all the font commands to also use \nullfont. We don't use % dummy.tfm, as suggested in the TeXbook, because not all sites % might have that installed. Therefore, math mode will still % produce output, but that should be an extremely small amount of % stuff compared to the main input. % \nullfont \let\tenrm=\nullfont \let\tenit=\nullfont \let\tensl=\nullfont \let\tenbf=\nullfont \let\tentt=\nullfont \let\smallcaps=\nullfont \let\tensf=\nullfont % Similarly for index fonts (mostly for their use in smallexample). \let\smallrm=\nullfont \let\smallit=\nullfont \let\smallsl=\nullfont \let\smallbf=\nullfont \let\smalltt=\nullfont \let\smallsc=\nullfont \let\smallsf=\nullfont % % Don't complain when characters are missing from the fonts. \tracinglostchars = 0 % % Don't bother to do space factor calculations. \frenchspacing % % Don't report underfull hboxes. \hbadness = 10000 % % Do minimal line-breaking. \pretolerance = 10000 % % Do not execute instructions in @tex \def\tex{\doignore{tex}}% % Do not execute macro definitions. % `c' is a comment character, so the word `macro' will get cut off. \def\macro{\doignore{ma}}% } % @set VAR sets the variable VAR to an empty value. % @set VAR REST-OF-LINE sets VAR to the value REST-OF-LINE. % % Since we want to separate VAR from REST-OF-LINE (which might be % empty), we can't just use \parsearg; we have to insert a space of our % own to delimit the rest of the line, and then take it out again if we % didn't need it. Make sure the catcode of space is correct to avoid % losing inside @example, for instance. % \def\set{\begingroup\catcode` =10 \catcode`\-=12 \catcode`\_=12 % Allow - and _ in VAR. \parsearg\setxxx} \def\setxxx#1{\setyyy#1 \endsetyyy} \def\setyyy#1 #2\endsetyyy{% \def\temp{#2}% \ifx\temp\empty \global\expandafter\let\csname SET#1\endcsname = \empty \else \setzzz{#1}#2\endsetzzz % Remove the trailing space \setxxx inserted. \fi \endgroup } % Can't use \xdef to pre-expand #2 and save some time, since \temp or % \next or other control sequences that we've defined might get us into % an infinite loop. Consider `@set foo @cite{bar}'. \def\setzzz#1#2 \endsetzzz{\expandafter\gdef\csname SET#1\endcsname{#2}} % @clear VAR clears (i.e., unsets) the variable VAR. % \def\clear{\parsearg\clearxxx} \def\clearxxx#1{\global\expandafter\let\csname SET#1\endcsname=\relax} % @value{foo} gets the text saved in variable foo. { \catcode`\_ = \active % % We might end up with active _ or - characters in the argument if % we're called from @code, as @code{@value{foo-bar_}}. So \let any % such active characters to their normal equivalents. \gdef\value{\begingroup \catcode`\-=12 \catcode`\_=12 \indexbreaks \let_\normalunderscore \valuexxx} } \def\valuexxx#1{\expandablevalue{#1}\endgroup} % We have this subroutine so that we can handle at least some @value's % properly in indexes (we \let\value to this in \indexdummies). Ones % whose names contain - or _ still won't work, but we can't do anything % about that. The command has to be fully expandable, since the result % winds up in the index file. This means that if the variable's value % contains other Texinfo commands, it's almost certain it will fail % (although perhaps we could fix that with sufficient work to do a % one-level expansion on the result, instead of complete). % \def\expandablevalue#1{% \expandafter\ifx\csname SET#1\endcsname\relax {[No value for ``#1'']}% \else \csname SET#1\endcsname \fi } % @ifset VAR ... @end ifset reads the `...' iff VAR has been defined % with @set. % \def\ifset{\parsearg\ifsetxxx} \def\ifsetxxx #1{% \expandafter\ifx\csname SET#1\endcsname\relax \expandafter\ifsetfail \else \expandafter\ifsetsucceed \fi } \def\ifsetsucceed{\conditionalsucceed{ifset}} \def\ifsetfail{\nestedignore{ifset}} \defineunmatchedend{ifset} % @ifclear VAR ... @end ifclear reads the `...' iff VAR has never been % defined with @set, or has been undefined with @clear. % \def\ifclear{\parsearg\ifclearxxx} \def\ifclearxxx #1{% \expandafter\ifx\csname SET#1\endcsname\relax \expandafter\ifclearsucceed \else \expandafter\ifclearfail \fi } \def\ifclearsucceed{\conditionalsucceed{ifclear}} \def\ifclearfail{\nestedignore{ifclear}} \defineunmatchedend{ifclear} % @iftex, @ifnothtml, @ifnotinfo always succeed; we read the text % following, through the first @end iftex (etc.). Make `@end iftex' % (etc.) valid only after an @iftex. % \def\iftex{\conditionalsucceed{iftex}} \def\ifnothtml{\conditionalsucceed{ifnothtml}} \def\ifnotinfo{\conditionalsucceed{ifnotinfo}} \defineunmatchedend{iftex} \defineunmatchedend{ifnothtml} \defineunmatchedend{ifnotinfo} % We can't just want to start a group at @iftex (for example) and end it % at @end iftex, since then @set commands inside the conditional have no % effect (they'd get reverted at the end of the group). So we must % define \Eiftex to redefine itself to be its previous value. (We can't % just define it to fail again with an ``unmatched end'' error, since % the @ifset might be nested.) % \def\conditionalsucceed#1{% \edef\temp{% % Remember the current value of \E#1. \let\nece{prevE#1} = \nece{E#1}% % % At the `@end #1', redefine \E#1 to be its previous value. \def\nece{E#1}{\let\nece{E#1} = \nece{prevE#1}}% }% \temp } % We need to expand lots of \csname's, but we don't want to expand the % control sequences after we've constructed them. % \def\nece#1{\expandafter\noexpand\csname#1\endcsname} % @defininfoenclose. \let\definfoenclose=\comment \message{indexing,} % Index generation facilities % Define \newwrite to be identical to plain tex's \newwrite % except not \outer, so it can be used within \newindex. {\catcode`\@=11 \gdef\newwrite{\alloc@7\write\chardef\sixt@@n}} % \newindex {foo} defines an index named foo. % It automatically defines \fooindex such that % \fooindex ...rest of line... puts an entry in the index foo. % It also defines \fooindfile to be the number of the output channel for % the file that accumulates this index. The file's extension is foo. % The name of an index should be no more than 2 characters long % for the sake of vms. % \def\newindex#1{% \iflinks \expandafter\newwrite \csname#1indfile\endcsname \openout \csname#1indfile\endcsname \jobname.#1 % Open the file \fi \expandafter\xdef\csname#1index\endcsname{% % Define @#1index \noexpand\doindex{#1}} } % @defindex foo == \newindex{foo} \def\defindex{\parsearg\newindex} % Define @defcodeindex, like @defindex except put all entries in @code. \def\newcodeindex#1{% \iflinks \expandafter\newwrite \csname#1indfile\endcsname \openout \csname#1indfile\endcsname \jobname.#1 \fi \expandafter\xdef\csname#1index\endcsname{% \noexpand\docodeindex{#1}} } \def\defcodeindex{\parsearg\newcodeindex} % @synindex foo bar makes index foo feed into index bar. % Do this instead of @defindex foo if you don't want it as a separate index. % The \closeout helps reduce unnecessary open files; the limit on the % Acorn RISC OS is a mere 16 files. \def\synindex#1 #2 {% \expandafter\let\expandafter\synindexfoo\expandafter=\csname#2indfile\endcsname \expandafter\closeout\csname#1indfile\endcsname \expandafter\let\csname#1indfile\endcsname=\synindexfoo \expandafter\xdef\csname#1index\endcsname{% define \xxxindex \noexpand\doindex{#2}}% } % @syncodeindex foo bar similar, but put all entries made for index foo % inside @code. \def\syncodeindex#1 #2 {% \expandafter\let\expandafter\synindexfoo\expandafter=\csname#2indfile\endcsname \expandafter\closeout\csname#1indfile\endcsname \expandafter\let\csname#1indfile\endcsname=\synindexfoo \expandafter\xdef\csname#1index\endcsname{% define \xxxindex \noexpand\docodeindex{#2}}% } % Define \doindex, the driver for all \fooindex macros. % Argument #1 is generated by the calling \fooindex macro, % and it is "foo", the name of the index. % \doindex just uses \parsearg; it calls \doind for the actual work. % This is because \doind is more useful to call from other macros. % There is also \dosubind {index}{topic}{subtopic} % which makes an entry in a two-level index such as the operation index. \def\doindex#1{\edef\indexname{#1}\parsearg\singleindexer} \def\singleindexer #1{\doind{\indexname}{#1}} % like the previous two, but they put @code around the argument. \def\docodeindex#1{\edef\indexname{#1}\parsearg\singlecodeindexer} \def\singlecodeindexer #1{\doind{\indexname}{\code{#1}}} \def\indexdummies{% \def\ { }% % Take care of the plain tex accent commands. \def\"{\realbackslash "}% \def\`{\realbackslash `}% \def\'{\realbackslash '}% \def\^{\realbackslash ^}% \def\~{\realbackslash ~}% \def\={\realbackslash =}% \def\b{\realbackslash b}% \def\c{\realbackslash c}% \def\d{\realbackslash d}% \def\u{\realbackslash u}% \def\v{\realbackslash v}% \def\H{\realbackslash H}% % Take care of the plain tex special European modified letters. \def\oe{\realbackslash oe}% \def\ae{\realbackslash ae}% \def\aa{\realbackslash aa}% \def\OE{\realbackslash OE}% \def\AE{\realbackslash AE}% \def\AA{\realbackslash AA}% \def\o{\realbackslash o}% \def\O{\realbackslash O}% \def\l{\realbackslash l}% \def\L{\realbackslash L}% \def\ss{\realbackslash ss}% % Take care of texinfo commands likely to appear in an index entry. % (Must be a way to avoid doing expansion at all, and thus not have to % laboriously list every single command here.) \def\@{@}% will be @@ when we switch to @ as escape char. % Need these in case \tex is in effect and \{ is a \delimiter again. % But can't use \lbracecmd and \rbracecmd because texindex assumes % braces and backslashes are used only as delimiters. \let\{ = \mylbrace \let\} = \myrbrace \def\_{{\realbackslash _}}% \def\w{\realbackslash w }% \def\bf{\realbackslash bf }% %\def\rm{\realbackslash rm }% \def\sl{\realbackslash sl }% \def\sf{\realbackslash sf}% \def\tt{\realbackslash tt}% \def\gtr{\realbackslash gtr}% \def\less{\realbackslash less}% \def\hat{\realbackslash hat}% \def\TeX{\realbackslash TeX}% \def\dots{\realbackslash dots }% \def\result{\realbackslash result}% \def\equiv{\realbackslash equiv}% \def\expansion{\realbackslash expansion}% \def\print{\realbackslash print}% \def\error{\realbackslash error}% \def\point{\realbackslash point}% \def\copyright{\realbackslash copyright}% \def\tclose##1{\realbackslash tclose {##1}}% \def\code##1{\realbackslash code {##1}}% \def\uref##1{\realbackslash uref {##1}}% \def\url##1{\realbackslash url {##1}}% \def\env##1{\realbackslash env {##1}}% \def\command##1{\realbackslash command {##1}}% \def\option##1{\realbackslash option {##1}}% \def\dotless##1{\realbackslash dotless {##1}}% \def\samp##1{\realbackslash samp {##1}}% \def\,##1{\realbackslash ,{##1}}% \def\t##1{\realbackslash t {##1}}% \def\r##1{\realbackslash r {##1}}% \def\i##1{\realbackslash i {##1}}% \def\b##1{\realbackslash b {##1}}% \def\sc##1{\realbackslash sc {##1}}% \def\cite##1{\realbackslash cite {##1}}% \def\key##1{\realbackslash key {##1}}% \def\file##1{\realbackslash file {##1}}% \def\var##1{\realbackslash var {##1}}% \def\kbd##1{\realbackslash kbd {##1}}% \def\dfn##1{\realbackslash dfn {##1}}% \def\emph##1{\realbackslash emph {##1}}% \def\acronym##1{\realbackslash acronym {##1}}% % % Handle some cases of @value -- where the variable name does not % contain - or _, and the value does not contain any % (non-fully-expandable) commands. \let\value = \expandablevalue % \unsepspaces % Turn off macro expansion \turnoffmacros } % If an index command is used in an @example environment, any spaces % therein should become regular spaces in the raw index file, not the % expansion of \tie (\\leavevmode \penalty \@M \ ). {\obeyspaces \gdef\unsepspaces{\obeyspaces\let =\space}} % \indexnofonts no-ops all font-change commands. % This is used when outputting the strings to sort the index by. \def\indexdummyfont#1{#1} \def\indexdummytex{TeX} \def\indexdummydots{...} \def\indexnofonts{% % Just ignore accents. \let\,=\indexdummyfont \let\"=\indexdummyfont \let\`=\indexdummyfont \let\'=\indexdummyfont \let\^=\indexdummyfont \let\~=\indexdummyfont \let\==\indexdummyfont \let\b=\indexdummyfont \let\c=\indexdummyfont \let\d=\indexdummyfont \let\u=\indexdummyfont \let\v=\indexdummyfont \let\H=\indexdummyfont \let\dotless=\indexdummyfont % Take care of the plain tex special European modified letters. \def\oe{oe}% \def\ae{ae}% \def\aa{aa}% \def\OE{OE}% \def\AE{AE}% \def\AA{AA}% \def\o{o}% \def\O{O}% \def\l{l}% \def\L{L}% \def\ss{ss}% \let\w=\indexdummyfont \let\t=\indexdummyfont \let\r=\indexdummyfont \let\i=\indexdummyfont \let\b=\indexdummyfont \let\emph=\indexdummyfont \let\strong=\indexdummyfont \let\cite=\indexdummyfont \let\sc=\indexdummyfont %Don't no-op \tt, since it isn't a user-level command % and is used in the definitions of the active chars like <, >, |... %\let\tt=\indexdummyfont \let\tclose=\indexdummyfont \let\code=\indexdummyfont \let\url=\indexdummyfont \let\uref=\indexdummyfont \let\env=\indexdummyfont \let\acronym=\indexdummyfont \let\command=\indexdummyfont \let\option=\indexdummyfont \let\file=\indexdummyfont \let\samp=\indexdummyfont \let\kbd=\indexdummyfont \let\key=\indexdummyfont \let\var=\indexdummyfont \let\TeX=\indexdummytex \let\dots=\indexdummydots \def\@{@}% } % To define \realbackslash, we must make \ not be an escape. % We must first make another character (@) an escape % so we do not become unable to do a definition. {\catcode`\@=0 \catcode`\\=\other @gdef@realbackslash{\}} \let\indexbackslash=0 %overridden during \printindex. \let\SETmarginindex=\relax % put index entries in margin (undocumented)? % For \ifx comparisons. \def\emptymacro{\empty} % Most index entries go through here, but \dosubind is the general case. % \def\doind#1#2{\dosubind{#1}{#2}\empty} % Workhorse for all \fooindexes. % #1 is name of index, #2 is stuff to put there, #3 is subentry -- % \empty if called from \doind, as we usually are. The main exception % is with defuns, which call us directly. % \def\dosubind#1#2#3{% % Put the index entry in the margin if desired. \ifx\SETmarginindex\relax\else \insert\margin{\hbox{\vrule height8pt depth3pt width0pt #2}}% \fi {% \count255=\lastpenalty {% \indexdummies % Must do this here, since \bf, etc expand at this stage \escapechar=`\\ {% \let\folio = 0% We will expand all macros now EXCEPT \folio. \def\rawbackslashxx{\indexbackslash}% \indexbackslash isn't defined now % so it will be output as is; and it will print as backslash. % \def\thirdarg{#3}% % % If third arg is present, precede it with space in sort key. \ifx\thirdarg\emptymacro \let\subentry = \empty \else \def\subentry{ #3}% \fi % % First process the index entry with all font commands turned % off to get the string to sort by. {\indexnofonts \xdef\indexsorttmp{#2\subentry}}% % % Now the real index entry with the fonts. \toks0 = {#2}% % % If third (subentry) arg is present, add it to the index % string. And include a space. \ifx\thirdarg\emptymacro \else \toks0 = \expandafter{\the\toks0 \space #3}% \fi % % Set up the complete index entry, with both the sort key % and the original text, including any font commands. We write % three arguments to \entry to the .?? file, texindex reduces to % two when writing the .??s sorted result. \edef\temp{% \write\csname#1indfile\endcsname{% \realbackslash entry{\indexsorttmp}{\folio}{\the\toks0}}% }% % % If a skip is the last thing on the list now, preserve it % by backing up by \lastskip, doing the \write, then inserting % the skip again. Otherwise, the whatsit generated by the % \write will make \lastskip zero. The result is that sequences % like this: % @end defun % @tindex whatever % @defun ... % will have extra space inserted, because the \medbreak in the % start of the @defun won't see the skip inserted by the @end of % the previous defun. % % But don't do any of this if we're not in vertical mode. We % don't want to do a \vskip and prematurely end a paragraph. % % Avoid page breaks due to these extra skips, too. % \iflinks \ifvmode \skip0 = \lastskip \ifdim\lastskip = 0pt \else \nobreak\vskip-\lastskip \fi \fi % \temp % do the write % % \ifvmode \ifdim\skip0 = 0pt \else \nobreak\vskip\skip0 \fi \fi \fi }% }% \penalty\count255 }% } % The index entry written in the file actually looks like % \entry {sortstring}{page}{topic} % or % \entry {sortstring}{page}{topic}{subtopic} % The texindex program reads in these files and writes files % containing these kinds of lines: % \initial {c} % before the first topic whose initial is c % \entry {topic}{pagelist} % for a topic that is used without subtopics % \primary {topic} % for the beginning of a topic that is used with subtopics % \secondary {subtopic}{pagelist} % for each subtopic. % Define the user-accessible indexing commands % @findex, @vindex, @kindex, @cindex. \def\findex {\fnindex} \def\kindex {\kyindex} \def\cindex {\cpindex} \def\vindex {\vrindex} \def\tindex {\tpindex} \def\pindex {\pgindex} \def\cindexsub {\begingroup\obeylines\cindexsub} {\obeylines % \gdef\cindexsub "#1" #2^^M{\endgroup % \dosubind{cp}{#2}{#1}}} % Define the macros used in formatting output of the sorted index material. % @printindex causes a particular index (the ??s file) to get printed. % It does not print any chapter heading (usually an @unnumbered). % \def\printindex{\parsearg\doprintindex} \def\doprintindex#1{\begingroup \dobreak \chapheadingskip{10000}% % \smallfonts \rm \tolerance = 9500 \indexbreaks % % See if the index file exists and is nonempty. % Change catcode of @ here so that if the index file contains % \initial {@} % as its first line, TeX doesn't complain about mismatched braces % (because it thinks @} is a control sequence). \catcode`\@ = 11 \openin 1 \jobname.#1s \ifeof 1 % \enddoublecolumns gets confused if there is no text in the index, % and it loses the chapter title and the aux file entries for the % index. The easiest way to prevent this problem is to make sure % there is some text. \putwordIndexNonexistent \else % % If the index file exists but is empty, then \openin leaves \ifeof % false. We have to make TeX try to read something from the file, so % it can discover if there is anything in it. \read 1 to \temp \ifeof 1 \putwordIndexIsEmpty \else % Index files are almost Texinfo source, but we use \ as the escape % character. It would be better to use @, but that's too big a change % to make right now. \def\indexbackslash{\rawbackslashxx}% \catcode`\\ = 0 \escapechar = `\\ \begindoublecolumns \input \jobname.#1s \enddoublecolumns \fi \fi \closein 1 \endgroup} % These macros are used by the sorted index file itself. % Change them to control the appearance of the index. \def\initial#1{{% % Some minor font changes for the special characters. \let\tentt=\sectt \let\tt=\sectt \let\sf=\sectt % % Remove any glue we may have, we'll be inserting our own. \removelastskip % % We like breaks before the index initials, so insert a bonus. \penalty -300 % % Typeset the initial. Making this add up to a whole number of % baselineskips increases the chance of the dots lining up from column % to column. It still won't often be perfect, because of the stretch % we need before each entry, but it's better. % % No shrink because it confuses \balancecolumns. \vskip 1.67\baselineskip plus .5\baselineskip \leftline{\secbf #1}% \vskip .33\baselineskip plus .1\baselineskip % % Do our best not to break after the initial. \nobreak }} % This typesets a paragraph consisting of #1, dot leaders, and then #2 % flush to the right margin. It is used for index and table of contents % entries. The paragraph is indented by \leftskip. % \def\entry#1#2{\begingroup % % Start a new paragraph if necessary, so our assignments below can't % affect previous text. \par % % Do not fill out the last line with white space. \parfillskip = 0in % % No extra space above this paragraph. \parskip = 0in % % Do not prefer a separate line ending with a hyphen to fewer lines. \finalhyphendemerits = 0 % % \hangindent is only relevant when the entry text and page number % don't both fit on one line. In that case, bob suggests starting the % dots pretty far over on the line. Unfortunately, a large % indentation looks wrong when the entry text itself is broken across % lines. So we use a small indentation and put up with long leaders. % % \hangafter is reset to 1 (which is the value we want) at the start % of each paragraph, so we need not do anything with that. \hangindent = 2em % % When the entry text needs to be broken, just fill out the first line % with blank space. \rightskip = 0pt plus1fil % % A bit of stretch before each entry for the benefit of balancing columns. \vskip 0pt plus1pt % % Start a ``paragraph'' for the index entry so the line breaking % parameters we've set above will have an effect. \noindent % % Insert the text of the index entry. TeX will do line-breaking on it. #1% % The following is kludged to not output a line of dots in the index if % there are no page numbers. The next person who breaks this will be % cursed by a Unix daemon. \def\tempa{{\rm }}% \def\tempb{#2}% \edef\tempc{\tempa}% \edef\tempd{\tempb}% \ifx\tempc\tempd\ \else% % % If we must, put the page number on a line of its own, and fill out % this line with blank space. (The \hfil is overwhelmed with the % fill leaders glue in \indexdotfill if the page number does fit.) \hfil\penalty50 \null\nobreak\indexdotfill % Have leaders before the page number. % % The `\ ' here is removed by the implicit \unskip that TeX does as % part of (the primitive) \par. Without it, a spurious underfull % \hbox ensues. \ifpdf \pdfgettoks#2.\ \the\toksA % The page number ends the paragraph. \else \ #2% The page number ends the paragraph. \fi \fi% \par \endgroup} % Like \dotfill except takes at least 1 em. \def\indexdotfill{\cleaders \hbox{$\mathsurround=0pt \mkern1.5mu ${\it .}$ \mkern1.5mu$}\hskip 1em plus 1fill} \def\primary #1{\line{#1\hfil}} \newskip\secondaryindent \secondaryindent=0.5cm \def\secondary #1#2{ {\parfillskip=0in \parskip=0in \hangindent =1in \hangafter=1 \noindent\hskip\secondaryindent\hbox{#1}\indexdotfill #2\par }} % Define two-column mode, which we use to typeset indexes. % Adapted from the TeXbook, page 416, which is to say, % the manmac.tex format used to print the TeXbook itself. \catcode`\@=11 \newbox\partialpage \newdimen\doublecolumnhsize \def\begindoublecolumns{\begingroup % ended by \enddoublecolumns % Grab any single-column material above us. \output = {% % % Here is a possibility not foreseen in manmac: if we accumulate a % whole lot of material, we might end up calling this \output % routine twice in a row (see the doublecol-lose test, which is % essentially a couple of indexes with @setchapternewpage off). In % that case we just ship out what is in \partialpage with the normal % output routine. Generally, \partialpage will be empty when this % runs and this will be a no-op. See the indexspread.tex test case. \ifvoid\partialpage \else \onepageout{\pagecontents\partialpage}% \fi % \global\setbox\partialpage = \vbox{% % Unvbox the main output page. \unvbox\PAGE \kern-\topskip \kern\baselineskip }% }% \eject % run that output routine to set \partialpage % % Use the double-column output routine for subsequent pages. \output = {\doublecolumnout}% % % Change the page size parameters. We could do this once outside this % routine, in each of @smallbook, @afourpaper, and the default 8.5x11 % format, but then we repeat the same computation. Repeating a couple % of assignments once per index is clearly meaningless for the % execution time, so we may as well do it in one place. % % First we halve the line length, less a little for the gutter between % the columns. We compute the gutter based on the line length, so it % changes automatically with the paper format. The magic constant % below is chosen so that the gutter has the same value (well, +-<1pt) % as it did when we hard-coded it. % % We put the result in a separate register, \doublecolumhsize, so we % can restore it in \pagesofar, after \hsize itself has (potentially) % been clobbered. % \doublecolumnhsize = \hsize \advance\doublecolumnhsize by -.04154\hsize \divide\doublecolumnhsize by 2 \hsize = \doublecolumnhsize % % Double the \vsize as well. (We don't need a separate register here, % since nobody clobbers \vsize.) \advance\vsize by -\ht\partialpage \vsize = 2\vsize } % The double-column output routine for all double-column pages except % the last. % \def\doublecolumnout{% \splittopskip=\topskip \splitmaxdepth=\maxdepth % Get the available space for the double columns -- the normal % (undoubled) page height minus any material left over from the % previous page. \dimen@ = \vsize \divide\dimen@ by 2 % % box0 will be the left-hand column, box2 the right. \setbox0=\vsplit255 to\dimen@ \setbox2=\vsplit255 to\dimen@ \onepageout\pagesofar \unvbox255 \penalty\outputpenalty } \def\pagesofar{% % Re-output the contents of the output page -- any previous material, % followed by the two boxes we just split, in box0 and box2. \unvbox\partialpage % \hsize = \doublecolumnhsize \wd0=\hsize \wd2=\hsize \hbox to\pagewidth{\box0\hfil\box2}% } \def\enddoublecolumns{% \output = {% % Split the last of the double-column material. Leave it on the % current page, no automatic page break. \balancecolumns % % If we end up splitting too much material for the current page, % though, there will be another page break right after this \output % invocation ends. Having called \balancecolumns once, we do not % want to call it again. Therefore, reset \output to its normal % definition right away. (We hope \balancecolumns will never be % called on to balance too much material, but if it is, this makes % the output somewhat more palatable.) \global\output = {\onepageout{\pagecontents\PAGE}}% }% \eject \endgroup % started in \begindoublecolumns % % \pagegoal was set to the doubled \vsize above, since we restarted % the current page. We're now back to normal single-column % typesetting, so reset \pagegoal to the normal \vsize (after the % \endgroup where \vsize got restored). \pagegoal = \vsize } \def\balancecolumns{% % Called at the end of the double column material. \setbox0 = \vbox{\unvbox255}% like \box255 but more efficient, see p.120. \dimen@ = \ht0 \advance\dimen@ by \topskip \advance\dimen@ by-\baselineskip \divide\dimen@ by 2 % target to split to %debug\message{final 2-column material height=\the\ht0, target=\the\dimen@.}% \splittopskip = \topskip % Loop until we get a decent breakpoint. {% \vbadness = 10000 \loop \global\setbox3 = \copy0 \global\setbox1 = \vsplit3 to \dimen@ \ifdim\ht3>\dimen@ \global\advance\dimen@ by 1pt \repeat }% %debug\message{split to \the\dimen@, column heights: \the\ht1, \the\ht3.}% \setbox0=\vbox to\dimen@{\unvbox1}% \setbox2=\vbox to\dimen@{\unvbox3}% % \pagesofar } \catcode`\@ = \other \message{sectioning,} % Chapters, sections, etc. \newcount\chapno \newcount\secno \secno=0 \newcount\subsecno \subsecno=0 \newcount\subsubsecno \subsubsecno=0 % This counter is funny since it counts through charcodes of letters A, B, ... \newcount\appendixno \appendixno = `\@ % \def\appendixletter{\char\the\appendixno} % We do the following for the sake of pdftex, which needs the actual % letter in the expansion, not just typeset. \def\appendixletter{% \ifnum\appendixno=`A A% \else\ifnum\appendixno=`B B% \else\ifnum\appendixno=`C C% \else\ifnum\appendixno=`D D% \else\ifnum\appendixno=`E E% \else\ifnum\appendixno=`F F% \else\ifnum\appendixno=`G G% \else\ifnum\appendixno=`H H% \else\ifnum\appendixno=`I I% \else\ifnum\appendixno=`J J% \else\ifnum\appendixno=`K K% \else\ifnum\appendixno=`L L% \else\ifnum\appendixno=`M M% \else\ifnum\appendixno=`N N% \else\ifnum\appendixno=`O O% \else\ifnum\appendixno=`P P% \else\ifnum\appendixno=`Q Q% \else\ifnum\appendixno=`R R% \else\ifnum\appendixno=`S S% \else\ifnum\appendixno=`T T% \else\ifnum\appendixno=`U U% \else\ifnum\appendixno=`V V% \else\ifnum\appendixno=`W W% \else\ifnum\appendixno=`X X% \else\ifnum\appendixno=`Y Y% \else\ifnum\appendixno=`Z Z% % The \the is necessary, despite appearances, because \appendixletter is % expanded while writing the .toc file. \char\appendixno is not % expandable, thus it is written literally, thus all appendixes come out % with the same letter (or @) in the toc without it. \else\char\the\appendixno \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi} % Each @chapter defines this as the name of the chapter. % page headings and footings can use it. @section does likewise. \def\thischapter{} \def\thissection{} \newcount\absseclevel % used to calculate proper heading level \newcount\secbase\secbase=0 % @raise/lowersections modify this count % @raisesections: treat @section as chapter, @subsection as section, etc. \def\raisesections{\global\advance\secbase by -1} \let\up=\raisesections % original BFox name % @lowersections: treat @chapter as section, @section as subsection, etc. \def\lowersections{\global\advance\secbase by 1} \let\down=\lowersections % original BFox name % Choose a numbered-heading macro % #1 is heading level if unmodified by @raisesections or @lowersections % #2 is text for heading \def\numhead#1#2{\absseclevel=\secbase\advance\absseclevel by #1 \ifcase\absseclevel \chapterzzz{#2} \or \seczzz{#2} \or \numberedsubseczzz{#2} \or \numberedsubsubseczzz{#2} \else \ifnum \absseclevel<0 \chapterzzz{#2} \else \numberedsubsubseczzz{#2} \fi \fi } % like \numhead, but chooses appendix heading levels \def\apphead#1#2{\absseclevel=\secbase\advance\absseclevel by #1 \ifcase\absseclevel \appendixzzz{#2} \or \appendixsectionzzz{#2} \or \appendixsubseczzz{#2} \or \appendixsubsubseczzz{#2} \else \ifnum \absseclevel<0 \appendixzzz{#2} \else \appendixsubsubseczzz{#2} \fi \fi } % like \numhead, but chooses numberless heading levels \def\unnmhead#1#2{\absseclevel=\secbase\advance\absseclevel by #1 \ifcase\absseclevel \unnumberedzzz{#2} \or \unnumberedseczzz{#2} \or \unnumberedsubseczzz{#2} \or \unnumberedsubsubseczzz{#2} \else \ifnum \absseclevel<0 \unnumberedzzz{#2} \else \unnumberedsubsubseczzz{#2} \fi \fi } % @chapter, @appendix, @unnumbered. \def\thischaptername{No Chapter Title} \outer\def\chapter{\parsearg\chapteryyy} \def\chapteryyy #1{\numhead0{#1}} % normally numhead0 calls chapterzzz \def\chapterzzz #1{% \secno=0 \subsecno=0 \subsubsecno=0 \global\advance \chapno by 1 \message{\putwordChapter\space \the\chapno}% \chapmacro {#1}{\the\chapno}% \gdef\thissection{#1}% \gdef\thischaptername{#1}% % We don't substitute the actual chapter name into \thischapter % because we don't want its macros evaluated now. \xdef\thischapter{\putwordChapter{} \the\chapno: \noexpand\thischaptername}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash chapentry{\the\toks0}% {\the\chapno}}}% \temp \donoderef \global\let\section = \numberedsec \global\let\subsection = \numberedsubsec \global\let\subsubsection = \numberedsubsubsec } \outer\def\appendix{\parsearg\appendixyyy} \def\appendixyyy #1{\apphead0{#1}} % normally apphead0 calls appendixzzz \def\appendixzzz #1{% \secno=0 \subsecno=0 \subsubsecno=0 \global\advance \appendixno by 1 \message{\putwordAppendix\space \appendixletter}% \chapmacro {#1}{\putwordAppendix{} \appendixletter}% \gdef\thissection{#1}% \gdef\thischaptername{#1}% \xdef\thischapter{\putwordAppendix{} \appendixletter: \noexpand\thischaptername}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash chapentry{\the\toks0}% {\putwordAppendix{} \appendixletter}}}% \temp \appendixnoderef \global\let\section = \appendixsec \global\let\subsection = \appendixsubsec \global\let\subsubsection = \appendixsubsubsec } % @centerchap is like @unnumbered, but the heading is centered. \outer\def\centerchap{\parsearg\centerchapyyy} \def\centerchapyyy #1{{\let\unnumbchapmacro=\centerchapmacro \unnumberedyyy{#1}}} % @top is like @unnumbered. \outer\def\top{\parsearg\unnumberedyyy} \outer\def\unnumbered{\parsearg\unnumberedyyy} \def\unnumberedyyy #1{\unnmhead0{#1}} % normally unnmhead0 calls unnumberedzzz \def\unnumberedzzz #1{% \secno=0 \subsecno=0 \subsubsecno=0 % % This used to be simply \message{#1}, but TeX fully expands the % argument to \message. Therefore, if #1 contained @-commands, TeX % expanded them. For example, in `@unnumbered The @cite{Book}', TeX % expanded @cite (which turns out to cause errors because \cite is meant % to be executed, not expanded). % % Anyway, we don't want the fully-expanded definition of @cite to appear % as a result of the \message, we just want `@cite' itself. We use % \the to achieve this: TeX expands \the only once, % simply yielding the contents of . (We also do this for % the toc entries.) \toks0 = {#1}\message{(\the\toks0)}% % \unnumbchapmacro {#1}% \gdef\thischapter{#1}\gdef\thissection{#1}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash unnumbchapentry{\the\toks0}}}% \temp \unnumbnoderef \global\let\section = \unnumberedsec \global\let\subsection = \unnumberedsubsec \global\let\subsubsection = \unnumberedsubsubsec } % Sections. \outer\def\numberedsec{\parsearg\secyyy} \def\secyyy #1{\numhead1{#1}} % normally calls seczzz \def\seczzz #1{% \subsecno=0 \subsubsecno=0 \global\advance \secno by 1 % \gdef\thissection{#1}\secheading {#1}{\the\chapno}{\the\secno}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash secentry{\the\toks0}% {\the\chapno}{\the\secno}}}% \temp \donoderef \nobreak } \outer\def\appendixsection{\parsearg\appendixsecyyy} \outer\def\appendixsec{\parsearg\appendixsecyyy} \def\appendixsecyyy #1{\apphead1{#1}} % normally calls appendixsectionzzz \def\appendixsectionzzz #1{% \subsecno=0 \subsubsecno=0 \global\advance \secno by 1 % \gdef\thissection{#1}\secheading {#1}{\appendixletter}{\the\secno}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash secentry{\the\toks0}% {\appendixletter}{\the\secno}}}% \temp \appendixnoderef \nobreak } \outer\def\unnumberedsec{\parsearg\unnumberedsecyyy} \def\unnumberedsecyyy #1{\unnmhead1{#1}} % normally calls unnumberedseczzz \def\unnumberedseczzz #1{% \plainsecheading {#1}\gdef\thissection{#1}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash unnumbsecentry{\the\toks0}}}% \temp \unnumbnoderef \nobreak } % Subsections. \outer\def\numberedsubsec{\parsearg\numberedsubsecyyy} \def\numberedsubsecyyy #1{\numhead2{#1}} % normally calls numberedsubseczzz \def\numberedsubseczzz #1{% \gdef\thissection{#1}\subsubsecno=0 \global\advance \subsecno by 1 % \subsecheading {#1}{\the\chapno}{\the\secno}{\the\subsecno}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash subsecentry{\the\toks0}% {\the\chapno}{\the\secno}{\the\subsecno}}}% \temp \donoderef \nobreak } \outer\def\appendixsubsec{\parsearg\appendixsubsecyyy} \def\appendixsubsecyyy #1{\apphead2{#1}} % normally calls appendixsubseczzz \def\appendixsubseczzz #1{% \gdef\thissection{#1}\subsubsecno=0 \global\advance \subsecno by 1 % \subsecheading {#1}{\appendixletter}{\the\secno}{\the\subsecno}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash subsecentry{\the\toks0}% {\appendixletter}{\the\secno}{\the\subsecno}}}% \temp \appendixnoderef \nobreak } \outer\def\unnumberedsubsec{\parsearg\unnumberedsubsecyyy} \def\unnumberedsubsecyyy #1{\unnmhead2{#1}} %normally calls unnumberedsubseczzz \def\unnumberedsubseczzz #1{% \plainsubsecheading {#1}\gdef\thissection{#1}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash unnumbsubsecentry% {\the\toks0}}}% \temp \unnumbnoderef \nobreak } % Subsubsections. \outer\def\numberedsubsubsec{\parsearg\numberedsubsubsecyyy} \def\numberedsubsubsecyyy #1{\numhead3{#1}} % normally numberedsubsubseczzz \def\numberedsubsubseczzz #1{% \gdef\thissection{#1}\global\advance \subsubsecno by 1 % \subsubsecheading {#1} {\the\chapno}{\the\secno}{\the\subsecno}{\the\subsubsecno}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash subsubsecentry{\the\toks0}% {\the\chapno}{\the\secno}{\the\subsecno}{\the\subsubsecno}}}% \temp \donoderef \nobreak } \outer\def\appendixsubsubsec{\parsearg\appendixsubsubsecyyy} \def\appendixsubsubsecyyy #1{\apphead3{#1}} % normally appendixsubsubseczzz \def\appendixsubsubseczzz #1{% \gdef\thissection{#1}\global\advance \subsubsecno by 1 % \subsubsecheading {#1} {\appendixletter}{\the\secno}{\the\subsecno}{\the\subsubsecno}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash subsubsecentry{\the\toks0}% {\appendixletter}{\the\secno}{\the\subsecno}{\the\subsubsecno}}}% \temp \appendixnoderef \nobreak } \outer\def\unnumberedsubsubsec{\parsearg\unnumberedsubsubsecyyy} \def\unnumberedsubsubsecyyy #1{\unnmhead3{#1}} %normally unnumberedsubsubseczzz \def\unnumberedsubsubseczzz #1{% \plainsubsubsecheading {#1}\gdef\thissection{#1}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash unnumbsubsubsecentry% {\the\toks0}}}% \temp \unnumbnoderef \nobreak } % These are variants which are not "outer", so they can appear in @ifinfo. % Actually, they should now be obsolete; ordinary section commands should work. \def\infotop{\parsearg\unnumberedzzz} \def\infounnumbered{\parsearg\unnumberedzzz} \def\infounnumberedsec{\parsearg\unnumberedseczzz} \def\infounnumberedsubsec{\parsearg\unnumberedsubseczzz} \def\infounnumberedsubsubsec{\parsearg\unnumberedsubsubseczzz} \def\infoappendix{\parsearg\appendixzzz} \def\infoappendixsec{\parsearg\appendixseczzz} \def\infoappendixsubsec{\parsearg\appendixsubseczzz} \def\infoappendixsubsubsec{\parsearg\appendixsubsubseczzz} \def\infochapter{\parsearg\chapterzzz} \def\infosection{\parsearg\sectionzzz} \def\infosubsection{\parsearg\subsectionzzz} \def\infosubsubsection{\parsearg\subsubsectionzzz} % These macros control what the section commands do, according % to what kind of chapter we are in (ordinary, appendix, or unnumbered). % Define them by default for a numbered chapter. \global\let\section = \numberedsec \global\let\subsection = \numberedsubsec \global\let\subsubsection = \numberedsubsubsec % Define @majorheading, @heading and @subheading % NOTE on use of \vbox for chapter headings, section headings, and such: % 1) We use \vbox rather than the earlier \line to permit % overlong headings to fold. % 2) \hyphenpenalty is set to 10000 because hyphenation in a % heading is obnoxious; this forbids it. % 3) Likewise, headings look best if no \parindent is used, and % if justification is not attempted. Hence \raggedright. \def\majorheading{\parsearg\majorheadingzzz} \def\majorheadingzzz #1{% {\advance\chapheadingskip by 10pt \chapbreak }% {\chapfonts \vbox{\hyphenpenalty=10000\tolerance=5000 \parindent=0pt\raggedright \rm #1\hfill}}\bigskip \par\penalty 200} \def\chapheading{\parsearg\chapheadingzzz} \def\chapheadingzzz #1{\chapbreak % {\chapfonts \vbox{\hyphenpenalty=10000\tolerance=5000 \parindent=0pt\raggedright \rm #1\hfill}}\bigskip \par\penalty 200} % @heading, @subheading, @subsubheading. \def\heading{\parsearg\plainsecheading} \def\subheading{\parsearg\plainsubsecheading} \def\subsubheading{\parsearg\plainsubsubsecheading} % These macros generate a chapter, section, etc. heading only % (including whitespace, linebreaking, etc. around it), % given all the information in convenient, parsed form. %%% Args are the skip and penalty (usually negative) \def\dobreak#1#2{\par\ifdim\lastskip<#1\removelastskip\penalty#2\vskip#1\fi} \def\setchapterstyle #1 {\csname CHAPF#1\endcsname} %%% Define plain chapter starts, and page on/off switching for it % Parameter controlling skip before chapter headings (if needed) \newskip\chapheadingskip \def\chapbreak{\dobreak \chapheadingskip {-4000}} \def\chappager{\par\vfill\supereject} \def\chapoddpage{\chappager \ifodd\pageno \else \hbox to 0pt{} \chappager\fi} \def\setchapternewpage #1 {\csname CHAPPAG#1\endcsname} \def\CHAPPAGoff{% \global\let\contentsalignmacro = \chappager \global\let\pchapsepmacro=\chapbreak \global\let\pagealignmacro=\chappager} \def\CHAPPAGon{% \global\let\contentsalignmacro = \chappager \global\let\pchapsepmacro=\chappager \global\let\pagealignmacro=\chappager \global\def\HEADINGSon{\HEADINGSsingle}} \def\CHAPPAGodd{ \global\let\contentsalignmacro = \chapoddpage \global\let\pchapsepmacro=\chapoddpage \global\let\pagealignmacro=\chapoddpage \global\def\HEADINGSon{\HEADINGSdouble}} \CHAPPAGon \def\CHAPFplain{ \global\let\chapmacro=\chfplain \global\let\unnumbchapmacro=\unnchfplain \global\let\centerchapmacro=\centerchfplain} % Plain chapter opening. % #1 is the text, #2 the chapter number or empty if unnumbered. \def\chfplain#1#2{% \pchapsepmacro {% \chapfonts \rm \def\chapnum{#2}% \setbox0 = \hbox{#2\ifx\chapnum\empty\else\enspace\fi}% \vbox{\hyphenpenalty=10000 \tolerance=5000 \parindent=0pt \raggedright \hangindent = \wd0 \centerparametersmaybe \unhbox0 #1\par}% }% \nobreak\bigskip % no page break after a chapter title \nobreak } % Plain opening for unnumbered. \def\unnchfplain#1{\chfplain{#1}{}} % @centerchap -- centered and unnumbered. \let\centerparametersmaybe = \relax \def\centerchfplain#1{{% \def\centerparametersmaybe{% \advance\rightskip by 3\rightskip \leftskip = \rightskip \parfillskip = 0pt }% \chfplain{#1}{}% }} \CHAPFplain % The default \def\unnchfopen #1{% \chapoddpage {\chapfonts \vbox{\hyphenpenalty=10000\tolerance=5000 \parindent=0pt\raggedright \rm #1\hfill}}\bigskip \par\nobreak } \def\chfopen #1#2{\chapoddpage {\chapfonts \vbox to 3in{\vfil \hbox to\hsize{\hfil #2} \hbox to\hsize{\hfil #1} \vfil}}% \par\penalty 5000 % } \def\centerchfopen #1{% \chapoddpage {\chapfonts \vbox{\hyphenpenalty=10000\tolerance=5000 \parindent=0pt \hfill {\rm #1}\hfill}}\bigskip \par\nobreak } \def\CHAPFopen{ \global\let\chapmacro=\chfopen \global\let\unnumbchapmacro=\unnchfopen \global\let\centerchapmacro=\centerchfopen} % Section titles. \newskip\secheadingskip \def\secheadingbreak{\dobreak \secheadingskip {-1000}} \def\secheading#1#2#3{\sectionheading{sec}{#2.#3}{#1}} \def\plainsecheading#1{\sectionheading{sec}{}{#1}} % Subsection titles. \newskip \subsecheadingskip \def\subsecheadingbreak{\dobreak \subsecheadingskip {-500}} \def\subsecheading#1#2#3#4{\sectionheading{subsec}{#2.#3.#4}{#1}} \def\plainsubsecheading#1{\sectionheading{subsec}{}{#1}} % Subsubsection titles. \let\subsubsecheadingskip = \subsecheadingskip \let\subsubsecheadingbreak = \subsecheadingbreak \def\subsubsecheading#1#2#3#4#5{\sectionheading{subsubsec}{#2.#3.#4.#5}{#1}} \def\plainsubsubsecheading#1{\sectionheading{subsubsec}{}{#1}} % Print any size section title. % % #1 is the section type (sec/subsec/subsubsec), #2 is the section % number (maybe empty), #3 the text. \def\sectionheading#1#2#3{% {% \expandafter\advance\csname #1headingskip\endcsname by \parskip \csname #1headingbreak\endcsname }% {% % Switch to the right set of fonts. \csname #1fonts\endcsname \rm % % Only insert the separating space if we have a section number. \def\secnum{#2}% \setbox0 = \hbox{#2\ifx\secnum\empty\else\enspace\fi}% % \vbox{\hyphenpenalty=10000 \tolerance=5000 \parindent=0pt \raggedright \hangindent = \wd0 % zero if no section number \unhbox0 #3}% }% \ifdim\parskip<10pt \nobreak\kern10pt\nobreak\kern-\parskip\fi \nobreak } \message{toc,} % Table of contents. \newwrite\tocfile % Write an entry to the toc file, opening it if necessary. % Called from @chapter, etc. We supply {\folio} at the end of the % argument, which will end up as the last argument to the \...entry macro. % % We open the .toc file here instead of at @setfilename or any other % given time so that @contents can be put in the document anywhere. % \newif\iftocfileopened \def\writetocentry#1{% \iftocfileopened\else \immediate\openout\tocfile = \jobname.toc \global\tocfileopenedtrue \fi \iflinks \write\tocfile{#1{\folio}}\fi } \newskip\contentsrightmargin \contentsrightmargin=1in \newcount\savepageno \newcount\lastnegativepageno \lastnegativepageno = -1 % Finish up the main text and prepare to read what we've written % to \tocfile. % \def\startcontents#1{% % If @setchapternewpage on, and @headings double, the contents should % start on an odd page, unlike chapters. Thus, we maintain % \contentsalignmacro in parallel with \pagealignmacro. % From: Torbjorn Granlund \contentsalignmacro \immediate\closeout\tocfile % % Don't need to put `Contents' or `Short Contents' in the headline. % It is abundantly clear what they are. \unnumbchapmacro{#1}\def\thischapter{}% \savepageno = \pageno \begingroup % Set up to handle contents files properly. \catcode`\\=0 \catcode`\{=1 \catcode`\}=2 \catcode`\@=11 % We can't do this, because then an actual ^ in a section % title fails, e.g., @chapter ^ -- exponentiation. --karl, 9jul97. %\catcode`\^=7 % to see ^^e4 as \"a etc. juha@piuha.ydi.vtt.fi \raggedbottom % Worry more about breakpoints than the bottom. \advance\hsize by -\contentsrightmargin % Don't use the full line length. % % Roman numerals for page numbers. \ifnum \pageno>0 \pageno = \lastnegativepageno \fi } % Normal (long) toc. \def\contents{% \startcontents{\putwordTOC}% \openin 1 \jobname.toc \ifeof 1 \else \closein 1 \input \jobname.toc \fi \vfill \eject \contentsalignmacro % in case @setchapternewpage odd is in effect \pdfmakeoutlines \endgroup \lastnegativepageno = \pageno \pageno = \savepageno } % And just the chapters. \def\summarycontents{% \startcontents{\putwordShortTOC}% % \let\chapentry = \shortchapentry \let\unnumbchapentry = \shortunnumberedentry % We want a true roman here for the page numbers. \secfonts \let\rm=\shortcontrm \let\bf=\shortcontbf \let\sl=\shortcontsl \rm \hyphenpenalty = 10000 \advance\baselineskip by 1pt % Open it up a little. \def\secentry ##1##2##3##4{} \def\unnumbsecentry ##1##2{} \def\subsecentry ##1##2##3##4##5{} \def\unnumbsubsecentry ##1##2{} \def\subsubsecentry ##1##2##3##4##5##6{} \def\unnumbsubsubsecentry ##1##2{} \openin 1 \jobname.toc \ifeof 1 \else \closein 1 \input \jobname.toc \fi \vfill \eject \contentsalignmacro % in case @setchapternewpage odd is in effect \endgroup \lastnegativepageno = \pageno \pageno = \savepageno } \let\shortcontents = \summarycontents \ifpdf \pdfcatalog{/PageMode /UseOutlines}% \fi % These macros generate individual entries in the table of contents. % The first argument is the chapter or section name. % The last argument is the page number. % The arguments in between are the chapter number, section number, ... % Chapter-level things, for both the long and short contents. \def\chapentry#1#2#3{\dochapentry{#2\labelspace#1}{#3}} % See comments in \dochapentry re vbox and related settings \def\shortchapentry#1#2#3{% \tocentry{\shortchaplabel{#2}\labelspace #1}{\doshortpageno\bgroup#3\egroup}% } % Typeset the label for a chapter or appendix for the short contents. % The arg is, e.g. `Appendix A' for an appendix, or `3' for a chapter. % We could simplify the code here by writing out an \appendixentry % command in the toc file for appendices, instead of using \chapentry % for both, but it doesn't seem worth it. % \newdimen\shortappendixwidth % \def\shortchaplabel#1{% % Compute width of word "Appendix", may change with language. \setbox0 = \hbox{\shortcontrm \putwordAppendix}% \shortappendixwidth = \wd0 % % We typeset #1 in a box of constant width, regardless of the text of % #1, so the chapter titles will come out aligned. \setbox0 = \hbox{#1}% \dimen0 = \ifdim\wd0 > \shortappendixwidth \shortappendixwidth \else 0pt \fi % % This space should be plenty, since a single number is .5em, and the % widest letter (M) is 1em, at least in the Computer Modern fonts. % (This space doesn't include the extra space that gets added after % the label; that gets put in by \shortchapentry above.) \advance\dimen0 by 1.1em \hbox to \dimen0{#1\hfil}% } \def\unnumbchapentry#1#2{\dochapentry{#1}{#2}} \def\shortunnumberedentry#1#2{\tocentry{#1}{\doshortpageno\bgroup#2\egroup}} % Sections. \def\secentry#1#2#3#4{\dosecentry{#2.#3\labelspace#1}{#4}} \def\unnumbsecentry#1#2{\dosecentry{#1}{#2}} % Subsections. \def\subsecentry#1#2#3#4#5{\dosubsecentry{#2.#3.#4\labelspace#1}{#5}} \def\unnumbsubsecentry#1#2{\dosubsecentry{#1}{#2}} % And subsubsections. \def\subsubsecentry#1#2#3#4#5#6{% \dosubsubsecentry{#2.#3.#4.#5\labelspace#1}{#6}} \def\unnumbsubsubsecentry#1#2{\dosubsubsecentry{#1}{#2}} % This parameter controls the indentation of the various levels. \newdimen\tocindent \tocindent = 3pc % Now for the actual typesetting. In all these, #1 is the text and #2 is the % page number. % % If the toc has to be broken over pages, we want it to be at chapters % if at all possible; hence the \penalty. \def\dochapentry#1#2{% \penalty-300 \vskip1\baselineskip plus.33\baselineskip minus.25\baselineskip \begingroup \chapentryfonts \tocentry{#1}{\dopageno\bgroup#2\egroup}% \endgroup \nobreak\vskip .25\baselineskip plus.1\baselineskip } \def\dosecentry#1#2{\begingroup \secentryfonts \leftskip=\tocindent \tocentry{#1}{\dopageno\bgroup#2\egroup}% \endgroup} \def\dosubsecentry#1#2{\begingroup \subsecentryfonts \leftskip=2\tocindent \tocentry{#1}{\dopageno\bgroup#2\egroup}% \endgroup} \def\dosubsubsecentry#1#2{\begingroup \subsubsecentryfonts \leftskip=3\tocindent \tocentry{#1}{\dopageno\bgroup#2\egroup}% \endgroup} % Final typesetting of a toc entry; we use the same \entry macro as for % the index entries, but we want to suppress hyphenation here. (We % can't do that in the \entry macro, since index entries might consist % of hyphenated-identifiers-that-do-not-fit-on-a-line-and-nothing-else.) \def\tocentry#1#2{\begingroup \vskip 0pt plus1pt % allow a little stretch for the sake of nice page breaks % Do not use \turnoffactive in these arguments. Since the toc is % typeset in cmr, so characters such as _ would come out wrong; we % have to do the usual translation tricks. \entry{#1}{#2}% \endgroup} % Space between chapter (or whatever) number and the title. \def\labelspace{\hskip1em \relax} \def\dopageno#1{{\rm #1}} \def\doshortpageno#1{{\rm #1}} \def\chapentryfonts{\secfonts \rm} \def\secentryfonts{\textfonts} \let\subsecentryfonts = \textfonts \let\subsubsecentryfonts = \textfonts \message{environments,} % @foo ... @end foo. % Since these characters are used in examples, it should be an even number of % \tt widths. Each \tt character is 1en, so two makes it 1em. % Furthermore, these definitions must come after we define our fonts. \newbox\dblarrowbox \newbox\longdblarrowbox \newbox\pushcharbox \newbox\bullbox \newbox\equivbox \newbox\errorbox %{\tentt %\global\setbox\dblarrowbox = \hbox to 1em{\hfil$\Rightarrow$\hfil} %\global\setbox\longdblarrowbox = \hbox to 1em{\hfil$\mapsto$\hfil} %\global\setbox\pushcharbox = \hbox to 1em{\hfil$\dashv$\hfil} %\global\setbox\equivbox = \hbox to 1em{\hfil$\ptexequiv$\hfil} % Adapted from the manmac format (p.420 of TeXbook) %\global\setbox\bullbox = \hbox to 1em{\kern.15em\vrule height .75ex width .85ex % depth .1ex\hfil} %} % @point{}, @result{}, @expansion{}, @print{}, @equiv{}. \def\point{$\star$} \def\result{\leavevmode\raise.15ex\hbox to 1em{\hfil$\Rightarrow$\hfil}} \def\expansion{\leavevmode\raise.1ex\hbox to 1em{\hfil$\mapsto$\hfil}} \def\print{\leavevmode\lower.1ex\hbox to 1em{\hfil$\dashv$\hfil}} \def\equiv{\leavevmode\lower.1ex\hbox to 1em{\hfil$\ptexequiv$\hfil}} % Adapted from the TeXbook's \boxit. {\tentt \global\dimen0 = 3em}% Width of the box. \dimen2 = .55pt % Thickness of rules % The text. (`r' is open on the right, `e' somewhat less so on the left.) \setbox0 = \hbox{\kern-.75pt \tensf error\kern-1.5pt} \global\setbox\errorbox=\hbox to \dimen0{\hfil \hsize = \dimen0 \advance\hsize by -5.8pt % Space to left+right. \advance\hsize by -2\dimen2 % Rules. \vbox{ \hrule height\dimen2 \hbox{\vrule width\dimen2 \kern3pt % Space to left of text. \vtop{\kern2.4pt \box0 \kern2.4pt}% Space above/below. \kern3pt\vrule width\dimen2}% Space to right. \hrule height\dimen2} \hfil} % The @error{} command. \def\error{\leavevmode\lower.7ex\copy\errorbox} % @tex ... @end tex escapes into raw Tex temporarily. % One exception: @ is still an escape character, so that @end tex works. % But \@ or @@ will get a plain tex @ character. \def\tex{\begingroup \catcode `\\=0 \catcode `\{=1 \catcode `\}=2 \catcode `\$=3 \catcode `\&=4 \catcode `\#=6 \catcode `\^=7 \catcode `\_=8 \catcode `\~=13 \let~=\tie \catcode `\%=14 \catcode 43=12 % plus \catcode`\"=12 \catcode`\==12 \catcode`\|=12 \catcode`\<=12 \catcode`\>=12 \escapechar=`\\ % \let\b=\ptexb \let\bullet=\ptexbullet \let\c=\ptexc \let\,=\ptexcomma \let\.=\ptexdot \let\dots=\ptexdots \let\equiv=\ptexequiv \let\!=\ptexexclam \let\i=\ptexi \let\{=\ptexlbrace \let\+=\tabalign \let\}=\ptexrbrace \let\*=\ptexstar \let\t=\ptext % \def\endldots{\mathinner{\ldots\ldots\ldots\ldots}}% \def\enddots{\relax\ifmmode\endldots\else$\mathsurround=0pt \endldots\,$\fi}% \def\@{@}% \let\Etex=\endgroup} % Define @lisp ... @endlisp. % @lisp does a \begingroup so it can rebind things, % including the definition of @endlisp (which normally is erroneous). % Amount to narrow the margins by for @lisp. \newskip\lispnarrowing \lispnarrowing=0.4in % This is the definition that ^^M gets inside @lisp, @example, and other % such environments. \null is better than a space, since it doesn't % have any width. \def\lisppar{\null\endgraf} % Make each space character in the input produce a normal interword % space in the output. Don't allow a line break at this space, as this % is used only in environments like @example, where each line of input % should produce a line of output anyway. % {\obeyspaces % \gdef\sepspaces{\obeyspaces\let =\tie}} % Define \obeyedspace to be our active space, whatever it is. This is % for use in \parsearg. {\sepspaces% \global\let\obeyedspace= } % This space is always present above and below environments. \newskip\envskipamount \envskipamount = 0pt % Make spacing and below environment symmetrical. We use \parskip here % to help in doing that, since in @example-like environments \parskip % is reset to zero; thus the \afterenvbreak inserts no space -- but the % start of the next paragraph will insert \parskip % \def\aboveenvbreak{{\advance\envskipamount by \parskip \endgraf \ifdim\lastskip<\envskipamount \removelastskip \penalty-50 \vskip\envskipamount \fi}} \let\afterenvbreak = \aboveenvbreak % \nonarrowing is a flag. If "set", @lisp etc don't narrow margins. \let\nonarrowing=\relax % @cartouche ... @end cartouche: draw rectangle w/rounded corners around % environment contents. \font\circle=lcircle10 \newdimen\circthick \newdimen\cartouter\newdimen\cartinner \newskip\normbskip\newskip\normpskip\newskip\normlskip \circthick=\fontdimen8\circle % \def\ctl{{\circle\char'013\hskip -6pt}}% 6pt from pl file: 1/2charwidth \def\ctr{{\hskip 6pt\circle\char'010}} \def\cbl{{\circle\char'012\hskip -6pt}} \def\cbr{{\hskip 6pt\circle\char'011}} \def\carttop{\hbox to \cartouter{\hskip\lskip \ctl\leaders\hrule height\circthick\hfil\ctr \hskip\rskip}} \def\cartbot{\hbox to \cartouter{\hskip\lskip \cbl\leaders\hrule height\circthick\hfil\cbr \hskip\rskip}} % \newskip\lskip\newskip\rskip \long\def\cartouche{% \begingroup \lskip=\leftskip \rskip=\rightskip \leftskip=0pt\rightskip=0pt %we want these *outside*. \cartinner=\hsize \advance\cartinner by-\lskip \advance\cartinner by-\rskip \cartouter=\hsize \advance\cartouter by 18.4pt % allow for 3pt kerns on either % side, and for 6pt waste from % each corner char, and rule thickness \normbskip=\baselineskip \normpskip=\parskip \normlskip=\lineskip % Flag to tell @lisp, etc., not to narrow margin. \let\nonarrowing=\comment \vbox\bgroup \baselineskip=0pt\parskip=0pt\lineskip=0pt \carttop \hbox\bgroup \hskip\lskip \vrule\kern3pt \vbox\bgroup \hsize=\cartinner \kern3pt \begingroup \baselineskip=\normbskip \lineskip=\normlskip \parskip=\normpskip \vskip -\parskip \def\Ecartouche{% \endgroup \kern3pt \egroup \kern3pt\vrule \hskip\rskip \egroup \cartbot \egroup \endgroup }} % This macro is called at the beginning of all the @example variants, % inside a group. \def\nonfillstart{% \aboveenvbreak \inENV % This group ends at the end of the body \hfuzz = 12pt % Don't be fussy \sepspaces % Make spaces be word-separators rather than space tokens. \singlespace \let\par = \lisppar % don't ignore blank lines \obeylines % each line of input is a line of output \parskip = 0pt \parindent = 0pt \emergencystretch = 0pt % don't try to avoid overfull boxes % @cartouche defines \nonarrowing to inhibit narrowing % at next level down. \ifx\nonarrowing\relax \advance \leftskip by \lispnarrowing \exdentamount=\lispnarrowing \let\exdent=\nofillexdent \let\nonarrowing=\relax \fi } % Define the \E... control sequence only if we are inside the particular % environment, so the error checking in \end will work. % % To end an @example-like environment, we first end the paragraph (via % \afterenvbreak's vertical glue), and then the group. That way we keep % the zero \parskip that the environments set -- \parskip glue will be % inserted at the beginning of the next paragraph in the document, after % the environment. % \def\nonfillfinish{\afterenvbreak\endgroup} % @lisp: indented, narrowed, typewriter font. \def\lisp{\begingroup \nonfillstart \let\Elisp = \nonfillfinish \tt \let\kbdfont = \kbdexamplefont % Allow @kbd to do something special. \gobble % eat return } % @example: Same as @lisp. \def\example{\begingroup \def\Eexample{\nonfillfinish\endgroup}\lisp} % @small... is usually equivalent to the non-small (@smallbook % redefines). We must call \example (or whatever) last in the % definition, since it reads the return following the @example (or % whatever) command. % % This actually allows (for example) @end display inside an % @smalldisplay. Too bad, but makeinfo will catch the error anyway. % \def\smalldisplay{\begingroup\def\Esmalldisplay{\nonfillfinish\endgroup}\display} \def\smallexample{\begingroup\def\Esmallexample{\nonfillfinish\endgroup}\lisp} \def\smallformat{\begingroup\def\Esmallformat{\nonfillfinish\endgroup}\format} \def\smalllisp{\begingroup\def\Esmalllisp{\nonfillfinish\endgroup}\lisp} % Real @smallexample and @smalllisp (when @smallbook): use smaller fonts. % Originally contributed by Pavel@xerox. \def\smalllispx{\begingroup \def\Esmalllisp{\nonfillfinish\endgroup}% \def\Esmallexample{\nonfillfinish\endgroup}% \smallfonts \lisp } % @display: same as @lisp except keep current font. % \def\display{\begingroup \nonfillstart \let\Edisplay = \nonfillfinish \gobble } % @smalldisplay (when @smallbook): @display plus smaller fonts. % \def\smalldisplayx{\begingroup \def\Esmalldisplay{\nonfillfinish\endgroup}% \smallfonts \rm \display } % @format: same as @display except don't narrow margins. % \def\format{\begingroup \let\nonarrowing = t \nonfillstart \let\Eformat = \nonfillfinish \gobble } % @smallformat (when @smallbook): @format plus smaller fonts. % \def\smallformatx{\begingroup \def\Esmallformat{\nonfillfinish\endgroup}% \smallfonts \rm \format } % @flushleft (same as @format). % \def\flushleft{\begingroup \def\Eflushleft{\nonfillfinish\endgroup}\format} % @flushright. % \def\flushright{\begingroup \let\nonarrowing = t \nonfillstart \let\Eflushright = \nonfillfinish \advance\leftskip by 0pt plus 1fill \gobble } % @quotation does normal linebreaking (hence we can't use \nonfillstart) % and narrows the margins. % \def\quotation{% \begingroup\inENV %This group ends at the end of the @quotation body {\parskip=0pt \aboveenvbreak}% because \aboveenvbreak inserts \parskip \singlespace \parindent=0pt % We have retained a nonzero parskip for the environment, since we're % doing normal filling. So to avoid extra space below the environment... \def\Equotation{\parskip = 0pt \nonfillfinish}% % % @cartouche defines \nonarrowing to inhibit narrowing at next level down. \ifx\nonarrowing\relax \advance\leftskip by \lispnarrowing \advance\rightskip by \lispnarrowing \exdentamount = \lispnarrowing \let\nonarrowing = \relax \fi } \message{defuns,} % @defun etc. % Allow user to change definition object font (\df) internally \def\setdeffont #1 {\csname DEF#1\endcsname} \newskip\defbodyindent \defbodyindent=.4in \newskip\defargsindent \defargsindent=50pt \newskip\deftypemargin \deftypemargin=12pt \newskip\deflastargmargin \deflastargmargin=18pt \newcount\parencount % define \functionparens, which makes ( and ) and & do special things. % \functionparens affects the group it is contained in. \def\activeparens{% \catcode`\(=\active \catcode`\)=\active \catcode`\&=\active \catcode`\[=\active \catcode`\]=\active} % Make control sequences which act like normal parenthesis chars. \let\lparen = ( \let\rparen = ) {\activeparens % Now, smart parens don't turn on until &foo (see \amprm) % Be sure that we always have a definition for `(', etc. For example, % if the fn name has parens in it, \boldbrax will not be in effect yet, % so TeX would otherwise complain about undefined control sequence. \global\let(=\lparen \global\let)=\rparen \global\let[=\lbrack \global\let]=\rbrack \gdef\functionparens{\boldbrax\let&=\amprm\parencount=0 } \gdef\boldbrax{\let(=\opnr\let)=\clnr\let[=\lbrb\let]=\rbrb} % This is used to turn on special parens % but make & act ordinary (given that it's active). \gdef\boldbraxnoamp{\let(=\opnr\let)=\clnr\let[=\lbrb\let]=\rbrb\let&=\ampnr} % Definitions of (, ) and & used in args for functions. % This is the definition of ( outside of all parentheses. \gdef\oprm#1 {{\rm\char`\(}#1 \bf \let(=\opnested \global\advance\parencount by 1 } % % This is the definition of ( when already inside a level of parens. \gdef\opnested{\char`\(\global\advance\parencount by 1 } % \gdef\clrm{% Print a paren in roman if it is taking us back to depth of 0. % also in that case restore the outer-level definition of (. \ifnum \parencount=1 {\rm \char `\)}\sl \let(=\oprm \else \char `\) \fi \global\advance \parencount by -1 } % If we encounter &foo, then turn on ()-hacking afterwards \gdef\amprm#1 {{\rm\}\let(=\oprm \let)=\clrm\ } % \gdef\normalparens{\boldbrax\let&=\ampnr} } % End of definition inside \activeparens %% These parens (in \boldbrax) actually are a little bolder than the %% contained text. This is especially needed for [ and ] \def\opnr{{\sf\char`\(}\global\advance\parencount by 1 } \def\clnr{{\sf\char`\)}\global\advance\parencount by -1 } \let\ampnr = \& \def\lbrb{{\bf\char`\[}} \def\rbrb{{\bf\char`\]}} % Active &'s sneak into the index arguments, so make sure it's defined. { \catcode`& = 13 \global\let& = \ampnr } % First, defname, which formats the header line itself. % #1 should be the function name. % #2 should be the type of definition, such as "Function". \def\defname #1#2{% % Get the values of \leftskip and \rightskip as they were % outside the @def... \dimen2=\leftskip \advance\dimen2 by -\defbodyindent \noindent \setbox0=\hbox{\hskip \deflastargmargin{\rm #2}\hskip \deftypemargin}% \dimen0=\hsize \advance \dimen0 by -\wd0 % compute size for first line \dimen1=\hsize \advance \dimen1 by -\defargsindent %size for continuations \parshape 2 0in \dimen0 \defargsindent \dimen1 % Now output arg 2 ("Function" or some such) % ending at \deftypemargin from the right margin, % but stuck inside a box of width 0 so it does not interfere with linebreaking {% Adjust \hsize to exclude the ambient margins, % so that \rightline will obey them. \advance \hsize by -\dimen2 \rlap{\rightline{{\rm #2}\hskip -1.25pc }}}% % Make all lines underfull and no complaints: \tolerance=10000 \hbadness=10000 \advance\leftskip by -\defbodyindent \exdentamount=\defbodyindent {\df #1}\enskip % Generate function name } % Actually process the body of a definition % #1 should be the terminating control sequence, such as \Edefun. % #2 should be the "another name" control sequence, such as \defunx. % #3 should be the control sequence that actually processes the header, % such as \defunheader. \def\defparsebody #1#2#3{\begingroup\inENV% Environment for definitionbody \medbreak % % Define the end token that this defining construct specifies % so that it will exit this group. \def#1{\endgraf\endgroup\medbreak}% \def#2{\begingroup\obeylines\activeparens\spacesplit#3}% \parindent=0in \advance\leftskip by \defbodyindent \exdentamount=\defbodyindent \begingroup % \catcode 61=\active % 61 is `=' \obeylines\activeparens\spacesplit#3} % #1 is the \E... control sequence to end the definition (which we define). % #2 is the \...x control sequence for consecutive fns (which we define). % #3 is the control sequence to call to resume processing. % #4, delimited by the space, is the class name. % \def\defmethparsebody#1#2#3#4 {\begingroup\inENV % \medbreak % % Define the end token that this defining construct specifies % so that it will exit this group. \def#1{\endgraf\endgroup\medbreak}% \def#2##1 {\begingroup\obeylines\activeparens\spacesplit{#3{##1}}}% \parindent=0in \advance\leftskip by \defbodyindent \exdentamount=\defbodyindent \begingroup\obeylines\activeparens\spacesplit{#3{#4}}} % Used for @deftypemethod and @deftypeivar. % #1 is the \E... control sequence to end the definition (which we define). % #2 is the \...x control sequence for consecutive fns (which we define). % #3 is the control sequence to call to resume processing. % #4, delimited by a space, is the class name. % #5 is the method's return type. % \def\deftypemethparsebody#1#2#3#4 #5 {\begingroup\inENV \medbreak \def#1{\endgraf\endgroup\medbreak}% \def#2##1 ##2 {\begingroup\obeylines\activeparens\spacesplit{#3{##1}{##2}}}% \parindent=0in \advance\leftskip by \defbodyindent \exdentamount=\defbodyindent \begingroup\obeylines\activeparens\spacesplit{#3{#4}{#5}}} % Used for @deftypeop. The change from \deftypemethparsebody is an % extra argument at the beginning which is the `category', instead of it % being the hardwired string `Method' or `Instance Variable'. We have % to account for this both in the \...x definition and in parsing the % input at hand. Thus also need a control sequence (passed as #5) for % the \E... definition to assign the category name to. % \def\deftypeopparsebody#1#2#3#4#5 #6 {\begingroup\inENV \medbreak \def#1{\endgraf\endgroup\medbreak}% \def#2##1 ##2 ##3 {% \def#4{##1}% \begingroup\obeylines\activeparens\spacesplit{#3{##2}{##3}}}% \parindent=0in \advance\leftskip by \defbodyindent \exdentamount=\defbodyindent \begingroup\obeylines\activeparens\spacesplit{#3{#5}{#6}}} \def\defopparsebody #1#2#3#4#5 {\begingroup\inENV % \medbreak % % Define the end token that this defining construct specifies % so that it will exit this group. \def#1{\endgraf\endgroup\medbreak}% \def#2##1 ##2 {\def#4{##1}% \begingroup\obeylines\activeparens\spacesplit{#3{##2}}}% \parindent=0in \advance\leftskip by \defbodyindent \exdentamount=\defbodyindent \begingroup\obeylines\activeparens\spacesplit{#3{#5}}} % These parsing functions are similar to the preceding ones % except that they do not make parens into active characters. % These are used for "variables" since they have no arguments. \def\defvarparsebody #1#2#3{\begingroup\inENV% Environment for definitionbody \medbreak % % Define the end token that this defining construct specifies % so that it will exit this group. \def#1{\endgraf\endgroup\medbreak}% \def#2{\begingroup\obeylines\spacesplit#3}% \parindent=0in \advance\leftskip by \defbodyindent \exdentamount=\defbodyindent \begingroup % \catcode 61=\active % \obeylines\spacesplit#3} % This is used for \def{tp,vr}parsebody. It could probably be used for % some of the others, too, with some judicious conditionals. % \def\parsebodycommon#1#2#3{% \begingroup\inENV % \medbreak % % Define the end token that this defining construct specifies % so that it will exit this group. \def#1{\endgraf\endgroup\medbreak}% \def#2##1 {\begingroup\obeylines\spacesplit{#3{##1}}}% \parindent=0in \advance\leftskip by \defbodyindent \exdentamount=\defbodyindent \begingroup\obeylines } \def\defvrparsebody#1#2#3#4 {% \parsebodycommon{#1}{#2}{#3}% \spacesplit{#3{#4}}% } % This loses on `@deftp {Data Type} {struct termios}' -- it thinks the % type is just `struct', because we lose the braces in `{struct % termios}' when \spacesplit reads its undelimited argument. Sigh. % \let\deftpparsebody=\defvrparsebody % % So, to get around this, we put \empty in with the type name. That % way, TeX won't find exactly `{...}' as an undelimited argument, and % won't strip off the braces. % \def\deftpparsebody #1#2#3#4 {% \parsebodycommon{#1}{#2}{#3}% \spacesplit{\parsetpheaderline{#3{#4}}}\empty } % Fine, but then we have to eventually remove the \empty *and* the % braces (if any). That's what this does. % \def\removeemptybraces\empty#1\relax{#1} % After \spacesplit has done its work, this is called -- #1 is the final % thing to call, #2 the type name (which starts with \empty), and #3 % (which might be empty) the arguments. % \def\parsetpheaderline#1#2#3{% #1{\removeemptybraces#2\relax}{#3}% }% \def\defopvarparsebody #1#2#3#4#5 {\begingroup\inENV % \medbreak % % Define the end token that this defining construct specifies % so that it will exit this group. \def#1{\endgraf\endgroup\medbreak}% \def#2##1 ##2 {\def#4{##1}% \begingroup\obeylines\spacesplit{#3{##2}}}% \parindent=0in \advance\leftskip by \defbodyindent \exdentamount=\defbodyindent \begingroup\obeylines\spacesplit{#3{#5}}} % Split up #2 at the first space token. % call #1 with two arguments: % the first is all of #2 before the space token, % the second is all of #2 after that space token. % If #2 contains no space token, all of it is passed as the first arg % and the second is passed as empty. {\obeylines \gdef\spacesplit#1#2^^M{\endgroup\spacesplitfoo{#1}#2 \relax\spacesplitfoo}% \long\gdef\spacesplitfoo#1#2 #3#4\spacesplitfoo{% \ifx\relax #3% #1{#2}{}\else #1{#2}{#3#4}\fi}} % So much for the things common to all kinds of definitions. % Define @defun. % First, define the processing that is wanted for arguments of \defun % Use this to expand the args and terminate the paragraph they make up \def\defunargs#1{\functionparens \sl % Expand, preventing hyphenation at `-' chars. % Note that groups don't affect changes in \hyphenchar. % Set the font temporarily and use \font in case \setfont made \tensl a macro. {\tensl\hyphenchar\font=0}% #1% {\tensl\hyphenchar\font=45}% \ifnum\parencount=0 \else \errmessage{Unbalanced parentheses in @def}\fi% \interlinepenalty=10000 \advance\rightskip by 0pt plus 1fil \endgraf\nobreak\vskip -\parskip\nobreak } \def\deftypefunargs #1{% % Expand, preventing hyphenation at `-' chars. % Note that groups don't affect changes in \hyphenchar. % Use \boldbraxnoamp, not \functionparens, so that & is not special. \boldbraxnoamp \tclose{#1}% avoid \code because of side effects on active chars \interlinepenalty=10000 \advance\rightskip by 0pt plus 1fil \endgraf\nobreak\vskip -\parskip\nobreak } % Do complete processing of one @defun or @defunx line already parsed. % @deffn Command forward-char nchars \def\deffn{\defmethparsebody\Edeffn\deffnx\deffnheader} \def\deffnheader #1#2#3{\doind {fn}{\code{#2}}% \begingroup\defname {#2}{#1}\defunargs{#3}\endgroup % \catcode 61=\other % Turn off change made in \defparsebody } % @defun == @deffn Function \def\defun{\defparsebody\Edefun\defunx\defunheader} \def\defunheader #1#2{\doind {fn}{\code{#1}}% Make entry in function index \begingroup\defname {#1}{\putwordDeffunc}% \defunargs {#2}\endgroup % \catcode 61=\other % Turn off change made in \defparsebody } % @deftypefun int foobar (int @var{foo}, float @var{bar}) \def\deftypefun{\defparsebody\Edeftypefun\deftypefunx\deftypefunheader} % #1 is the data type. #2 is the name and args. \def\deftypefunheader #1#2{\deftypefunheaderx{#1}#2 \relax} % #1 is the data type, #2 the name, #3 the args. \def\deftypefunheaderx #1#2 #3\relax{% \doind {fn}{\code{#2}}% Make entry in function index \begingroup\defname {\defheaderxcond#1\relax$$$#2}{\putwordDeftypefun}% \deftypefunargs {#3}\endgroup % \catcode 61=\other % Turn off change made in \defparsebody } % @deftypefn {Library Function} int foobar (int @var{foo}, float @var{bar}) \def\deftypefn{\defmethparsebody\Edeftypefn\deftypefnx\deftypefnheader} % \defheaderxcond#1\relax$$$ % puts #1 in @code, followed by a space, but does nothing if #1 is null. \def\defheaderxcond#1#2$$${\ifx#1\relax\else\code{#1#2} \fi} % #1 is the classification. #2 is the data type. #3 is the name and args. \def\deftypefnheader #1#2#3{\deftypefnheaderx{#1}{#2}#3 \relax} % #1 is the classification, #2 the data type, #3 the name, #4 the args. \def\deftypefnheaderx #1#2#3 #4\relax{% \doind {fn}{\code{#3}}% Make entry in function index \begingroup \normalparens % notably, turn off `&' magic, which prevents % at least some C++ text from working \defname {\defheaderxcond#2\relax$$$#3}{#1}% \deftypefunargs {#4}\endgroup % \catcode 61=\other % Turn off change made in \defparsebody } % @defmac == @deffn Macro \def\defmac{\defparsebody\Edefmac\defmacx\defmacheader} \def\defmacheader #1#2{\doind {fn}{\code{#1}}% Make entry in function index \begingroup\defname {#1}{\putwordDefmac}% \defunargs {#2}\endgroup % \catcode 61=\other % Turn off change made in \defparsebody } % @defspec == @deffn Special Form \def\defspec{\defparsebody\Edefspec\defspecx\defspecheader} \def\defspecheader #1#2{\doind {fn}{\code{#1}}% Make entry in function index \begingroup\defname {#1}{\putwordDefspec}% \defunargs {#2}\endgroup % \catcode 61=\other % Turn off change made in \defparsebody } % @defop CATEGORY CLASS OPERATION ARG... % \def\defop #1 {\def\defoptype{#1}% \defopparsebody\Edefop\defopx\defopheader\defoptype} % \def\defopheader#1#2#3{% \dosubind {fn}{\code{#2}}{\putwordon\ #1}% Make entry in function index \begingroup\defname {#2}{\defoptype\ \putwordon\ #1}% \defunargs {#3}\endgroup % } % @deftypeop CATEGORY CLASS TYPE OPERATION ARG... % \def\deftypeop #1 {\def\deftypeopcategory{#1}% \deftypeopparsebody\Edeftypeop\deftypeopx\deftypeopheader \deftypeopcategory} % % #1 is the class name, #2 the data type, #3 the operation name, #4 the args. \def\deftypeopheader#1#2#3#4{% \dosubind{fn}{\code{#3}}{\putwordon\ \code{#1}}% entry in function index \begingroup \defname{\defheaderxcond#2\relax$$$#3} {\deftypeopcategory\ \putwordon\ \code{#1}}% \deftypefunargs{#4}% \endgroup } % @deftypemethod CLASS TYPE METHOD ARG... % \def\deftypemethod{% \deftypemethparsebody\Edeftypemethod\deftypemethodx\deftypemethodheader} % % #1 is the class name, #2 the data type, #3 the method name, #4 the args. \def\deftypemethodheader#1#2#3#4{% \dosubind{fn}{\code{#3}}{\putwordon\ \code{#1}}% entry in function index \begingroup \defname{\defheaderxcond#2\relax$$$#3}{\putwordMethodon\ \code{#1}}% \deftypefunargs{#4}% \endgroup } % @deftypeivar CLASS TYPE VARNAME % \def\deftypeivar{% \deftypemethparsebody\Edeftypeivar\deftypeivarx\deftypeivarheader} % % #1 is the class name, #2 the data type, #3 the variable name. \def\deftypeivarheader#1#2#3{% \dosubind{vr}{\code{#3}}{\putwordof\ \code{#1}}% entry in variable index \begingroup \defname{#3}{\putwordInstanceVariableof\ \code{#1}}% \defvarargs{#3}% \endgroup } % @defmethod == @defop Method % \def\defmethod{\defmethparsebody\Edefmethod\defmethodx\defmethodheader} % % #1 is the class name, #2 the method name, #3 the args. \def\defmethodheader#1#2#3{% \dosubind{fn}{\code{#2}}{\putwordon\ \code{#1}}% entry in function index \begingroup \defname{#2}{\putwordMethodon\ \code{#1}}% \defunargs{#3}% \endgroup } % @defcv {Class Option} foo-class foo-flag \def\defcv #1 {\def\defcvtype{#1}% \defopvarparsebody\Edefcv\defcvx\defcvarheader\defcvtype} \def\defcvarheader #1#2#3{% \dosubind {vr}{\code{#2}}{\putwordof\ #1}% Make entry in var index \begingroup\defname {#2}{\defcvtype\ \putwordof\ #1}% \defvarargs {#3}\endgroup % } % @defivar CLASS VARNAME == @defcv {Instance Variable} CLASS VARNAME % \def\defivar{\defvrparsebody\Edefivar\defivarx\defivarheader} % \def\defivarheader#1#2#3{% \dosubind {vr}{\code{#2}}{\putwordof\ #1}% entry in var index \begingroup \defname{#2}{\putwordInstanceVariableof\ #1}% \defvarargs{#3}% \endgroup } % @defvar % First, define the processing that is wanted for arguments of @defvar. % This is actually simple: just print them in roman. % This must expand the args and terminate the paragraph they make up \def\defvarargs #1{\normalparens #1% \interlinepenalty=10000 \endgraf\nobreak\vskip -\parskip\nobreak} % @defvr Counter foo-count \def\defvr{\defvrparsebody\Edefvr\defvrx\defvrheader} \def\defvrheader #1#2#3{\doind {vr}{\code{#2}}% \begingroup\defname {#2}{#1}\defvarargs{#3}\endgroup} % @defvar == @defvr Variable \def\defvar{\defvarparsebody\Edefvar\defvarx\defvarheader} \def\defvarheader #1#2{\doind {vr}{\code{#1}}% Make entry in var index \begingroup\defname {#1}{\putwordDefvar}% \defvarargs {#2}\endgroup % } % @defopt == @defvr {User Option} \def\defopt{\defvarparsebody\Edefopt\defoptx\defoptheader} \def\defoptheader #1#2{\doind {vr}{\code{#1}}% Make entry in var index \begingroup\defname {#1}{\putwordDefopt}% \defvarargs {#2}\endgroup % } % @deftypevar int foobar \def\deftypevar{\defvarparsebody\Edeftypevar\deftypevarx\deftypevarheader} % #1 is the data type. #2 is the name, perhaps followed by text that % is actually part of the data type, which should not be put into the index. \def\deftypevarheader #1#2{% \dovarind#2 \relax% Make entry in variables index \begingroup\defname {\defheaderxcond#1\relax$$$#2}{\putwordDeftypevar}% \interlinepenalty=10000 \endgraf\nobreak\vskip -\parskip\nobreak \endgroup} \def\dovarind#1 #2\relax{\doind{vr}{\code{#1}}} % @deftypevr {Global Flag} int enable \def\deftypevr{\defvrparsebody\Edeftypevr\deftypevrx\deftypevrheader} \def\deftypevrheader #1#2#3{\dovarind#3 \relax% \begingroup\defname {\defheaderxcond#2\relax$$$#3}{#1} \interlinepenalty=10000 \endgraf\nobreak\vskip -\parskip\nobreak \endgroup} % Now define @deftp % Args are printed in bold, a slight difference from @defvar. \def\deftpargs #1{\bf \defvarargs{#1}} % @deftp Class window height width ... \def\deftp{\deftpparsebody\Edeftp\deftpx\deftpheader} \def\deftpheader #1#2#3{\doind {tp}{\code{#2}}% \begingroup\defname {#2}{#1}\deftpargs{#3}\endgroup} % These definitions are used if you use @defunx (etc.) % anywhere other than immediately after a @defun or @defunx. % \def\defcvx#1 {\errmessage{@defcvx in invalid context}} \def\deffnx#1 {\errmessage{@deffnx in invalid context}} \def\defivarx#1 {\errmessage{@defivarx in invalid context}} \def\defmacx#1 {\errmessage{@defmacx in invalid context}} \def\defmethodx#1 {\errmessage{@defmethodx in invalid context}} \def\defoptx #1 {\errmessage{@defoptx in invalid context}} \def\defopx#1 {\errmessage{@defopx in invalid context}} \def\defspecx#1 {\errmessage{@defspecx in invalid context}} \def\deftpx#1 {\errmessage{@deftpx in invalid context}} \def\deftypefnx#1 {\errmessage{@deftypefnx in invalid context}} \def\deftypefunx#1 {\errmessage{@deftypefunx in invalid context}} \def\deftypeivarx#1 {\errmessage{@deftypeivarx in invalid context}} \def\deftypemethodx#1 {\errmessage{@deftypemethodx in invalid context}} \def\deftypeopx#1 {\errmessage{@deftypeopx in invalid context}} \def\deftypevarx#1 {\errmessage{@deftypevarx in invalid context}} \def\deftypevrx#1 {\errmessage{@deftypevrx in invalid context}} \def\defunx#1 {\errmessage{@defunx in invalid context}} \def\defvarx#1 {\errmessage{@defvarx in invalid context}} \def\defvrx#1 {\errmessage{@defvrx in invalid context}} \message{macros,} % @macro. % To do this right we need a feature of e-TeX, \scantokens, % which we arrange to emulate with a temporary file in ordinary TeX. \ifx\eTeXversion\undefined \newwrite\macscribble \def\scanmacro#1{% \begingroup \newlinechar`\^^M % Undo catcode changes of \startcontents and \doprintindex \catcode`\@=0 \catcode`\\=12 \escapechar=`\@ % Append \endinput to make sure that TeX does not see the ending newline. \toks0={#1\endinput}% \immediate\openout\macscribble=\jobname.tmp \immediate\write\macscribble{\the\toks0}% \immediate\closeout\macscribble \let\xeatspaces\eatspaces \input \jobname.tmp \endgroup } \else \def\scanmacro#1{% \begingroup \newlinechar`\^^M % Undo catcode changes of \startcontents and \doprintindex \catcode`\@=0 \catcode`\\=12 \escapechar=`\@ \let\xeatspaces\eatspaces\scantokens{#1\endinput}\endgroup} \fi \newcount\paramno % Count of parameters \newtoks\macname % Macro name \newif\ifrecursive % Is it recursive? \def\macrolist{} % List of all defined macros in the form % \do\macro1\do\macro2... % Utility routines. % Thisdoes \let #1 = #2, except with \csnames. \def\cslet#1#2{% \expandafter\expandafter \expandafter\let \expandafter\expandafter \csname#1\endcsname \csname#2\endcsname} % Trim leading and trailing spaces off a string. % Concepts from aro-bend problem 15 (see CTAN). {\catcode`\@=11 \gdef\eatspaces #1{\expandafter\trim@\expandafter{#1 }} \gdef\trim@ #1{\trim@@ @#1 @ #1 @ @@} \gdef\trim@@ #1@ #2@ #3@@{\trim@@@\empty #2 @} \def\unbrace#1{#1} \unbrace{\gdef\trim@@@ #1 } #2@{#1} } % Trim a single trailing ^^M off a string. {\catcode`\^^M=12\catcode`\Q=3% \gdef\eatcr #1{\eatcra #1Q^^MQ}% \gdef\eatcra#1^^MQ{\eatcrb#1Q}% \gdef\eatcrb#1Q#2Q{#1}% } % Macro bodies are absorbed as an argument in a context where % all characters are catcode 10, 11 or 12, except \ which is active % (as in normal texinfo). It is necessary to change the definition of \. % It's necessary to have hard CRs when the macro is executed. This is % done by making ^^M (\endlinechar) catcode 12 when reading the macro % body, and then making it the \newlinechar in \scanmacro. \def\macrobodyctxt{% \catcode`\~=12 \catcode`\^=12 \catcode`\_=12 \catcode`\|=12 \catcode`\<=12 \catcode`\>=12 \catcode`\+=12 \catcode`\{=12 \catcode`\}=12 \catcode`\@=12 \catcode`\^^M=12 \usembodybackslash} \def\macroargctxt{% \catcode`\~=12 \catcode`\^=12 \catcode`\_=12 \catcode`\|=12 \catcode`\<=12 \catcode`\>=12 \catcode`\+=12 \catcode`\@=12 \catcode`\\=12} % \mbodybackslash is the definition of \ in @macro bodies. % It maps \foo\ => \csname macarg.foo\endcsname => #N % where N is the macro parameter number. % We define \csname macarg.\endcsname to be \realbackslash, so % \\ in macro replacement text gets you a backslash. {\catcode`@=0 @catcode`@\=@active @gdef@usembodybackslash{@let\=@mbodybackslash} @gdef@mbodybackslash#1\{@csname macarg.#1@endcsname} } \expandafter\def\csname macarg.\endcsname{\realbackslash} \def\macro{\recursivefalse\parsearg\macroxxx} \def\rmacro{\recursivetrue\parsearg\macroxxx} \def\macroxxx#1{% \getargs{#1}% now \macname is the macname and \argl the arglist \ifx\argl\empty % no arguments \paramno=0% \else \expandafter\parsemargdef \argl;% \fi \if1\csname ismacro.\the\macname\endcsname \message{Warning: redefining \the\macname}% \else \expandafter\ifx\csname \the\macname\endcsname \relax \else \errmessage{The name \the\macname\space is reserved}\fi \global\cslet{macsave.\the\macname}{\the\macname}% \global\expandafter\let\csname ismacro.\the\macname\endcsname=1% % Add the macroname to \macrolist \toks0 = \expandafter{\macrolist\do}% \xdef\macrolist{\the\toks0 \expandafter\noexpand\csname\the\macname\endcsname}% \fi \begingroup \macrobodyctxt \ifrecursive \expandafter\parsermacbody \else \expandafter\parsemacbody \fi} \def\unmacro{\parsearg\unmacroxxx} \def\unmacroxxx#1{% \if1\csname ismacro.#1\endcsname \global\cslet{#1}{macsave.#1}% \global\expandafter\let \csname ismacro.#1\endcsname=0% % Remove the macro name from \macrolist \begingroup \edef\tempa{\expandafter\noexpand\csname#1\endcsname}% \def\do##1{% \def\tempb{##1}% \ifx\tempa\tempb % remove this \else \toks0 = \expandafter{\newmacrolist\do}% \edef\newmacrolist{\the\toks0\expandafter\noexpand\tempa}% \fi}% \def\newmacrolist{}% % Execute macro list to define \newmacrolist \macrolist \global\let\macrolist\newmacrolist \endgroup \else \errmessage{Macro #1 not defined}% \fi } % This makes use of the obscure feature that if the last token of a % is #, then the preceding argument is delimited by % an opening brace, and that opening brace is not consumed. \def\getargs#1{\getargsxxx#1{}} \def\getargsxxx#1#{\getmacname #1 \relax\getmacargs} \def\getmacname #1 #2\relax{\macname={#1}} \def\getmacargs#1{\def\argl{#1}} % Parse the optional {params} list. Set up \paramno and \paramlist % so \defmacro knows what to do. Define \macarg.blah for each blah % in the params list, to be ##N where N is the position in that list. % That gets used by \mbodybackslash (above). % We need to get `macro parameter char #' into several definitions. % The technique used is stolen from LaTeX: let \hash be something % unexpandable, insert that wherever you need a #, and then redefine % it to # just before using the token list produced. % % The same technique is used to protect \eatspaces till just before % the macro is used. \def\parsemargdef#1;{\paramno=0\def\paramlist{}% \let\hash\relax\let\xeatspaces\relax\parsemargdefxxx#1,;,} \def\parsemargdefxxx#1,{% \if#1;\let\next=\relax \else \let\next=\parsemargdefxxx \advance\paramno by 1% \expandafter\edef\csname macarg.\eatspaces{#1}\endcsname {\xeatspaces{\hash\the\paramno}}% \edef\paramlist{\paramlist\hash\the\paramno,}% \fi\next} % These two commands read recursive and nonrecursive macro bodies. % (They're different since rec and nonrec macros end differently.) \long\def\parsemacbody#1@end macro% {\xdef\temp{\eatcr{#1}}\endgroup\defmacro}% \long\def\parsermacbody#1@end rmacro% {\xdef\temp{\eatcr{#1}}\endgroup\defmacro}% % This defines the macro itself. There are six cases: recursive and % nonrecursive macros of zero, one, and many arguments. % Much magic with \expandafter here. % \xdef is used so that macro definitions will survive the file % they're defined in; @include reads the file inside a group. \def\defmacro{% \let\hash=##% convert placeholders to macro parameter chars \ifrecursive \ifcase\paramno % 0 \expandafter\xdef\csname\the\macname\endcsname{% \noexpand\scanmacro{\temp}}% \or % 1 \expandafter\xdef\csname\the\macname\endcsname{% \bgroup\noexpand\macroargctxt \noexpand\braceorline \expandafter\noexpand\csname\the\macname xxx\endcsname}% \expandafter\xdef\csname\the\macname xxx\endcsname##1{% \egroup\noexpand\scanmacro{\temp}}% \else % many \expandafter\xdef\csname\the\macname\endcsname{% \bgroup\noexpand\macroargctxt \noexpand\csname\the\macname xx\endcsname}% \expandafter\xdef\csname\the\macname xx\endcsname##1{% \expandafter\noexpand\csname\the\macname xxx\endcsname ##1,}% \expandafter\expandafter \expandafter\xdef \expandafter\expandafter \csname\the\macname xxx\endcsname \paramlist{\egroup\noexpand\scanmacro{\temp}}% \fi \else \ifcase\paramno % 0 \expandafter\xdef\csname\the\macname\endcsname{% \noexpand\norecurse{\the\macname}% \noexpand\scanmacro{\temp}\egroup}% \or % 1 \expandafter\xdef\csname\the\macname\endcsname{% \bgroup\noexpand\macroargctxt \noexpand\braceorline \expandafter\noexpand\csname\the\macname xxx\endcsname}% \expandafter\xdef\csname\the\macname xxx\endcsname##1{% \egroup \noexpand\norecurse{\the\macname}% \noexpand\scanmacro{\temp}\egroup}% \else % many \expandafter\xdef\csname\the\macname\endcsname{% \bgroup\noexpand\macroargctxt \expandafter\noexpand\csname\the\macname xx\endcsname}% \expandafter\xdef\csname\the\macname xx\endcsname##1{% \expandafter\noexpand\csname\the\macname xxx\endcsname ##1,}% \expandafter\expandafter \expandafter\xdef \expandafter\expandafter \csname\the\macname xxx\endcsname \paramlist{% \egroup \noexpand\norecurse{\the\macname}% \noexpand\scanmacro{\temp}\egroup}% \fi \fi} \def\norecurse#1{\bgroup\cslet{#1}{macsave.#1}} % \braceorline decides whether the next nonwhitespace character is a % {. If so it reads up to the closing }, if not, it reads the whole % line. Whatever was read is then fed to the next control sequence % as an argument (by \parsebrace or \parsearg) \def\braceorline#1{\let\next=#1\futurelet\nchar\braceorlinexxx} \def\braceorlinexxx{% \ifx\nchar\bgroup\else \expandafter\parsearg \fi \next} % We mant to disable all macros during \shipout so that they are not % expanded by \write. \def\turnoffmacros{\begingroup \def\do##1{\let\noexpand##1=\relax}% \edef\next{\macrolist}\expandafter\endgroup\next} % @alias. % We need some trickery to remove the optional spaces around the equal % sign. Just make them active and then expand them all to nothing. \def\alias{\begingroup\obeyspaces\parsearg\aliasxxx} \def\aliasxxx #1{\aliasyyy#1\relax} \def\aliasyyy #1=#2\relax{\ignoreactivespaces \edef\next{\global\let\expandafter\noexpand\csname#1\endcsname=% \expandafter\noexpand\csname#2\endcsname}% \expandafter\endgroup\next} \message{cross references,} % @xref etc. \newwrite\auxfile \newif\ifhavexrefs % True if xref values are known. \newif\ifwarnedxrefs % True if we warned once that they aren't known. % @inforef is relatively simple. \def\inforef #1{\inforefzzz #1,,,,**} \def\inforefzzz #1,#2,#3,#4**{\putwordSee{} \putwordInfo{} \putwordfile{} \file{\ignorespaces #3{}}, node \samp{\ignorespaces#1{}}} % @node's job is to define \lastnode. \def\node{\ENVcheck\parsearg\nodezzz} \def\nodezzz#1{\nodexxx [#1,]} \def\nodexxx[#1,#2]{\gdef\lastnode{#1}} \let\nwnode=\node \let\lastnode=\relax % The sectioning commands (@chapter, etc.) call these. \def\donoderef{% \ifx\lastnode\relax\else \expandafter\expandafter\expandafter\setref{\lastnode}% {Ysectionnumberandtype}% \global\let\lastnode=\relax \fi } \def\unnumbnoderef{% \ifx\lastnode\relax\else \expandafter\expandafter\expandafter\setref{\lastnode}{Ynothing}% \global\let\lastnode=\relax \fi } \def\appendixnoderef{% \ifx\lastnode\relax\else \expandafter\expandafter\expandafter\setref{\lastnode}% {Yappendixletterandtype}% \global\let\lastnode=\relax \fi } % @anchor{NAME} -- define xref target at arbitrary point. % \newcount\savesfregister \gdef\savesf{\relax \ifhmode \savesfregister=\spacefactor \fi} \gdef\restoresf{\relax \ifhmode \spacefactor=\savesfregister \fi} \gdef\anchor#1{\savesf \setref{#1}{Ynothing}\restoresf \ignorespaces} % \setref{NAME}{SNT} defines a cross-reference point NAME, namely % NAME-title, NAME-pg, and NAME-SNT. Called from \foonoderef. We have % to set \indexdummies so commands such as @code in a section title % aren't expanded. It would be nicer not to expand the titles in the % first place, but there's so many layers that that is hard to do. % \def\setref#1#2{{% \indexdummies \pdfmkdest{#1}% \dosetq{#1-title}{Ytitle}% \dosetq{#1-pg}{Ypagenumber}% \dosetq{#1-snt}{#2}% }} % @xref, @pxref, and @ref generate cross-references. For \xrefX, #1 is % the node name, #2 the name of the Info cross-reference, #3 the printed % node name, #4 the name of the Info file, #5 the name of the printed % manual. All but the node name can be omitted. % \def\pxref#1{\putwordsee{} \xrefX[#1,,,,,,,]} \def\xref#1{\putwordSee{} \xrefX[#1,,,,,,,]} \def\ref#1{\xrefX[#1,,,,,,,]} \def\xrefX[#1,#2,#3,#4,#5,#6]{\begingroup \unsepspaces \def\printedmanual{\ignorespaces #5}% \def\printednodename{\ignorespaces #3}% \setbox1=\hbox{\printedmanual}% \setbox0=\hbox{\printednodename}% \ifdim \wd0 = 0pt % No printed node name was explicitly given. \expandafter\ifx\csname SETxref-automatic-section-title\endcsname\relax % Use the node name inside the square brackets. \def\printednodename{\ignorespaces #1}% \else % Use the actual chapter/section title appear inside % the square brackets. Use the real section title if we have it. \ifdim \wd1 > 0pt % It is in another manual, so we don't have it. \def\printednodename{\ignorespaces #1}% \else \ifhavexrefs % We know the real title if we have the xref values. \def\printednodename{\refx{#1-title}{}}% \else % Otherwise just copy the Info node name. \def\printednodename{\ignorespaces #1}% \fi% \fi \fi \fi % % If we use \unhbox0 and \unhbox1 to print the node names, TeX does not % insert empty discretionaries after hyphens, which means that it will % not find a line break at a hyphen in a node names. Since some manuals % are best written with fairly long node names, containing hyphens, this % is a loss. Therefore, we give the text of the node name again, so it % is as if TeX is seeing it for the first time. \ifpdf \leavevmode \getfilename{#4}% \ifnum\filenamelength>0 \startlink attr{/Border [0 0 0]}% goto file{\the\filename.pdf} name{#1@}% \else \startlink attr{/Border [0 0 0]}% goto name{#1@}% \fi \linkcolor \fi % \ifdim \wd1 > 0pt \putwordsection{} ``\printednodename'' \putwordin{} \cite{\printedmanual}% \else % _ (for example) has to be the character _ for the purposes of the % control sequence corresponding to the node, but it has to expand % into the usual \leavevmode...\vrule stuff for purposes of % printing. So we \turnoffactive for the \refx-snt, back on for the % printing, back off for the \refx-pg. {\normalturnoffactive % Only output a following space if the -snt ref is nonempty; for % @unnumbered and @anchor, it won't be. \setbox2 = \hbox{\ignorespaces \refx{#1-snt}{}}% \ifdim \wd2 > 0pt \refx{#1-snt}\space\fi }% % [mynode], [\printednodename],\space % page 3 \turnoffactive \putwordpage\tie\refx{#1-pg}{}% \fi \endlink \endgroup} % \dosetq is the interface for calls from other macros % Use \normalturnoffactive so that punctuation chars such as underscore % and backslash work in node names. (\turnoffactive doesn't do \.) \def\dosetq#1#2{% {\let\folio=0% \normalturnoffactive \edef\next{\write\auxfile{\internalsetq{#1}{#2}}}% \iflinks \next \fi }% } % \internalsetq {foo}{page} expands into % CHARACTERS 'xrdef {foo}{...expansion of \Ypage...} % When the aux file is read, ' is the escape character \def\internalsetq #1#2{'xrdef {#1}{\csname #2\endcsname}} % Things to be expanded by \internalsetq \def\Ypagenumber{\folio} \def\Ytitle{\thissection} \def\Ynothing{} \def\Ysectionnumberandtype{% \ifnum\secno=0 \putwordChapter\xreftie\the\chapno % \else \ifnum \subsecno=0 \putwordSection\xreftie\the\chapno.\the\secno % \else \ifnum \subsubsecno=0 % \putwordSection\xreftie\the\chapno.\the\secno.\the\subsecno % \else % \putwordSection\xreftie\the\chapno.\the\secno.\the\subsecno.\the\subsubsecno % \fi \fi \fi } \def\Yappendixletterandtype{% \ifnum\secno=0 \putwordAppendix\xreftie'char\the\appendixno{}% \else \ifnum \subsecno=0 \putwordSection\xreftie'char\the\appendixno.\the\secno % \else \ifnum \subsubsecno=0 % \putwordSection\xreftie'char\the\appendixno.\the\secno.\the\subsecno % \else % \putwordSection\xreftie'char\the\appendixno.\the\secno.\the\subsecno.\the\subsubsecno % \fi \fi \fi } \gdef\xreftie{'tie} % Use TeX 3.0's \inputlineno to get the line number, for better error % messages, but if we're using an old version of TeX, don't do anything. % \ifx\inputlineno\thisisundefined \let\linenumber = \empty % Non-3.0. \else \def\linenumber{\the\inputlineno:\space} \fi % Define \refx{NAME}{SUFFIX} to reference a cross-reference string named NAME. % If its value is nonempty, SUFFIX is output afterward. \def\refx#1#2{% \expandafter\ifx\csname X#1\endcsname\relax % If not defined, say something at least. \angleleft un\-de\-fined\angleright \iflinks \ifhavexrefs \message{\linenumber Undefined cross reference `#1'.}% \else \ifwarnedxrefs\else \global\warnedxrefstrue \message{Cross reference values unknown; you must run TeX again.}% \fi \fi \fi \else % It's defined, so just use it. \csname X#1\endcsname \fi #2% Output the suffix in any case. } % This is the macro invoked by entries in the aux file. % \def\xrdef#1{\begingroup % Reenable \ as an escape while reading the second argument. \catcode`\\ = 0 \afterassignment\endgroup \expandafter\gdef\csname X#1\endcsname } % Read the last existing aux file, if any. No error if none exists. \def\readauxfile{\begingroup \catcode`\^^@=\other \catcode`\^^A=\other \catcode`\^^B=\other \catcode`\^^C=\other \catcode`\^^D=\other \catcode`\^^E=\other \catcode`\^^F=\other \catcode`\^^G=\other \catcode`\^^H=\other \catcode`\^^K=\other \catcode`\^^L=\other \catcode`\^^N=\other \catcode`\^^P=\other \catcode`\^^Q=\other \catcode`\^^R=\other \catcode`\^^S=\other \catcode`\^^T=\other \catcode`\^^U=\other \catcode`\^^V=\other \catcode`\^^W=\other \catcode`\^^X=\other \catcode`\^^Z=\other \catcode`\^^[=\other \catcode`\^^\=\other \catcode`\^^]=\other \catcode`\^^^=\other \catcode`\^^_=\other \catcode`\@=\other \catcode`\^=\other % It was suggested to define this as 7, which would allow ^^e4 etc. % in xref tags, i.e., node names. But since ^^e4 notation isn't % supported in the main text, it doesn't seem desirable. Furthermore, % that is not enough: for node names that actually contain a ^ % character, we would end up writing a line like this: 'xrdef {'hat % b-title}{'hat b} and \xrdef does a \csname...\endcsname on the first % argument, and \hat is not an expandable control sequence. It could % all be worked out, but why? Either we support ^^ or we don't. % % The other change necessary for this was to define \auxhat: % \def\auxhat{\def^{'hat }}% extra space so ok if followed by letter % and then to call \auxhat in \setq. % \catcode`\~=\other \catcode`\[=\other \catcode`\]=\other \catcode`\"=\other \catcode`\_=\other \catcode`\|=\other \catcode`\<=\other \catcode`\>=\other \catcode`\$=\other \catcode`\#=\other \catcode`\&=\other \catcode`+=\other % avoid \+ for paranoia even though we've turned it off % Make the characters 128-255 be printing characters {% \count 1=128 \def\loop{% \catcode\count 1=\other \advance\count 1 by 1 \ifnum \count 1<256 \loop \fi }% }% % The aux file uses ' as the escape (for now). % Turn off \ as an escape so we do not lose on % entries which were dumped with control sequences in their names. % For example, 'xrdef {$\leq $-fun}{page ...} made by @defun ^^ % Reference to such entries still does not work the way one would wish, % but at least they do not bomb out when the aux file is read in. \catcode`\{=1 \catcode`\}=2 \catcode`\%=\other \catcode`\'=0 \catcode`\\=\other % \openin 1 \jobname.aux \ifeof 1 \else \closein 1 \input \jobname.aux \global\havexrefstrue \global\warnedobstrue \fi % Open the new aux file. TeX will close it automatically at exit. \openout\auxfile=\jobname.aux \endgroup} % Footnotes. \newcount \footnoteno % The trailing space in the following definition for supereject is % vital for proper filling; pages come out unaligned when you do a % pagealignmacro call if that space before the closing brace is % removed. (Generally, numeric constants should always be followed by a % space to prevent strange expansion errors.) \def\supereject{\par\penalty -20000\footnoteno =0 } % @footnotestyle is meaningful for info output only. \let\footnotestyle=\comment \let\ptexfootnote=\footnote {\catcode `\@=11 % % Auto-number footnotes. Otherwise like plain. \gdef\footnote{% \global\advance\footnoteno by \@ne \edef\thisfootno{$^{\the\footnoteno}$}% % % In case the footnote comes at the end of a sentence, preserve the % extra spacing after we do the footnote number. \let\@sf\empty \ifhmode\edef\@sf{\spacefactor\the\spacefactor}\/\fi % % Remove inadvertent blank space before typesetting the footnote number. \unskip \thisfootno\@sf \footnotezzz }% % Don't bother with the trickery in plain.tex to not require the % footnote text as a parameter. Our footnotes don't need to be so general. % % Oh yes, they do; otherwise, @ifset and anything else that uses % \parseargline fail inside footnotes because the tokens are fixed when % the footnote is read. --karl, 16nov96. % \long\gdef\footnotezzz{\insert\footins\bgroup % We want to typeset this text as a normal paragraph, even if the % footnote reference occurs in (for example) a display environment. % So reset some parameters. \interlinepenalty\interfootnotelinepenalty \splittopskip\ht\strutbox % top baseline for broken footnotes \splitmaxdepth\dp\strutbox \floatingpenalty\@MM \leftskip\z@skip \rightskip\z@skip \spaceskip\z@skip \xspaceskip\z@skip \parindent\defaultparindent % \smallfonts \rm % % Hang the footnote text off the number. \hang \textindent{\thisfootno}% % % Don't crash into the line above the footnote text. Since this % expands into a box, it must come within the paragraph, lest it % provide a place where TeX can split the footnote. \footstrut \futurelet\next\fo@t } \def\fo@t{\ifcat\bgroup\noexpand\next \let\next\f@@t \else\let\next\f@t\fi \next} \def\f@@t{\bgroup\aftergroup\@foot\let\next} \def\f@t#1{#1\@foot} \def\@foot{\strut\par\egroup} }%end \catcode `\@=11 % Set the baselineskip to #1, and the lineskip and strut size % correspondingly. There is no deep meaning behind these magic numbers % used as factors; they just match (closely enough) what Knuth defined. % \def\lineskipfactor{.08333} \def\strutheightpercent{.70833} \def\strutdepthpercent {.29167} % \def\setleading#1{% \normalbaselineskip = #1\relax \normallineskip = \lineskipfactor\normalbaselineskip \normalbaselines \setbox\strutbox =\hbox{% \vrule width0pt height\strutheightpercent\baselineskip depth \strutdepthpercent \baselineskip }% } % @| inserts a changebar to the left of the current line. It should % surround any changed text. This approach does *not* work if the % change spans more than two lines of output. To handle that, we would % have adopt a much more difficult approach (putting marks into the main % vertical list for the beginning and end of each change). % \def\|{% % \vadjust can only be used in horizontal mode. \leavevmode % % Append this vertical mode material after the current line in the output. \vadjust{% % We want to insert a rule with the height and depth of the current % leading; that is exactly what \strutbox is supposed to record. \vskip-\baselineskip % % \vadjust-items are inserted at the left edge of the type. So % the \llap here moves out into the left-hand margin. \llap{% % % For a thicker or thinner bar, change the `1pt'. \vrule height\baselineskip width1pt % % This is the space between the bar and the text. \hskip 12pt }% }% } % For a final copy, take out the rectangles % that mark overfull boxes (in case you have decided % that the text looks ok even though it passes the margin). % \def\finalout{\overfullrule=0pt} % @image. We use the macros from epsf.tex to support this. % If epsf.tex is not installed and @image is used, we complain. % % Check for and read epsf.tex up front. If we read it only at @image % time, we might be inside a group, and then its definitions would get % undone and the next image would fail. \openin 1 = epsf.tex \ifeof 1 \else \closein 1 % Do not bother showing banner with post-v2.7 epsf.tex (available in % doc/epsf.tex until it shows up on ctan). \def\epsfannounce{\toks0 = }% \input epsf.tex \fi % % We will only complain once about lack of epsf.tex. \newif\ifwarnednoepsf \newhelp\noepsfhelp{epsf.tex must be installed for images to work. It is also included in the Texinfo distribution, or you can get it from ftp://tug.org/tex/epsf.tex.} % \def\image#1{% \ifx\epsfbox\undefined \ifwarnednoepsf \else \errhelp = \noepsfhelp \errmessage{epsf.tex not found, images will be ignored}% \global\warnednoepsftrue \fi \else \imagexxx #1,,,\finish \fi } % % Arguments to @image: % #1 is (mandatory) image filename; we tack on .eps extension. % #2 is (optional) width, #3 is (optional) height. % #4 is just the usual extra ignored arg for parsing this stuff. \def\imagexxx#1,#2,#3,#4\finish{% \ifpdf \centerline{\dopdfimage{#1}{#2}{#3}}% \else % \epsfbox itself resets \epsf?size at each figure. \setbox0 = \hbox{\ignorespaces #2}\ifdim\wd0 > 0pt \epsfxsize=#2\relax \fi \setbox0 = \hbox{\ignorespaces #3}\ifdim\wd0 > 0pt \epsfysize=#3\relax \fi \begingroup \catcode`\^^M = 5 % in case we're inside an example % If the image is by itself, center it. \ifvmode \nobreak\bigskip % Usually we'll have text after the image which will insert % \parskip glue, so insert it here too to equalize the space % above and below. \nobreak\vskip\parskip \nobreak \centerline{\epsfbox{#1.eps}}% \bigbreak \else % In the middle of a paragraph, no extra space. \epsfbox{#1.eps}% \fi \endgroup \fi } \message{localization,} % and i18n. % @documentlanguage is usually given very early, just after % @setfilename. If done too late, it may not override everything % properly. Single argument is the language abbreviation. % It would be nice if we could set up a hyphenation file here. % \def\documentlanguage{\parsearg\dodocumentlanguage} \def\dodocumentlanguage#1{% \tex % read txi-??.tex file in plain TeX. % Read the file if it exists. \openin 1 txi-#1.tex \ifeof1 \errhelp = \nolanghelp \errmessage{Cannot read language file txi-#1.tex}% \let\temp = \relax \else \def\temp{\input txi-#1.tex }% \fi \temp \endgroup } \newhelp\nolanghelp{The given language definition file cannot be found or is empty. Maybe you need to install it? In the current directory should work if nowhere else does.} % @documentencoding should change something in TeX eventually, most % likely, but for now just recognize it. \let\documentencoding = \comment % Page size parameters. % \newdimen\defaultparindent \defaultparindent = 15pt \chapheadingskip = 15pt plus 4pt minus 2pt \secheadingskip = 12pt plus 3pt minus 2pt \subsecheadingskip = 9pt plus 2pt minus 2pt % Prevent underfull vbox error messages. \vbadness = 10000 % Don't be so finicky about underfull hboxes, either. \hbadness = 2000 % Following George Bush, just get rid of widows and orphans. \widowpenalty=10000 \clubpenalty=10000 % Use TeX 3.0's \emergencystretch to help line breaking, but if we're % using an old version of TeX, don't do anything. We want the amount of % stretch added to depend on the line length, hence the dependence on % \hsize. We call this whenever the paper size is set. % \def\setemergencystretch{% \ifx\emergencystretch\thisisundefined % Allow us to assign to \emergencystretch anyway. \def\emergencystretch{\dimen0}% \else \emergencystretch = .15\hsize \fi } % Parameters in order: 1) textheight; 2) textwidth; 3) voffset; % 4) hoffset; 5) binding offset; 6) topskip. Then whoever calls us can % set \parskip and call \setleading for \baselineskip. % \def\internalpagesizes#1#2#3#4#5#6{% \voffset = #3\relax \topskip = #6\relax \splittopskip = \topskip % \vsize = #1\relax \advance\vsize by \topskip \outervsize = \vsize \advance\outervsize by 2\topandbottommargin \pageheight = \vsize % \hsize = #2\relax \outerhsize = \hsize \advance\outerhsize by 0.5in \pagewidth = \hsize % \normaloffset = #4\relax \bindingoffset = #5\relax % \parindent = \defaultparindent \setemergencystretch } % @letterpaper (the default). \def\letterpaper{{\globaldefs = 1 \parskip = 3pt plus 2pt minus 1pt \setleading{13.2pt}% % % If page is nothing but text, make it come out even. \internalpagesizes{46\baselineskip}{6in}{\voffset}{.25in}{\bindingoffset}{36pt}% }} % Use @smallbook to reset parameters for 7x9.5 (or so) format. \def\smallbook{{\globaldefs = 1 \parskip = 2pt plus 1pt \setleading{12pt}% % \internalpagesizes{7.5in}{5.in}{\voffset}{.25in}{\bindingoffset}{16pt}% % \lispnarrowing = 0.3in \tolerance = 700 \hfuzz = 1pt \contentsrightmargin = 0pt \deftypemargin = 0pt \defbodyindent = .5cm % \let\smalldisplay = \smalldisplayx \let\smallexample = \smalllispx \let\smallformat = \smallformatx \let\smalllisp = \smalllispx }} % Use @afourpaper to print on European A4 paper. \def\afourpaper{{\globaldefs = 1 \setleading{12pt}% \parskip = 3pt plus 2pt minus 1pt % \internalpagesizes{53\baselineskip}{160mm}{\voffset}{4mm}{\bindingoffset}{44pt}% % \tolerance = 700 \hfuzz = 1pt }} % A specific text layout, 24x15cm overall, intended for A4 paper. Top margin % 29mm, hence bottom margin 28mm, nominal side margin 3cm. \def\afourlatex{{\globaldefs = 1 \setleading{13.6pt}% % \afourpaper \internalpagesizes{237mm}{150mm}{3.6mm}{3.6mm}{3mm}{7mm}% % \globaldefs = 0 }} % Use @afourwide to print on European A4 paper in wide format. \def\afourwide{% \afourpaper \internalpagesizes{9.5in}{6.5in}{\hoffset}{\normaloffset}{\bindingoffset}{7mm}% % \globaldefs = 0 } % @pagesizes TEXTHEIGHT[,TEXTWIDTH] % Perhaps we should allow setting the margins, \topskip, \parskip, % and/or leading, also. Or perhaps we should compute them somehow. % \def\pagesizes{\parsearg\pagesizesxxx} \def\pagesizesxxx#1{\pagesizesyyy #1,,\finish} \def\pagesizesyyy#1,#2,#3\finish{{% \setbox0 = \hbox{\ignorespaces #2}\ifdim\wd0 > 0pt \hsize=#2\relax \fi \globaldefs = 1 % \parskip = 3pt plus 2pt minus 1pt \setleading{13.2pt}% % \internalpagesizes{#1}{\hsize}{\voffset}{\normaloffset}{\bindingoffset}{44pt}% }} % Set default to letter. % \letterpaper \message{and turning on texinfo input format.} % Define macros to output various characters with catcode for normal text. \catcode`\"=\other \catcode`\~=\other \catcode`\^=\other \catcode`\_=\other \catcode`\|=\other \catcode`\<=\other \catcode`\>=\other \catcode`\+=\other \catcode`\$=\other \def\normaldoublequote{"} \def\normaltilde{~} \def\normalcaret{^} \def\normalunderscore{_} \def\normalverticalbar{|} \def\normalless{<} \def\normalgreater{>} \def\normalplus{+} \def\normaldollar{$} % This macro is used to make a character print one way in ttfont % where it can probably just be output, and another way in other fonts, % where something hairier probably needs to be done. % % #1 is what to print if we are indeed using \tt; #2 is what to print % otherwise. Since all the Computer Modern typewriter fonts have zero % interword stretch (and shrink), and it is reasonable to expect all % typewriter fonts to have this, we can check that font parameter. % \def\ifusingtt#1#2{\ifdim \fontdimen3\font=0pt #1\else #2\fi} % Same as above, but check for italic font. Actually this also catches % non-italic slanted fonts since it is impossible to distinguish them from % italic fonts. But since this is only used by $ and it uses \sl anyway % this is not a problem. \def\ifusingit#1#2{\ifdim \fontdimen1\font>0pt #1\else #2\fi} % Turn off all special characters except @ % (and those which the user can use as if they were ordinary). % Most of these we simply print from the \tt font, but for some, we can % use math or other variants that look better in normal text. \catcode`\"=\active \def\activedoublequote{{\tt\char34}} \let"=\activedoublequote \catcode`\~=\active \def~{{\tt\char126}} \chardef\hat=`\^ \catcode`\^=\active \def^{{\tt \hat}} \catcode`\_=\active \def_{\ifusingtt\normalunderscore\_} % Subroutine for the previous macro. \def\_{\leavevmode \kern.06em \vbox{\hrule width.3em height.1ex}} \catcode`\|=\active \def|{{\tt\char124}} \chardef \less=`\< \catcode`\<=\active \def<{{\tt \less}} \chardef \gtr=`\> \catcode`\>=\active \def>{{\tt \gtr}} \catcode`\+=\active \def+{{\tt \char 43}} \catcode`\$=\active \def${\ifusingit{{\sl\$}}\normaldollar} %\catcode 27=\active %\def^^[{$\diamondsuit$} % Set up an active definition for =, but don't enable it most of the time. {\catcode`\==\active \global\def={{\tt \char 61}}} \catcode`+=\active \catcode`\_=\active % If a .fmt file is being used, characters that might appear in a file % name cannot be active until we have parsed the command line. % So turn them off again, and have \everyjob (or @setfilename) turn them on. % \otherifyactive is called near the end of this file. \def\otherifyactive{\catcode`+=\other \catcode`\_=\other} \catcode`\@=0 % \rawbackslashxx output one backslash character in current font \global\chardef\rawbackslashxx=`\\ %{\catcode`\\=\other %@gdef@rawbackslashxx{\}} % \rawbackslash redefines \ as input to do \rawbackslashxx. {\catcode`\\=\active @gdef@rawbackslash{@let\=@rawbackslashxx }} % \normalbackslash outputs one backslash in fixed width font. \def\normalbackslash{{\tt\rawbackslashxx}} % \catcode 17=0 % Define control-q \catcode`\\=\active % Used sometimes to turn off (effectively) the active characters % even after parsing them. @def@turnoffactive{@let"=@normaldoublequote @let\=@realbackslash @let~=@normaltilde @let^=@normalcaret @let_=@normalunderscore @let|=@normalverticalbar @let<=@normalless @let>=@normalgreater @let+=@normalplus @let$=@normaldollar} @def@normalturnoffactive{@let"=@normaldoublequote @let\=@normalbackslash @let~=@normaltilde @let^=@normalcaret @let_=@normalunderscore @let|=@normalverticalbar @let<=@normalless @let>=@normalgreater @let+=@normalplus @let$=@normaldollar} % Make _ and + \other characters, temporarily. % This is canceled by @fixbackslash. @otherifyactive % If a .fmt file is being used, we don't want the `\input texinfo' to show up. % That is what \eatinput is for; after that, the `\' should revert to printing % a backslash. % @gdef@eatinput input texinfo{@fixbackslash} @global@let\ = @eatinput % On the other hand, perhaps the file did not have a `\input texinfo'. Then % the first `\{ in the file would cause an error. This macro tries to fix % that, assuming it is called before the first `\' could plausibly occur. % Also back turn on active characters that might appear in the input % file name, in case not using a pre-dumped format. % @gdef@fixbackslash{% @ifx\@eatinput @let\ = @normalbackslash @fi @catcode`+=@active @catcode`@_=@active } % Say @foo, not \foo, in error messages. @escapechar = `@@ % These look ok in all fonts, so just make them not special. @catcode`@& = @other @catcode`@# = @other @catcode`@% = @other @c Set initial fonts. @textfonts @rm @c Local variables: @c eval: (add-hook 'write-file-hooks 'time-stamp) @c page-delimiter: "^\\\\message" @c time-stamp-start: "def\\\\texinfoversion{" @c time-stamp-format: "%:y-%02m-%02d.%02H" @c time-stamp-end: "}" @c End: gsl-1.0.8/doc/gsl_sf.ps0000644000175000017500000115116411201030403012472 0ustar shsh%!PS-Adobe-2.0 %%Creator: dvips(k) 5.95a Copyright 2005 Radical Eye Software %%Title: gsl_sf.dvi %%Pages: 51 %%PageOrder: Ascend %%BoundingBox: 0 0 595 842 %%DocumentFonts: CMR10 CMTT10 CMSS10 CMSLTT10 CMSL10 CMMI10 CMEX10 CMMI7 %%+ CMR7 CMSY10 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -o gsl_sf.ps gsl_sf.dvi %DVIPSParameters: dpi=600 %DVIPSSource: TeX output 2008.06.20:1545 %%BeginProcSet: tex.pro 0 0 %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S /BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: texps.pro 0 0 %! 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All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /zero put dup 50 /two put readonly def /FontBBox{-27 -250 1122 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 25 /pi put dup 61 /slash put readonly def /FontBBox{0 -250 1171 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 90 /integraldisplay put dup 113 /radicalBig put readonly def /FontBBox{-24 -2960 1454 772}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 69 /E put dup 75 /K put dup 100 /d put dup 107 /k put dup 109 /m put dup 116 /t put readonly def /FontBBox{-32 -250 1048 750}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTT10 %!PS-AdobeFont-1.1: CMTT10 1.00B %%CreationDate: 1992 Apr 26 10:42:42 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTT10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def /FontName /CMTT10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 42 /asterisk put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 58 /colon put dup 60 /less put dup 61 /equal put dup 62 /greater put dup 65 /A put dup 66 /B put dup 67 /C put dup 69 /E put dup 70 /F put dup 73 /I put dup 74 /J put dup 75 /K put dup 80 /P put dup 81 /Q put dup 83 /S put dup 85 /U put dup 87 /W put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 93 /bracketright put dup 94 /asciicircum put dup 95 /underscore put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /braceleft put dup 124 /bar put dup 125 /braceright put readonly def /FontBBox{-4 -235 731 800}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F00F963068B8232429ED8B7CF6A3D879A2D19 38DD5C4467F9DD8C5D1A2000B3A6BF2F25629BAEC199AE8BD4BA6ED9BBF7DABF 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSL10 %!PS-AdobeFont-1.1: CMSL10 1.0 %%CreationDate: 1991 Aug 20 16:40:20 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSL10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -9.46 def /isFixedPitch false def end readonly def /FontName /CMSL10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 44 /comma put dup 46 /period put dup 77 /M put dup 78 /N put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 104 /h put dup 105 /i put dup 107 /k put dup 109 /m put dup 111 /o put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 121 /y put dup 122 /z put readonly def /FontBBox{-62 -250 1123 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSLTT10 %!PS-AdobeFont-1.1: CMSLTT10 1.0 %%CreationDate: 1991 Aug 20 16:41:43 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSLTT10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -9.46 def /isFixedPitch true def end readonly def /FontName /CMSLTT10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /zero put dup 49 /one put dup 50 /two put dup 100 /d put dup 101 /e put dup 109 /m put dup 110 /n put dup 111 /o put dup 114 /r put dup 116 /t put dup 117 /u put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-20 -233 617 696}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSS10 %!PS-AdobeFont-1.1: CMSS10 1.0 %%CreationDate: 1991 Aug 20 17:33:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSS10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put readonly def /FontBBox{-61 -250 999 759}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 31 /Oslash put dup 33 /exclam put dup 36 /dollar put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 55 /seven put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 93 /bracketright put dup 95 /dotaccent put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-251 -250 1009 969}readonly def currentdict end currentfile eexec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(-*-)2960 476 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(lncosh)47 b Fi(\()p Fh(x)12 b Fi(\))2960 585 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(lncosh)47 b Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 695 y Fk(These)30 b(routines)g(compute)h(log\(cosh\(x\)\))i(for)d(an)m(y)h(x.)390 827 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute) g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 959 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g (Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 979 42 84 v 390 1069 a Fk(for)30 b(do)s(cumen)m(tation.)275 1246 y(\037zeta)h(-*-)h(texinfo)f(-*-)2960 1423 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(zeta)46 b Fi(\()p Fh(x)12 b Fi(\))2960 1532 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(zeta)47 b Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 1642 y Fk(These)30 b(routines)g(compute)h(the)g(Riemann)f(zeta)i(function)e(zeta\(s\))i (for)e(arbitrary)g(s,)h(s)f(e)h(1.)390 1774 y(The)d(Riemann)g(zeta)h (function)f(is)g(de\014ned)f(b)m(y)h(the)h(in\014nite)f(sum)f (zeta\(s\))j(=)e(sum_)p Ff({)p Fk(k=1)p Ff(}^)p Fk(inft)m(y)390 1884 y(k)p Ff(^{)p Fk(-s)p Ff(})p Fk(.)390 2016 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g (the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 2148 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 2168 V 390 2257 a Fk(for)30 b(do)s(cumen)m(tation.)275 2434 y(\037eta)h(-*-)g(texinfo)g(-*-)2960 2611 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(eta)46 b Fi(\()p Fh(x)12 b Fi(\))2960 2721 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(eta)46 b Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 2831 y Fk(These)30 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b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 1163 42 84 v 390 1252 a Fk(for)30 b(do)s(cumen)m(tation.)275 1467 y(\037b)s(essel_il_scaled)h(-*-)h(texinfo)f(-*-)2960 1682 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(bessel_il_scaled)d Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 1791 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_il_scaled)d Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 1901 y Fk(These)26 b(routines)g(compute)h(the)f(scaled)h(regular)g(mo)s(di\014ed)e (spherical)i(Bessel)g(function)f(of)g(order)390 2011 y(l,)31 b(exp\(-)p Ff(|)p Fk(x)p Ff(|)p Fk(\))f(i_l\(x\))390 2160 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 2310 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o 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y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(exprel_n)48 b Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 4128 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(exprel_n)48 b Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 4237 y Fk(These)33 b(routines)h(compute)f(the)h(N-relativ)m(e)i(exp)s(onen)m(tial,)g(whic) m(h)d(is)g(the)h(n-th)f(generalization)390 4347 y(of)k(the)f(functions) g(gsl_sf_exprel)i(and)e(gsl_sf_exprel2.)60 b(The)36 b(N-relativ)m(e)j (exp)s(onen)m(tial)e(is)g(giv)m(en)390 4456 y(b)m(y)-8 b(,)390 4606 y(exprel_N\(x\))49 b(=)f(N!/x)p Ff(^)p Fk(N)h(\(exp\(x\))g (-)f(sum_)p Ff({)p Fk(k=0)p Ff(}^{)p Fk(N-1)p Ff(})f Fk(x)p Ff(^)p Fk(k/k!\))94 b(=)48 b(1)g(+)g(x/\(N+1\))h(+)390 4716 y(x)p Ff(^)p Fk(2/\(\(N+1\)\(N+2\)\))34 b(+)c(...)41 b(=)30 b(1F1)h(\(1,1+N,x\))390 4866 y Fg(err)36 b Fk(con)m(tains)c(an)e (estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 5015 y(This)19 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b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g (Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 929 42 84 v 390 1019 a Fk(for)30 b(do)s(cumen)m(tation.)275 1215 y(\037ta)m(ylorco)s(e\013)i(-*-)f(texinfo)g(-*-)2960 1412 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(taylorcoeff)c Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 1522 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(taylorcoeff)c Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 1631 y Fk(These)30 b(routines)g(compute)h(the)g(T)-8 b(a)m(ylor)31 b(co)s(e\016cien)m(t)h (x)p Ff(^)p Fk(n)e(/)h(n!)40 b(for)30 b(x)g Ff(>)p Fk(=)g(0,)h(n)f Ff(>)p Fk(=)g(0.)390 1772 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate) i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 1913 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 1933 V 390 2022 a Fk(for)30 b(do)s(cumen)m(tation.)275 2219 y(\037legendre_Pl)g(-*-)i(texinfo)f(-*-)2960 2416 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(legendre_Pl)c Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 2526 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(legendre_Pl)c Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 2635 y Fk(These)36 b(functions)f(ev)-5 b(aluate)38 b(the)e(Legendre)f(p)s(olynomial)i(P_l\(x\))g(for)e(a)h(sp) s(eci\014c)g(v)-5 b(alue)36 b(of)g(l,)i(x)390 2745 y(sub)5 b(ject)30 b(to)h(l)g Ff(>)p Fk(=)f(0,)h Ff(|)p Fk(x)p Ff(|)e(<)p Fk(=)h(1)390 2885 y Fg(err)36 b Fk(con)m(tains)c(an)e (estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 3026 y(This)19 b(function)h(is)h(from)f (the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 3046 V 390 3136 a Fk(for)30 b(do)s(cumen)m(tation.)275 3333 y(\037legendre_Ql)g(-*-)i(texinfo)f(-*-)2960 3529 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1454 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 1474 V 390 1563 a Fk(for)30 b(do)s(cumen)m(tation.)275 1729 y(\037psi_1_in)m(t)h(-*-)g(texinfo)g(-*-)2960 1895 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(psi_1_int)48 b Fi(\()p Fh(n)12 b Fi(\))2960 2004 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(psi_1_int)48 b Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 2114 y Fk(These)30 b(routines)g(compute)h(the)g(T)-8 b(rigamma)31 b(function)f(psi\(n\))g(for)g(p)s(ositiv)m(e)h(in)m(teger) h(n.)390 2242 y Fg(err)k Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 2370 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o (re/g)o(sl/)p 3977 2391 V 390 2480 a Fk(for)30 b(do)s(cumen)m(tation.) 275 2646 y(\037zeta_in)m(t)i(-*-)f(texinfo)g(-*-)2960 2811 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(zeta_int)48 b Fi(\()p Fh(n)12 b Fi(\))2960 2921 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(zeta_int)48 b Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 3031 y Fk(These)30 b(routines)g(compute)h(the)g(Riemann)f(zeta)i(function)e(zeta\(n\))i (for)e(in)m(teger)i(n,)e(n)g(e)g(1.)390 3159 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g (the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 3287 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 3307 V 390 3397 a Fk(for)30 b(do)s(cumen)m(tation.)275 3562 y(\037eta_in)m(t)i(-*-)f(texinfo)g(-*-)2960 3728 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(eta_int)47 b Fi(\()p Fh(n)12 b Fi(\))2960 3838 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b 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Fi(\))2960 4736 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_il_scaled)d Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 4845 y Fk(These)26 b(routines)g(compute)h(the)f(scaled)h(regular)g(mo)s(di\014ed)e (spherical)i(Bessel)g(function)f(of)g(order)390 4955 y(l,)31 b(exp\(-)p Ff(|)p Fk(x)p Ff(|)p Fk(\))f(i_l\(x\))390 5093 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 5230 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o (re/g)o(sl/)p 3977 5251 V 390 5340 a Fk(for)30 b(do)s(cumen)m(tation.)p eop end %%Page: 39 39 TeXDict begin 39 38 bop 275 299 a Fk(\037b)s(essel_kl_scaled)31 b(-*-)g(texinfo)g(-*-)2960 482 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(bessel_kl_scaled)d Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 591 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p 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Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 3087 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(fermi_dirac_int)d Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 3197 y Fk(These)27 b(routines)h(compute)g(the)f(complete)i(F)-8 b(ermi-Dirac)30 b(in)m(tegral)f(with)f(an)f(in)m(teger)i(index)e(of)h(j,)390 3306 y(F_j\(x\))j(=)f(\(1/Gamma\(j+1\)\))k(in)m(t_0)p Ff(^)p Fk(inft)m(y)d(dt)g(\(t)p Ff(^)p Fk(j)f(/\(exp\(t-x\)+1\)\).)390 3440 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 3574 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o (re/g)o(sl/)p 3977 3595 V 390 3684 a Fk(for)30 b(do)s(cumen)m(tation.) 275 3867 y(\037ta)m(ylorco)s(e\013)i(-*-)f(texinfo)g(-*-)2960 4049 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(taylorcoeff)c Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 4159 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(taylorcoeff)c Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 4268 y Fk(These)30 b(routines)g(compute)h(the)g(T)-8 b(a)m(ylor)31 b(co)s(e\016cien)m(t)h (x)p Ff(^)p Fk(n)e(/)h(n!)40 b(for)30 b(x)g Ff(>)p Fk(=)g(0,)h(n)f Ff(>)p Fk(=)g(0.)390 4402 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate) i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 4536 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 4557 V 390 4646 a Fk(for)30 b(do)s(cumen)m(tation.)275 4829 y(\037legendre_Pl)g(-*-)i(texinfo)f(-*-)2960 5011 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(legendre_Pl)c Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 5121 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(legendre_Pl)c Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 5230 y Fk(These)36 b(functions)f(ev)-5 b(aluate)38 b(the)e(Legendre)f(p)s(olynomial)i(P_l\(x\))g(for)e(a)h(sp) s(eci\014c)g(v)-5 b(alue)36 b(of)g(l,)i(x)390 5340 y(sub)5 b(ject)30 b(to)h(l)g Ff(>)p Fk(=)f(0,)h Ff(|)p Fk(x)p Ff(|)e(<)p Fk(=)h(1)p eop end %%Page: 40 40 TeXDict begin 40 39 bop 390 299 a Fg(err)36 b Fk(con)m(tains)c(an)e (estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 434 y(This)19 b(function)h(is)h(from)f(the) g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 454 42 84 v 390 543 a Fk(for)30 b(do)s(cumen)m(tation.)275 729 y(\037legendre_Ql)g(-*-)i(texinfo)f(-*-)2960 914 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(legendre_Ql)c Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 1024 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(legendre_Ql)c Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 1133 y Fk(These)30 b(routines)g (compute)h(the)g(Legendre)f(function)g(Q_l\(x\))h(for)f(x)h Ff(>)f Fk(-1,)h(x)f(!=)h(1)f(and)g(l)h Ff(>)p Fk(=)e(0.)390 1268 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 1403 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o (re/g)o(sl/)p 3977 1424 V 390 1513 a Fk(for)30 b(do)s(cumen)m(tation.) 275 1698 y(\037psi_n)f(-*-)i(texinfo)g(-*-)2960 1884 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(psi_n)47 b Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 1993 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(psi_n)47 b Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 2103 y Fk(These)30 b(routines)g(compute)h(the)g(p)s(olygamma)g(function)f(psi)p Ff(^{)p Fk(\(m\))p Ff(})p Fk(\(x\))g(for)g(m)g Ff(>)p Fk(=)g(0,)h(x)f Ff(>)g Fk(0.)390 2238 y Fg(err)36 b Fk(con)m(tains)c (an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 2373 y(This)19 b(function)h(is)h(from)f (the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 2393 V 390 2482 a Fk(for)30 b(do)s(cumen)m(tation.)275 2668 y(\037b)s(essel_Jn)m(u)f(-*-)i(texinfo)g(-*-)2960 2853 y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53 b(bessel_Jnu)48 b Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b Fi(\))2960 2963 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_Jnu)48 b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 3072 y Fk(These)28 b(routines)f(compute)h(the)g(regular)g(cylindrical)h(Bessel)f(function) g(of)g(fractional)h(order)e(n)m(u,)390 3182 y(J_u\(x\).)390 3317 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(z)p Fk(.)390 3452 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o (re/g)o(sl/)p 3977 3472 V 390 3561 a Fk(for)30 b(do)s(cumen)m(tation.) 275 3747 y(\037b)s(essel_Yn)m(u)f(-*-)j(texinfo)f(-*-)2960 3932 y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53 b(bessel_Ynu)48 b Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b Fi(\))2960 4042 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_Ynu)48 b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 4151 y Fk(These)37 b(routines)f(compute)h(the)g(irregular)g(cylindrical)h(Bessel)g (function)e(of)h(fractional)h(order)390 4261 y(n)m(u,)30 b(Y_u\(x\).)390 4396 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of) f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(z)p Fk(.)390 4531 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 4551 V 390 4641 a Fk(for)30 b(do)s(cumen)m(tation.)275 4826 y(\037b)s(essel_In)m(u)f(-*-)i(texinfo)g(-*-)2960 5011 y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53 b(bessel_Inu)48 b Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b Fi(\))2960 5121 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_Inu)48 b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 5230 y Fk(These)34 b(routines)g(compute)h(the)f(regular)g(mo)s(di\014ed)f(Bessel)j (function)e(of)g(fractional)i(order)d(n)m(u,)390 5340 y(I_u\(x\))e(for)f(x)p Ff(>)p Fk(0,)g(u)p Ff(>)p Fk(0.)p eop end %%Page: 41 41 TeXDict begin 41 40 bop 390 299 a Fg(err)36 b Fk(con)m(tains)c(an)e (estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(z)p Fk(.)390 445 y(This)19 b(function)h(is)h(from)f(the) g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 465 42 84 v 390 554 a Fk(for)30 b(do)s(cumen)m(tation.)275 762 y(\037b)s(essel_In)m(u_scaled)g(-*-)h(texinfo)g(-*-)2960 969 y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53 b(bessel_Inu_scaled)d Fi(\()p Fh(x)p Fg(,)32 b Fh(y)12 b Fi(\))2960 1078 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_Inu_scaled)d Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 1188 y Fk(These)24 b(routines)f(compute)h(the)g(scaled)h(regular)f(mo)s(di\014ed)f(Bessel) i(function)e(of)h(fractional)h(order)390 1298 y(n)m(u,)30 b(exp\(-)p Ff(|)p Fk(x)p Ff(|)p Fk(\)I_u\(x\))h(for)f(x)p Ff(>)p Fk(0,)h(u)p Ff(>)p Fk(0.)390 1443 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g (the)g(v)-5 b(alue)31 b Fg(z)p Fk(.)390 1589 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 1610 V 390 1699 a Fk(for)30 b(do)s(cumen)m(tation.)275 1906 y(\037b)s(essel_Kn)m(u)f(-*-)i(texinfo)g(-*-)2960 2113 y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53 b(bessel_Knu)48 b Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b Fi(\))2960 2223 y Fk([Loadable)31 b(F)-8 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All GSL functions can be called with by the GSL names within octave. @@end deftypefn clausen -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} clausen (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} clausen (@@dots{}) The Clausen function is defined by the following integral, Cl_2(x) = - \\int_0^x dt \\log(2 \\sin(t/2)) It is related to the dilogarithm by Cl_2(\\theta) = \\Im Li_2(\\exp(i \\theta)). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn dawson -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} dawson (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} dawson (@@dots{}) The Dawson integral is defined by \\exp(-x^2) \\int_0^x dt \\exp(t^2). A table of Dawson integral can be found in Abramowitz & Stegun, Table 7.5. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn debye_1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} debye_1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_1 (@@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn debye_2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} debye_2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_2 (@@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn debye_3 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} debye_3 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_3 (@@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn debye_4 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} debye_4 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_4 (@@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn erf_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} erf_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erf_gsl (@@dots{}) These routines compute the error function erf(x) = (2/\\sqrt(\\pi)) \\int_0^x dt \\exp(-t^2). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn erfc_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} erfc_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erfc_gsl (@@dots{}) These routines compute the complementary error function erfc(x) = 1 - erf(x) = (2/\\sqrt(\\pi)) \\int_x^\\infty \\exp(-t^2). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn log_erfc -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} log_erfc (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} log_erfc (@@dots{}) These routines compute the logarithm of the complementary error function \\log(\\erfc(x)). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn erf_Z -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} erf_Z (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erf_Z (@@dots{}) These routines compute the Gaussian probability function Z(x) = (1/(2\\pi)) \\exp(-x^2/2). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn erf_Q -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} erf_Q (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erf_Q (@@dots{}) These routines compute the upper tail of the Gaussian probability function Q(x) = (1/(2\\pi)) \\int_x^\\infty dt \\exp(-t^2/2). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hazard -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} hazard (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} hazard (@@dots{}) The hazard function for the normal distrbution, also known as the inverse Mill\\'s ratio, is defined as h(x) = Z(x)/Q(x) = \\sqrt@@{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2)@@}. It decreases rapidly as x approaches -\\infty and asymptotes to h(x) \\sim x as x approaches +\\infty. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expm1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expm1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expm1 (@@dots{}) These routines compute the quantity \\exp(x)-1 using an algorithm that is accurate for small x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn exprel -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} exprel (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} exprel (@@dots{}) These routines compute the quantity (\\exp(x)-1)/x using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion (\\exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\dots. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn exprel_2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} exprel_2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} exprel_2 (@@dots{}) These routines compute the quantity 2(\\exp(x)-1-x)/x^2 using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion 2(\\exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\dots. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expint_E1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expint_E1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_E1 (@@dots{}) These routines compute the exponential integral E_1(x), E_1(x) := Re \\int_1^\\infty dt \\exp(-xt)/t. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expint_E2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expint_E2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_E2 (@@dots{}) These routines compute the second-order exponential integral E_2(x), E_2(x) := \\Re \\int_1^\\infty dt \\exp(-xt)/t^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expint_Ei -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expint_Ei (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_Ei (@@dots{}) These routines compute the exponential integral E_i(x), Ei(x) := - PV(\\int_@@{-x@@}^\\infty dt \\exp(-t)/t) where PV denotes the principal value of the integral. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn Shi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} Shi (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Shi (@@dots{}) These routines compute the integral Shi(x) = \\int_0^x dt \\sinh(t)/t. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn Chi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} Chi (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Chi (@@dots{}) These routines compute the integral Chi(x) := Re[ \\gamma_E + \\log(x) + \\int_0^x dt (\\cosh[t]-1)/t] , where \\gamma_E is the Euler constant. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expint_3 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expint_3 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_3 (@@dots{}) These routines compute the exponential integral Ei_3(x) = \\int_0^x dt \\exp(-t^3) for x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn Si -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} Si (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Si (@@dots{}) These routines compute the Sine integral Si(x) = \\int_0^x dt \\sin(t)/t. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn Ci -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} Ci (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Ci (@@dots{}) These routines compute the Cosine integral Ci(x) = -\\int_x^\\infty dt \\cos(t)/t for x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn atanint -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} atanint (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} atanint (@@dots{}) These routines compute the Arctangent integral AtanInt(x) = \\int_0^x dt \\arctan(t)/t. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_mhalf -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_mhalf (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_mhalf (@@dots{}) These routines compute the complete Fermi-Dirac integral F_@@{-1/2@@}(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_half -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_half (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_half (@@dots{}) These routines compute the complete Fermi-Dirac integral F_@@{1/2@@}(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_3half -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_3half (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_3half (@@dots{}) These routines compute the complete Fermi-Dirac integral F_@@{3/2@@}(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gamma_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} gamma_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} gamma_gsl (@@dots{}) These routines compute the Gamma function \\Gamma(x), subject to x not being a negative integer. The function is computed using the real Lanczos method. The maximum value of x such that \\Gamma(x) is not considered an overflow is given by the macro GSL_SF_GAMMA_XMAX and is 171.0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lngamma_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lngamma_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lngamma_gsl (@@dots{}) These routines compute the logarithm of the Gamma function, \\log(\\Gamma(x)), subject to x not a being negative integer. For x<0 the real part of \\log(\\Gamma(x)) is returned, which is equivalent to \\log(|\\Gamma(x)|). The function is computed using the real Lanczos method. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gammastar -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} gammastar (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} gammastar (@@dots{}) These routines compute the regulated Gamma Function \\Gamma^*(x) for x > 0. The regulated gamma function is given by, \\Gamma^*(x) = \\Gamma(x)/(\\sqrt@@{2\\pi@@} x^@@{(x-1/2)@@} \\exp(-x)) = (1 + (1/12x) + ...) for x \\to \\infty and is a useful suggestion of Temme. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gammainv_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} gammainv_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} gammainv_gsl (@@dots{}) These routines compute the reciprocal of the gamma function, 1/\\Gamma(x) using the real Lanczos method. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lambert_W0 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lambert_W0 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lambert_W0 (@@dots{}) These compute the principal branch of the Lambert W function, W_0(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@@{-1@@}(x) to be the other real branch, where W < -1 for x < 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lambert_Wm1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lambert_Wm1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lambert_Wm1 (@@dots{}) These compute the secondary real-valued branch of the Lambert W function, W_@@{-1@@}(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@@{-1@@}(x) to be the other real branch, where W < -1 for x < 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn log_1plusx -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} log_1plusx (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} log_1plusx (@@dots{}) These routines compute \\log(1 + x) for x > -1 using an algorithm that is accurate for small x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn log_1plusx_mx -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} log_1plusx_mx (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} log_1plusx_mx (@@dots{}) These routines compute \\log(1 + x) - x for x > -1 using an algorithm that is accurate for small x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn psi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} psi (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi (@@dots{}) These routines compute the digamma function \\psi(x) for general x, x \ e 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn psi_1piy -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} psi_1piy (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi_1piy (@@dots{}) These routines compute the real part of the digamma function on the line 1+i y, Re[\\psi(1 + i y)]. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn synchrotron_1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} synchrotron_1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} synchrotron_1 (@@dots{}) These routines compute the first synchrotron function x \\int_x^\\infty dt K_@@{5/3@@}(t) for x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn synchrotron_2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} synchrotron_2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} synchrotron_2 (@@dots{}) These routines compute the second synchrotron function x K_@@{2/3@@}(x) for x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn transport_2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} transport_2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_2 (@@dots{}) These routines compute the transport function J(2,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn transport_3 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} transport_3 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_3 (@@dots{}) These routines compute the transport function J(3,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn transport_4 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} transport_4 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_4 (@@dots{}) These routines compute the transport function J(4,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn transport_5 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} transport_5 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_5 (@@dots{}) These routines compute the transport function J(5,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn sinc_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} sinc_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} sinc_gsl (@@dots{}) These routines compute \\sinc(x) = \\sin(\\pi x) / (\\pi x) for any value of x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lnsinh -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lnsinh (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lnsinh (@@dots{}) These routines compute \\log(\\sinh(x)) for x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lncosh -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lncosh (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lncosh (@@dots{}) These routines compute \\log(\\cosh(x)) for any x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn zeta -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} zeta (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} zeta (@@dots{}) These routines compute the Riemann zeta function \\zeta(s) for arbitrary s, s \ e 1. The Riemann zeta function is defined by the infinite sum \\zeta(s) = \\sum_@@{k=1@@}^\\infty k^@@{-s@@}. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn eta -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} eta (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} eta (@@dots{}) These routines compute the eta function \\eta(s) for arbitrary s. The eta function is defined by \\eta(s) = (1-2^@@{1-s@@}) \\zeta(s). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Jn -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_Jn (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Jn (@@dots{}) These routines compute the regular cylindrical Bessel function of order n, J_n(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Yn -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_Yn (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Yn (@@dots{}) These routines compute the irregular cylindrical Bessel function of order n, Y_n(x), for x>0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_In -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_In (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_In (@@dots{}) These routines compute the regular modified cylindrical Bessel function of order n, I_n(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_In_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_In_scaled (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_In_scaled (@@dots{}) These routines compute the scaled regular modified cylindrical Bessel function of order n, \\exp(-|x|) I_n(x) @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Kn -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_Kn (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Kn (@@dots{}) These routines compute the irregular modified cylindrical Bessel function of order n, K_n(x), for x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Kn_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_Kn_scaled (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Kn_scaled (@@dots{}) @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_jl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_jl (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_jl (@@dots{}) These routines compute the regular spherical Bessel function of order l, j_l(x), for l >= 0 and x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_yl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_yl (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_yl (@@dots{}) These routines compute the irregular spherical Bessel function of order l, y_l(x), for l >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_il_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_il_scaled (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_il_scaled (@@dots{}) These routines compute the scaled regular modified spherical Bessel function of order l, \\exp(-|x|) i_l(x) @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_kl_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_kl_scaled (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_kl_scaled (@@dots{}) These routines compute the scaled irregular modified spherical Bessel function of order l, \\exp(x) k_l(x), for x>0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn exprel_n -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} exprel_n (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} exprel_n (@@dots{}) These routines compute the N-relative exponential, which is the n-th generalization of the functions gsl_sf_exprel and gsl_sf_exprel2. The N-relative exponential is given by, exprel_N(x) = N!/x^N (\\exp(x) - \\sum_@@{k=0@@}^@@{N-1@@} x^k/k!) = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ... = 1F1 (1,1+N,x) @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_int -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_int (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_int (@@dots{}) These routines compute the complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/\\Gamma(j+1)) \\int_0^\\infty dt (t^j /(\\exp(t-x)+1)). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn taylorcoeff -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} taylorcoeff (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} taylorcoeff (@@dots{}) These routines compute the Taylor coefficient x^n / n! for x >= 0, n >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn legendre_Pl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} legendre_Pl (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_Pl (@@dots{}) These functions evaluate the Legendre polynomial P_l(x) for a specific value of l, x subject to l >= 0, |x| <= 1 @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn legendre_Ql -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} legendre_Ql (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_Ql (@@dots{}) These routines compute the Legendre function Q_l(x) for x > -1, x != 1 and l >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn psi_n -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} psi_n (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi_n (@@dots{}) These routines compute the polygamma function \\psi^@@{(m)@@}(x) for m >= 0, x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Jnu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Jnu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Jnu (@@dots{}) These routines compute the regular cylindrical Bessel function of fractional order nu, J_\ u(x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Ynu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Ynu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Ynu (@@dots{}) These routines compute the irregular cylindrical Bessel function of fractional order nu, Y_\ u(x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Inu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Inu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Inu (@@dots{}) These routines compute the regular modified Bessel function of fractional order nu, I_\ u(x) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Inu_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Inu_scaled (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Inu_scaled (@@dots{}) These routines compute the scaled regular modified Bessel function of fractional order nu, \\exp(-|x|)I_\ u(x) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Knu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Knu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Knu (@@dots{}) These routines compute the irregular modified Bessel function of fractional order nu, K_\ u(x) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_lnKnu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_lnKnu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_lnKnu (@@dots{}) These routines compute the logarithm of the irregular modified Bessel function of fractional order nu, \\ln(K_\ u(x)) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Knu_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Knu_scaled (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Knu_scaled (@@dots{}) These routines compute the scaled irregular modified Bessel function of fractional order nu, \\exp(+|x|) K_\ u(x) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn exp_mult -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} exp_mult (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} exp_mult (@@dots{}) These routines exponentiate x and multiply by the factor y to return the product y \\exp(x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_inc_0 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} fermi_dirac_inc_0 (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} fermi_dirac_inc_0 (@@dots{}) These routines compute the incomplete Fermi-Dirac integral with an index of zero, F_0(x,b) = \\ln(1 + e^@@{b-x@@}) - (b-x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn poch -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} poch (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} poch (@@dots{}) These routines compute the Pochhammer symbol (a)_x := \\Gamma(a + x)/\\Gamma(a), subject to a and a+x not being negative integers. The Pochhammer symbol is also known as the Apell symbol. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lnpoch -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} lnpoch (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} lnpoch (@@dots{}) These routines compute the logarithm of the Pochhammer symbol, \\log((a)_x) = \\log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn pochrel -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} pochrel (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} pochrel (@@dots{}) These routines compute the relative Pochhammer symbol ((a,x) - 1)/x where (a,x) = (a)_x := \\Gamma(a + x)/\\Gamma(a). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gamma_inc_Q -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} gamma_inc_Q (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} gamma_inc_Q (@@dots{}) These routines compute the normalized incomplete Gamma Function Q(a,x) = 1/\\Gamma(a) \\int_x\\infty dt t^@@{a-1@@} \\exp(-t) for a > 0, x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gamma_inc_P -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} gamma_inc_P (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} gamma_inc_P (@@dots{}) These routines compute the complementary normalized incomplete Gamma Function P(a,x) = 1/\\Gamma(a) \\int_0^x dt t^@@{a-1@@} \\exp(-t) for a > 0, x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gamma_inc -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} gamma_inc (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} gamma_inc (@@dots{}) These functions compute the incomplete Gamma Function the normalization factor included in the previously defined functions: \\Gamma(a,x) = \\int_x\\infty dt t^@@{a-1@@} \\exp(-t) for a real and x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn beta_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} beta_gsl (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} beta_gsl (@@dots{}) These routines compute the Beta Function, B(a,b) = \\Gamma(a)\\Gamma(b)/\\Gamma(a+b) for a > 0, b > 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lnbeta -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} lnbeta (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} lnbeta (@@dots{}) These routines compute the logarithm of the Beta Function, \\log(B(a,b)) for a > 0, b > 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hyperg_0F1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} hyperg_0F1 (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} hyperg_0F1 (@@dots{}) These routines compute the hypergeometric function 0F1(c,x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn conicalP_half -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} conicalP_half (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_half (@@dots{}) These routines compute the irregular Spherical Conical Function P^@@{1/2@@}_@@{-1/2 + i \\lambda@@}(x) for x > -1. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn conicalP_mhalf -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} conicalP_mhalf (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_mhalf (@@dots{}) These routines compute the regular Spherical Conical Function P^@@{-1/2@@}_@@{-1/2 + i \\lambda@@}(x) for x > -1. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn conicalP_0 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} conicalP_0 (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_0 (@@dots{}) These routines compute the conical function P^0_@@{-1/2 + i \\lambda@@}(x) for x > -1. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn conicalP_1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} conicalP_1 (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_1 (@@dots{}) These routines compute the conical function P^1_@@{-1/2 + i \\lambda@@}(x) for x > -1. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hzeta -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} hzeta (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} hzeta (@@dots{}) These routines compute the Hurwitz zeta function \\zeta(s,q) for s > 1, q > 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Ai -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai (@@dots{}) These routines compute the Airy function Ai(x) with an accuracy specified by mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Bi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi (@@dots{}) These routines compute the Airy function Bi(x) with an accuracy specified by mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Ai_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai_scaled (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai_scaled (@@dots{}) These routines compute a scaled version of the Airy function S_A(x) Ai(x). For x>0 the scaling factor S_A(x) is \\exp(+(2/3) x^(3/2)), and is 1 for x<0. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Bi_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi_scaled (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi_scaled (@@dots{}) These routines compute a scaled version of the Airy function S_B(x) Bi(x). For x>0 the scaling factor S_B(x) is exp(-(2/3) x^(3/2)), and is 1 for x<0. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Ai_deriv -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai_deriv (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai_deriv (@@dots{}) These routines compute the Airy function derivative Ai'(x) with an accuracy specified by mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Bi_deriv -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi_deriv (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi_deriv (@@dots{}) These routines compute the Airy function derivative Bi'(x) with an accuracy specified by mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Ai_deriv_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai_deriv_scaled (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai_deriv_scaled (@@dots{}) These routines compute the derivative of the scaled Airy function S_A(x) Ai(x). The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Bi_deriv_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi_deriv_scaled (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi_deriv_scaled (@@dots{}) These routines compute the derivative of the scaled Airy function S_B(x) Bi(x). The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn ellint_Kcomp -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} ellint_Kcomp (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} ellint_Kcomp (@@dots{}) These routines compute the complete elliptic integral K(k) @@tex \beforedisplay $$ \eqalign{ K(k) &= \int_0^{\pi/2} {dt \over \sqrt{(1 - k^2 \sin^2(t))}} \cr } $$ \afterdisplay @@end tex The notation used here is based on Carlson, @@cite{Numerische Mathematik} 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter @@math{m = k^2}. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn ellint_Ecomp -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} ellint_Ecomp (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} ellint_Ecomp (@@dots{}) These routines compute the complete elliptic integral E(k) to the accuracy specified by the mode variable mode. @@tex \beforedisplay $$ \eqalign{ E(k) &= \int_0^{\pi/2} \sqrt{(1 - k^2 \sin^2(t))} dt \cr } $$ \afterdisplay @@end tex The notation used here is based on Carlson, @@cite{Numerische Mathematik} 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter @@math{m = k^2}. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_zero_Ai -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Ai (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Ai (@@dots{}) These routines compute the location of the s-th zero of the Airy function Ai(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_zero_Bi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Bi (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Bi (@@dots{}) These routines compute the location of the s-th zero of the Airy function Bi(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_zero_Ai_deriv -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Ai_deriv (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Ai_deriv (@@dots{}) These routines compute the location of the s-th zero of the Airy function derivative Ai(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_zero_Bi_deriv -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Bi_deriv (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Bi_deriv (@@dots{}) These routines compute the location of the s-th zero of the Airy function derivative Bi(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_zero_J0 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_zero_J0 (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_zero_J0 (@@dots{}) These routines compute the location of the s-th positive zero of the Bessel function J_0(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_zero_J1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_zero_J1 (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_zero_J1 (@@dots{}) These routines compute the location of the s-th positive zero of the Bessel function J_1(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn psi_1_int -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} psi_1_int (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi_1_int (@@dots{}) These routines compute the Trigamma function \\psi(n) for positive integer n. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn zeta_int -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} zeta_int (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} zeta_int (@@dots{}) These routines compute the Riemann zeta function \\zeta(n) for integer n, n \ e 1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn eta_int -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} eta_int (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} eta_int (@@dots{}) These routines compute the eta function \\eta(n) for integer n. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn legendre_Plm -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} legendre_Plm (@@var{n}, @@var{m}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_Plm (@@dots{}) These routines compute the associated Legendre polynomial P_l^m(x) for m >= 0, l >= m, |x| <= 1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn legendre_sphPlm -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} legendre_sphPlm (@@var{n}, @@var{m}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_sphPlm (@@dots{}) These routines compute the normalized associated Legendre polynomial $\\sqrt@@{(2l+1)/(4\\pi)@@} \\sqrt@@{(l-m)!/(l+m)!@@} P_l^m(x)$ suitable for use in spherical harmonics. The parameters must satisfy m >= 0, l >= m, |x| <= 1. Theses routines avoid the overflows that occur for the standard normalization of P_l^m(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hyperg_U -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{out} =} hyperg_U (@@var{x0}, @@var{x1}, @@var{x2}) @@deftypefnx {Loadable Function} {[@@var{out}, @@var{err}] =} hyperg_U (@@dots{}) Secondary Confluent Hypergoemetric U function A&E 13.1.3 All input are double as is the output. @@var{err} contains an estimate of the absolute error in the value @@var{out}.a. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hyperg_1F1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{out} =} hyperg_1F1 (@@var{x0}, @@var{x1}, @@var{x2}) @@deftypefnx {Loadable Function} {[@@var{out}, @@var{err}] =} hyperg_1F1 (@@dots{}) Primary Confluent Hypergoemetric U function A&E 13.1.3 All inputs are double as is the output. @@var{err} contains an estimate of the absolute error in the value @@var{out}.a. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gsl_sf -*- texinfo -*- @@deftypefn {Loadable Function} {} gsl_sf () Octave bindings to the GNU Scientific Library. All GSL functions can be called with by the GSL names within octave. @@end deftypefn clausen -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} clausen (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} clausen (@@dots{}) The Clausen function is defined by the following integral, Cl_2(x) = - \\int_0^x dt \\log(2 \\sin(t/2)) It is related to the dilogarithm by Cl_2(\\theta) = \\Im Li_2(\\exp(i \\theta)). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn dawson -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} dawson (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} dawson (@@dots{}) The Dawson integral is defined by \\exp(-x^2) \\int_0^x dt \\exp(t^2). A table of Dawson integral can be found in Abramowitz & Stegun, Table 7.5. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn debye_1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} debye_1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_1 (@@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn debye_2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} debye_2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_2 (@@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn debye_3 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} debye_3 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_3 (@@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn debye_4 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} debye_4 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_4 (@@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn erf_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} erf_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erf_gsl (@@dots{}) These routines compute the error function erf(x) = (2/\\sqrt(\\pi)) \\int_0^x dt \\exp(-t^2). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn erfc_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} erfc_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erfc_gsl (@@dots{}) These routines compute the complementary error function erfc(x) = 1 - erf(x) = (2/\\sqrt(\\pi)) \\int_x^\\infty \\exp(-t^2). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn log_erfc -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} log_erfc (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} log_erfc (@@dots{}) These routines compute the logarithm of the complementary error function \\log(\\erfc(x)). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn erf_Z -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} erf_Z (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erf_Z (@@dots{}) These routines compute the Gaussian probability function Z(x) = (1/(2\\pi)) \\exp(-x^2/2). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn erf_Q -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} erf_Q (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erf_Q (@@dots{}) These routines compute the upper tail of the Gaussian probability function Q(x) = (1/(2\\pi)) \\int_x^\\infty dt \\exp(-t^2/2). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hazard -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} hazard (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} hazard (@@dots{}) The hazard function for the normal distrbution, also known as the inverse Mill\\'s ratio, is defined as h(x) = Z(x)/Q(x) = \\sqrt@@{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2)@@}. It decreases rapidly as x approaches -\\infty and asymptotes to h(x) \\sim x as x approaches +\\infty. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expm1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expm1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expm1 (@@dots{}) These routines compute the quantity \\exp(x)-1 using an algorithm that is accurate for small x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn exprel -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} exprel (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} exprel (@@dots{}) These routines compute the quantity (\\exp(x)-1)/x using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion (\\exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\dots. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn exprel_2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} exprel_2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} exprel_2 (@@dots{}) These routines compute the quantity 2(\\exp(x)-1-x)/x^2 using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion 2(\\exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\dots. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expint_E1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expint_E1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_E1 (@@dots{}) These routines compute the exponential integral E_1(x), E_1(x) := Re \\int_1^\\infty dt \\exp(-xt)/t. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expint_E2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expint_E2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_E2 (@@dots{}) These routines compute the second-order exponential integral E_2(x), E_2(x) := \\Re \\int_1^\\infty dt \\exp(-xt)/t^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expint_Ei -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expint_Ei (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_Ei (@@dots{}) These routines compute the exponential integral E_i(x), Ei(x) := - PV(\\int_@@{-x@@}^\\infty dt \\exp(-t)/t) where PV denotes the principal value of the integral. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn Shi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} Shi (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Shi (@@dots{}) These routines compute the integral Shi(x) = \\int_0^x dt \\sinh(t)/t. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn Chi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} Chi (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Chi (@@dots{}) These routines compute the integral Chi(x) := Re[ \\gamma_E + \\log(x) + \\int_0^x dt (\\cosh[t]-1)/t] , where \\gamma_E is the Euler constant. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expint_3 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expint_3 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_3 (@@dots{}) These routines compute the exponential integral Ei_3(x) = \\int_0^x dt \\exp(-t^3) for x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn Si -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} Si (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Si (@@dots{}) These routines compute the Sine integral Si(x) = \\int_0^x dt \\sin(t)/t. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn Ci -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} Ci (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Ci (@@dots{}) These routines compute the Cosine integral Ci(x) = -\\int_x^\\infty dt \\cos(t)/t for x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn atanint -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} atanint (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} atanint (@@dots{}) These routines compute the Arctangent integral AtanInt(x) = \\int_0^x dt \\arctan(t)/t. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_mhalf -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_mhalf (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_mhalf (@@dots{}) These routines compute the complete Fermi-Dirac integral F_@@{-1/2@@}(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_half -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_half (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_half (@@dots{}) These routines compute the complete Fermi-Dirac integral F_@@{1/2@@}(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_3half -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_3half (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_3half (@@dots{}) These routines compute the complete Fermi-Dirac integral F_@@{3/2@@}(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gamma_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} gamma_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} gamma_gsl (@@dots{}) These routines compute the Gamma function \\Gamma(x), subject to x not being a negative integer. The function is computed using the real Lanczos method. The maximum value of x such that \\Gamma(x) is not considered an overflow is given by the macro GSL_SF_GAMMA_XMAX and is 171.0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lngamma_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lngamma_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lngamma_gsl (@@dots{}) These routines compute the logarithm of the Gamma function, \\log(\\Gamma(x)), subject to x not a being negative integer. For x<0 the real part of \\log(\\Gamma(x)) is returned, which is equivalent to \\log(|\\Gamma(x)|). The function is computed using the real Lanczos method. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gammastar -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} gammastar (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} gammastar (@@dots{}) These routines compute the regulated Gamma Function \\Gamma^*(x) for x > 0. The regulated gamma function is given by, \\Gamma^*(x) = \\Gamma(x)/(\\sqrt@@{2\\pi@@} x^@@{(x-1/2)@@} \\exp(-x)) = (1 + (1/12x) + ...) for x \\to \\infty and is a useful suggestion of Temme. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gammainv_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} gammainv_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} gammainv_gsl (@@dots{}) These routines compute the reciprocal of the gamma function, 1/\\Gamma(x) using the real Lanczos method. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lambert_W0 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lambert_W0 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lambert_W0 (@@dots{}) These compute the principal branch of the Lambert W function, W_0(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@@{-1@@}(x) to be the other real branch, where W < -1 for x < 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lambert_Wm1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lambert_Wm1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lambert_Wm1 (@@dots{}) These compute the secondary real-valued branch of the Lambert W function, W_@@{-1@@}(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@@{-1@@}(x) to be the other real branch, where W < -1 for x < 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn log_1plusx -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} log_1plusx (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} log_1plusx (@@dots{}) These routines compute \\log(1 + x) for x > -1 using an algorithm that is accurate for small x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn log_1plusx_mx -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} log_1plusx_mx (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} log_1plusx_mx (@@dots{}) These routines compute \\log(1 + x) - x for x > -1 using an algorithm that is accurate for small x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn psi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} psi (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi (@@dots{}) These routines compute the digamma function \\psi(x) for general x, x \ e 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn psi_1piy -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} psi_1piy (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi_1piy (@@dots{}) These routines compute the real part of the digamma function on the line 1+i y, Re[\\psi(1 + i y)]. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn synchrotron_1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} synchrotron_1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} synchrotron_1 (@@dots{}) These routines compute the first synchrotron function x \\int_x^\\infty dt K_@@{5/3@@}(t) for x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn synchrotron_2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} synchrotron_2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} synchrotron_2 (@@dots{}) These routines compute the second synchrotron function x K_@@{2/3@@}(x) for x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn transport_2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} transport_2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_2 (@@dots{}) These routines compute the transport function J(2,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn transport_3 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} transport_3 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_3 (@@dots{}) These routines compute the transport function J(3,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn transport_4 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} transport_4 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_4 (@@dots{}) These routines compute the transport function J(4,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn transport_5 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} transport_5 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_5 (@@dots{}) These routines compute the transport function J(5,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn sinc_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} sinc_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} sinc_gsl (@@dots{}) These routines compute \\sinc(x) = \\sin(\\pi x) / (\\pi x) for any value of x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lnsinh -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lnsinh (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lnsinh (@@dots{}) These routines compute \\log(\\sinh(x)) for x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lncosh -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lncosh (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lncosh (@@dots{}) These routines compute \\log(\\cosh(x)) for any x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn zeta -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} zeta (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} zeta (@@dots{}) These routines compute the Riemann zeta function \\zeta(s) for arbitrary s, s \ e 1. The Riemann zeta function is defined by the infinite sum \\zeta(s) = \\sum_@@{k=1@@}^\\infty k^@@{-s@@}. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn eta -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} eta (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} eta (@@dots{}) These routines compute the eta function \\eta(s) for arbitrary s. The eta function is defined by \\eta(s) = (1-2^@@{1-s@@}) \\zeta(s). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Jn -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_Jn (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Jn (@@dots{}) These routines compute the regular cylindrical Bessel function of order n, J_n(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Yn -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_Yn (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Yn (@@dots{}) These routines compute the irregular cylindrical Bessel function of order n, Y_n(x), for x>0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_In -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_In (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_In (@@dots{}) These routines compute the regular modified cylindrical Bessel function of order n, I_n(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_In_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_In_scaled (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_In_scaled (@@dots{}) These routines compute the scaled regular modified cylindrical Bessel function of order n, \\exp(-|x|) I_n(x) @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Kn -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_Kn (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Kn (@@dots{}) These routines compute the irregular modified cylindrical Bessel function of order n, K_n(x), for x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Kn_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_Kn_scaled (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Kn_scaled (@@dots{}) @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_jl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_jl (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_jl (@@dots{}) These routines compute the regular spherical Bessel function of order l, j_l(x), for l >= 0 and x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_yl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_yl (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_yl (@@dots{}) These routines compute the irregular spherical Bessel function of order l, y_l(x), for l >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_il_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_il_scaled (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_il_scaled (@@dots{}) These routines compute the scaled regular modified spherical Bessel function of order l, \\exp(-|x|) i_l(x) @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_kl_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_kl_scaled (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_kl_scaled (@@dots{}) These routines compute the scaled irregular modified spherical Bessel function of order l, \\exp(x) k_l(x), for x>0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn exprel_n -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} exprel_n (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} exprel_n (@@dots{}) These routines compute the N-relative exponential, which is the n-th generalization of the functions gsl_sf_exprel and gsl_sf_exprel2. The N-relative exponential is given by, exprel_N(x) = N!/x^N (\\exp(x) - \\sum_@@{k=0@@}^@@{N-1@@} x^k/k!) = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ... = 1F1 (1,1+N,x) @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_int -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_int (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_int (@@dots{}) These routines compute the complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/\\Gamma(j+1)) \\int_0^\\infty dt (t^j /(\\exp(t-x)+1)). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn taylorcoeff -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} taylorcoeff (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} taylorcoeff (@@dots{}) These routines compute the Taylor coefficient x^n / n! for x >= 0, n >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn legendre_Pl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} legendre_Pl (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_Pl (@@dots{}) These functions evaluate the Legendre polynomial P_l(x) for a specific value of l, x subject to l >= 0, |x| <= 1 @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn legendre_Ql -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} legendre_Ql (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_Ql (@@dots{}) These routines compute the Legendre function Q_l(x) for x > -1, x != 1 and l >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn psi_n -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} psi_n (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi_n (@@dots{}) These routines compute the polygamma function \\psi^@@{(m)@@}(x) for m >= 0, x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Jnu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Jnu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Jnu (@@dots{}) These routines compute the regular cylindrical Bessel function of fractional order nu, J_\ u(x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Ynu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Ynu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Ynu (@@dots{}) These routines compute the irregular cylindrical Bessel function of fractional order nu, Y_\ u(x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Inu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Inu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Inu (@@dots{}) These routines compute the regular modified Bessel function of fractional order nu, I_\ u(x) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Inu_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Inu_scaled (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Inu_scaled (@@dots{}) These routines compute the scaled regular modified Bessel function of fractional order nu, \\exp(-|x|)I_\ u(x) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Knu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Knu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Knu (@@dots{}) These routines compute the irregular modified Bessel function of fractional order nu, K_\ u(x) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_lnKnu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_lnKnu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_lnKnu (@@dots{}) These routines compute the logarithm of the irregular modified Bessel function of fractional order nu, \\ln(K_\ u(x)) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Knu_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Knu_scaled (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Knu_scaled (@@dots{}) These routines compute the scaled irregular modified Bessel function of fractional order nu, \\exp(+|x|) K_\ u(x) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn exp_mult -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} exp_mult (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} exp_mult (@@dots{}) These routines exponentiate x and multiply by the factor y to return the product y \\exp(x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_inc_0 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} fermi_dirac_inc_0 (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} fermi_dirac_inc_0 (@@dots{}) These routines compute the incomplete Fermi-Dirac integral with an index of zero, F_0(x,b) = \\ln(1 + e^@@{b-x@@}) - (b-x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn poch -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} poch (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} poch (@@dots{}) These routines compute the Pochhammer symbol (a)_x := \\Gamma(a + x)/\\Gamma(a), subject to a and a+x not being negative integers. The Pochhammer symbol is also known as the Apell symbol. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lnpoch -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} lnpoch (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} lnpoch (@@dots{}) These routines compute the logarithm of the Pochhammer symbol, \\log((a)_x) = \\log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn pochrel -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} pochrel (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} pochrel (@@dots{}) These routines compute the relative Pochhammer symbol ((a,x) - 1)/x where (a,x) = (a)_x := \\Gamma(a + x)/\\Gamma(a). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gamma_inc_Q -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} gamma_inc_Q (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} gamma_inc_Q (@@dots{}) These routines compute the normalized incomplete Gamma Function Q(a,x) = 1/\\Gamma(a) \\int_x\\infty dt t^@@{a-1@@} \\exp(-t) for a > 0, x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gamma_inc_P -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} gamma_inc_P (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} gamma_inc_P (@@dots{}) These routines compute the complementary normalized incomplete Gamma Function P(a,x) = 1/\\Gamma(a) \\int_0^x dt t^@@{a-1@@} \\exp(-t) for a > 0, x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gamma_inc -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} gamma_inc (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} gamma_inc (@@dots{}) These functions compute the incomplete Gamma Function the normalization factor included in the previously defined functions: \\Gamma(a,x) = \\int_x\\infty dt t^@@{a-1@@} \\exp(-t) for a real and x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn beta_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} beta_gsl (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} beta_gsl (@@dots{}) These routines compute the Beta Function, B(a,b) = \\Gamma(a)\\Gamma(b)/\\Gamma(a+b) for a > 0, b > 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lnbeta -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} lnbeta (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} lnbeta (@@dots{}) These routines compute the logarithm of the Beta Function, \\log(B(a,b)) for a > 0, b > 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hyperg_0F1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} hyperg_0F1 (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} hyperg_0F1 (@@dots{}) These routines compute the hypergeometric function 0F1(c,x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn conicalP_half -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} conicalP_half (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_half (@@dots{}) These routines compute the irregular Spherical Conical Function P^@@{1/2@@}_@@{-1/2 + i \\lambda@@}(x) for x > -1. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn conicalP_mhalf -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} conicalP_mhalf (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_mhalf (@@dots{}) These routines compute the regular Spherical Conical Function P^@@{-1/2@@}_@@{-1/2 + i \\lambda@@}(x) for x > -1. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn conicalP_0 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} conicalP_0 (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_0 (@@dots{}) These routines compute the conical function P^0_@@{-1/2 + i \\lambda@@}(x) for x > -1. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn conicalP_1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} conicalP_1 (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_1 (@@dots{}) These routines compute the conical function P^1_@@{-1/2 + i \\lambda@@}(x) for x > -1. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hzeta -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} hzeta (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} hzeta (@@dots{}) These routines compute the Hurwitz zeta function \\zeta(s,q) for s > 1, q > 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Ai -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai (@@dots{}) These routines compute the Airy function Ai(x) with an accuracy specified by mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Bi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi (@@dots{}) These routines compute the Airy function Bi(x) with an accuracy specified by mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Ai_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai_scaled (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai_scaled (@@dots{}) These routines compute a scaled version of the Airy function S_A(x) Ai(x). For x>0 the scaling factor S_A(x) is \\exp(+(2/3) x^(3/2)), and is 1 for x<0. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Bi_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi_scaled (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi_scaled (@@dots{}) These routines compute a scaled version of the Airy function S_B(x) Bi(x). For x>0 the scaling factor S_B(x) is exp(-(2/3) x^(3/2)), and is 1 for x<0. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Ai_deriv -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai_deriv (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai_deriv (@@dots{}) These routines compute the Airy function derivative Ai'(x) with an accuracy specified by mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Bi_deriv -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi_deriv (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi_deriv (@@dots{}) These routines compute the Airy function derivative Bi'(x) with an accuracy specified by mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Ai_deriv_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai_deriv_scaled (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai_deriv_scaled (@@dots{}) These routines compute the derivative of the scaled Airy function S_A(x) Ai(x). The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Bi_deriv_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi_deriv_scaled (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi_deriv_scaled (@@dots{}) These routines compute the derivative of the scaled Airy function S_B(x) Bi(x). The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn ellint_Kcomp -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} ellint_Kcomp (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} ellint_Kcomp (@@dots{}) These routines compute the complete elliptic integral K(k) @@tex \beforedisplay $$ \eqalign{ K(k) &= \int_0^{\pi/2} {dt \over \sqrt{(1 - k^2 \sin^2(t))}} \cr } $$ \afterdisplay @@end tex The notation used here is based on Carlson, @@cite{Numerische Mathematik} 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter @@math{m = k^2}. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn ellint_Ecomp -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} ellint_Ecomp (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} ellint_Ecomp (@@dots{}) These routines compute the complete elliptic integral E(k) to the accuracy specified by the mode variable mode. @@tex \beforedisplay $$ \eqalign{ E(k) &= \int_0^{\pi/2} \sqrt{(1 - k^2 \sin^2(t))} dt \cr } $$ \afterdisplay @@end tex The notation used here is based on Carlson, @@cite{Numerische Mathematik} 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter @@math{m = k^2}. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_zero_Ai -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Ai (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Ai (@@dots{}) These routines compute the location of the s-th zero of the Airy function Ai(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_zero_Bi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Bi (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Bi (@@dots{}) These routines compute the location of the s-th zero of the Airy function Bi(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_zero_Ai_deriv -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Ai_deriv (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Ai_deriv (@@dots{}) These routines compute the location of the s-th zero of the Airy function derivative Ai(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_zero_Bi_deriv -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Bi_deriv (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Bi_deriv (@@dots{}) These routines compute the location of the s-th zero of the Airy function derivative Bi(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_zero_J0 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_zero_J0 (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_zero_J0 (@@dots{}) These routines compute the location of the s-th positive zero of the Bessel function J_0(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_zero_J1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_zero_J1 (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_zero_J1 (@@dots{}) These routines compute the location of the s-th positive zero of the Bessel function J_1(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn psi_1_int -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} psi_1_int (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi_1_int (@@dots{}) These routines compute the Trigamma function \\psi(n) for positive integer n. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn zeta_int -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} zeta_int (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} zeta_int (@@dots{}) These routines compute the Riemann zeta function \\zeta(n) for integer n, n \ e 1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn eta_int -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} eta_int (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} eta_int (@@dots{}) These routines compute the eta function \\eta(n) for integer n. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn legendre_Plm -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} legendre_Plm (@@var{n}, @@var{m}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_Plm (@@dots{}) These routines compute the associated Legendre polynomial P_l^m(x) for m >= 0, l >= m, |x| <= 1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn legendre_sphPlm -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} legendre_sphPlm (@@var{n}, @@var{m}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_sphPlm (@@dots{}) These routines compute the normalized associated Legendre polynomial $\\sqrt@@{(2l+1)/(4\\pi)@@} \\sqrt@@{(l-m)!/(l+m)!@@} P_l^m(x)$ suitable for use in spherical harmonics. The parameters must satisfy m >= 0, l >= m, |x| <= 1. Theses routines avoid the overflows that occur for the standard normalization of P_l^m(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hyperg_U -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{out} =} hyperg_U (@@var{x0}, @@var{x1}, @@var{x2}) @@deftypefnx {Loadable Function} {[@@var{out}, @@var{err}] =} hyperg_U (@@dots{}) Secondary Confluent Hypergoemetric U function A&E 13.1.3 All input are double as is the output. @@var{err} contains an estimate of the absolute error in the value @@var{out}.a. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hyperg_1F1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{out} =} hyperg_1F1 (@@var{x0}, @@var{x1}, @@var{x2}) @@deftypefnx {Loadable Function} {[@@var{out}, @@var{err}] =} hyperg_1F1 (@@dots{}) Primary Confluent Hypergoemetric U function A&E 13.1.3 All inputs are double as is the output. @@var{err} contains an estimate of the absolute error in the value @@var{out}.a. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn @@bye@ gsl-1.0.8/doc/RCS/make.lst,v0000644000175000017500000011364411201030376013214 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @# @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @GNU Make 3.81 Copyright (C) 2006 Free Software Foundation, Inc. This is free software; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. This program built for i386-redhat-linux-gnu Reading makefiles... Reading makefile `Makefile'... Reading makefile `../../../Makeconf' (search path) (don't care) (no ~ expansion)... Updating makefiles.... Considering target file `../../../Makeconf'. Looking for an implicit rule for `../../../Makeconf'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.o'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.c'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.cc'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.C'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.cpp'. Trying pattern rule with stem `Makeconf'. 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Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.C'. Looking for a rule with intermediate file `../../../Makeconf.C'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makeconf.C'. Trying implicit prerequisite `../../../Makeconf.C,v'. Trying pattern rule with stem `Makeconf.C'. Trying implicit prerequisite `../../../RCS/Makeconf.C,v'. Trying pattern rule with stem `Makeconf.C'. Trying implicit prerequisite `../../../RCS/Makeconf.C'. Trying pattern rule with stem `Makeconf.C'. Trying implicit prerequisite `../../../s.Makeconf.C'. Trying pattern rule with stem `Makeconf.C'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.C'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.cpp'. Looking for a rule with intermediate file `../../../Makeconf.cpp'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. 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Trying implicit prerequisite `../../../RCS/Makeconf.p,v'. Trying pattern rule with stem `Makeconf.p'. Trying implicit prerequisite `../../../RCS/Makeconf.p'. Trying pattern rule with stem `Makeconf.p'. Trying implicit prerequisite `../../../s.Makeconf.p'. Trying pattern rule with stem `Makeconf.p'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.p'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.web'. Looking for a rule with intermediate file `../../../Makeconf.web'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makeconf.web'. Trying implicit prerequisite `../../../Makeconf.web,v'. Trying pattern rule with stem `Makeconf.web'. Trying implicit prerequisite `../../../RCS/Makeconf.web,v'. Trying pattern rule with stem `Makeconf.web'. Trying implicit prerequisite `../../../RCS/Makeconf.web'. Trying pattern rule with stem `Makeconf.web'. Trying implicit prerequisite `../../../s.Makeconf.web'. Trying pattern rule with stem `Makeconf.web'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.web'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.F'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.r'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.s'. Looking for a rule with intermediate file `../../../Makeconf.s'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.S'. Trying pattern rule with stem `Makeconf.s'. Trying implicit prerequisite `../../../Makeconf.s,v'. Trying pattern rule with stem `Makeconf.s'. Trying implicit prerequisite `../../../RCS/Makeconf.s,v'. Trying pattern rule with stem `Makeconf.s'. Trying implicit prerequisite `../../../RCS/Makeconf.s'. Trying pattern rule with stem `Makeconf.s'. Trying implicit prerequisite `../../../s.Makeconf.s'. Trying pattern rule with stem `Makeconf.s'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.s'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.S'. Looking for a rule with intermediate file `../../../Makeconf.S'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makeconf.S'. Trying implicit prerequisite `../../../Makeconf.S,v'. Trying pattern rule with stem `Makeconf.S'. Trying implicit prerequisite `../../../RCS/Makeconf.S,v'. Trying pattern rule with stem `Makeconf.S'. Trying implicit prerequisite `../../../RCS/Makeconf.S'. Trying pattern rule with stem `Makeconf.S'. Trying implicit prerequisite `../../../s.Makeconf.S'. Trying pattern rule with stem `Makeconf.S'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.S'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.S'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.mod'. Looking for a rule with intermediate file `../../../Makeconf.mod'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makeconf.mod'. Trying implicit prerequisite `../../../Makeconf.mod,v'. Trying pattern rule with stem `Makeconf.mod'. Trying implicit prerequisite `../../../RCS/Makeconf.mod,v'. Trying pattern rule with stem `Makeconf.mod'. Trying implicit prerequisite `../../../RCS/Makeconf.mod'. Trying pattern rule with stem `Makeconf.mod'. Trying implicit prerequisite `../../../s.Makeconf.mod'. Trying pattern rule with stem `Makeconf.mod'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.mod'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.c'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.cc'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.C'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.cpp'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.p'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.f'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.F'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.r'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.s'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.S'. Trying pattern rule with stem `Makeconf'. Rejecting impossible implicit prerequisite `../../../Makeconf.mod'. Trying pattern rule with stem `Makeconf'. Trying implicit prerequisite `../../../Makeconf.sh'. Looking for a rule with intermediate file `../../../Makeconf.sh'. Avoiding implicit rule recursion. Trying pattern rule with stem `Makeconf.sh'. Trying implicit prerequisite `../../../Makeconf.sh,v'. Trying pattern rule with stem `Makeconf.sh'. Trying implicit prerequisite `../../../RCS/Makeconf.sh,v'. Trying pattern rule with stem `Makeconf.sh'. Trying implicit prerequisite `../../../RCS/Makeconf.sh'. Trying pattern rule with stem `Makeconf.sh'. Trying implicit prerequisite `../../../s.Makeconf.sh'. Trying pattern rule with stem `Makeconf.sh'. Trying implicit prerequisite `../../../SCCS/s.Makeconf.sh'. No implicit rule found for `../../../Makeconf'. Finished prerequisites of target file `../../../Makeconf'. No need to remake target `../../../Makeconf'. Considering target file `Makefile'. Looking for an implicit rule for `Makefile'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.o'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.c'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.cc'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.C'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.cpp'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.p'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.f'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.F'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.r'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.s'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.S'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.mod'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.sh'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile,v'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `RCS/Makefile,v'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `RCS/Makefile'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `s.Makefile'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `SCCS/s.Makefile'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.o'. Looking for a rule with intermediate file `Makefile.o'. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.c'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.f'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.cc'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.C'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.cpp'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.p'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.F'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.r'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.s'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.S'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.mod'. Trying pattern rule with stem `Makefile.o'. Trying implicit prerequisite `Makefile.o,v'. Trying pattern rule with stem `Makefile.o'. Trying implicit prerequisite `RCS/Makefile.o,v'. Trying pattern rule with stem `Makefile.o'. Trying implicit prerequisite `RCS/Makefile.o'. Trying pattern rule with stem `Makefile.o'. Trying implicit prerequisite `s.Makefile.o'. Trying pattern rule with stem `Makefile.o'. Trying implicit prerequisite `SCCS/s.Makefile.o'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.c'. Looking for a rule with intermediate file `Makefile.c'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.y'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.l'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.w'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.w'. Trying pattern rule with stem `Makefile.c'. Trying implicit prerequisite `Makefile.c,v'. Trying pattern rule with stem `Makefile.c'. Trying implicit prerequisite `RCS/Makefile.c,v'. Trying pattern rule with stem `Makefile.c'. Trying implicit prerequisite `RCS/Makefile.c'. Trying pattern rule with stem `Makefile.c'. Trying implicit prerequisite `s.Makefile.c'. Trying pattern rule with stem `Makefile.c'. Trying implicit prerequisite `SCCS/s.Makefile.c'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.y'. Looking for a rule with intermediate file `Makefile.y'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.y'. Trying implicit prerequisite `Makefile.y,v'. Trying pattern rule with stem `Makefile.y'. Trying implicit prerequisite `RCS/Makefile.y,v'. Trying pattern rule with stem `Makefile.y'. Trying implicit prerequisite `RCS/Makefile.y'. Trying pattern rule with stem `Makefile.y'. Trying implicit prerequisite `s.Makefile.y'. Trying pattern rule with stem `Makefile.y'. Trying implicit prerequisite `SCCS/s.Makefile.y'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.l'. Looking for a rule with intermediate file `Makefile.l'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.l'. Trying implicit prerequisite `Makefile.l,v'. Trying pattern rule with stem `Makefile.l'. Trying implicit prerequisite `RCS/Makefile.l,v'. Trying pattern rule with stem `Makefile.l'. Trying implicit prerequisite `RCS/Makefile.l'. Trying pattern rule with stem `Makefile.l'. Trying implicit prerequisite `s.Makefile.l'. Trying pattern rule with stem `Makefile.l'. Trying implicit prerequisite `SCCS/s.Makefile.l'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.w'. Looking for a rule with intermediate file `Makefile.w'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.w'. Trying implicit prerequisite `Makefile.w,v'. Trying pattern rule with stem `Makefile.w'. Trying implicit prerequisite `RCS/Makefile.w,v'. Trying pattern rule with stem `Makefile.w'. Trying implicit prerequisite `RCS/Makefile.w'. Trying pattern rule with stem `Makefile.w'. Trying implicit prerequisite `s.Makefile.w'. Trying pattern rule with stem `Makefile.w'. Trying implicit prerequisite `SCCS/s.Makefile.w'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.w'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.f'. Looking for a rule with intermediate file `Makefile.f'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.F'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.r'. Trying pattern rule with stem `Makefile.f'. Trying implicit prerequisite `Makefile.f,v'. Trying pattern rule with stem `Makefile.f'. Trying implicit prerequisite `RCS/Makefile.f,v'. Trying pattern rule with stem `Makefile.f'. Trying implicit prerequisite `RCS/Makefile.f'. Trying pattern rule with stem `Makefile.f'. Trying implicit prerequisite `s.Makefile.f'. Trying pattern rule with stem `Makefile.f'. Trying implicit prerequisite `SCCS/s.Makefile.f'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.F'. Looking for a rule with intermediate file `Makefile.F'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.F'. Trying implicit prerequisite `Makefile.F,v'. Trying pattern rule with stem `Makefile.F'. Trying implicit prerequisite `RCS/Makefile.F,v'. Trying pattern rule with stem `Makefile.F'. Trying implicit prerequisite `RCS/Makefile.F'. Trying pattern rule with stem `Makefile.F'. Trying implicit prerequisite `s.Makefile.F'. Trying pattern rule with stem `Makefile.F'. Trying implicit prerequisite `SCCS/s.Makefile.F'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.r'. Looking for a rule with intermediate file `Makefile.r'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.l'. Trying pattern rule with stem `Makefile.r'. Trying implicit prerequisite `Makefile.r,v'. Trying pattern rule with stem `Makefile.r'. Trying implicit prerequisite `RCS/Makefile.r,v'. Trying pattern rule with stem `Makefile.r'. Trying implicit prerequisite `RCS/Makefile.r'. Trying pattern rule with stem `Makefile.r'. Trying implicit prerequisite `s.Makefile.r'. Trying pattern rule with stem `Makefile.r'. Trying implicit prerequisite `SCCS/s.Makefile.r'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.cc'. Looking for a rule with intermediate file `Makefile.cc'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.cc'. Trying implicit prerequisite `Makefile.cc,v'. Trying pattern rule with stem `Makefile.cc'. Trying implicit prerequisite `RCS/Makefile.cc,v'. Trying pattern rule with stem `Makefile.cc'. Trying implicit prerequisite `RCS/Makefile.cc'. Trying pattern rule with stem `Makefile.cc'. Trying implicit prerequisite `s.Makefile.cc'. Trying pattern rule with stem `Makefile.cc'. Trying implicit prerequisite `SCCS/s.Makefile.cc'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.C'. Looking for a rule with intermediate file `Makefile.C'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.C'. Trying implicit prerequisite `Makefile.C,v'. Trying pattern rule with stem `Makefile.C'. Trying implicit prerequisite `RCS/Makefile.C,v'. Trying pattern rule with stem `Makefile.C'. Trying implicit prerequisite `RCS/Makefile.C'. Trying pattern rule with stem `Makefile.C'. Trying implicit prerequisite `s.Makefile.C'. Trying pattern rule with stem `Makefile.C'. Trying implicit prerequisite `SCCS/s.Makefile.C'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.cpp'. Looking for a rule with intermediate file `Makefile.cpp'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.cpp'. Trying implicit prerequisite `Makefile.cpp,v'. Trying pattern rule with stem `Makefile.cpp'. Trying implicit prerequisite `RCS/Makefile.cpp,v'. Trying pattern rule with stem `Makefile.cpp'. Trying implicit prerequisite `RCS/Makefile.cpp'. Trying pattern rule with stem `Makefile.cpp'. Trying implicit prerequisite `s.Makefile.cpp'. Trying pattern rule with stem `Makefile.cpp'. Trying implicit prerequisite `SCCS/s.Makefile.cpp'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.p'. Looking for a rule with intermediate file `Makefile.p'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.web'. Trying pattern rule with stem `Makefile.p'. Trying implicit prerequisite `Makefile.p,v'. Trying pattern rule with stem `Makefile.p'. Trying implicit prerequisite `RCS/Makefile.p,v'. Trying pattern rule with stem `Makefile.p'. Trying implicit prerequisite `RCS/Makefile.p'. Trying pattern rule with stem `Makefile.p'. Trying implicit prerequisite `s.Makefile.p'. Trying pattern rule with stem `Makefile.p'. Trying implicit prerequisite `SCCS/s.Makefile.p'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.web'. Looking for a rule with intermediate file `Makefile.web'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.web'. Trying implicit prerequisite `Makefile.web,v'. Trying pattern rule with stem `Makefile.web'. Trying implicit prerequisite `RCS/Makefile.web,v'. Trying pattern rule with stem `Makefile.web'. Trying implicit prerequisite `RCS/Makefile.web'. Trying pattern rule with stem `Makefile.web'. Trying implicit prerequisite `s.Makefile.web'. Trying pattern rule with stem `Makefile.web'. Trying implicit prerequisite `SCCS/s.Makefile.web'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.F'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.r'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.s'. Looking for a rule with intermediate file `Makefile.s'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.S'. Trying pattern rule with stem `Makefile.s'. Trying implicit prerequisite `Makefile.s,v'. Trying pattern rule with stem `Makefile.s'. Trying implicit prerequisite `RCS/Makefile.s,v'. Trying pattern rule with stem `Makefile.s'. Trying implicit prerequisite `RCS/Makefile.s'. Trying pattern rule with stem `Makefile.s'. Trying implicit prerequisite `s.Makefile.s'. Trying pattern rule with stem `Makefile.s'. Trying implicit prerequisite `SCCS/s.Makefile.s'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.S'. Looking for a rule with intermediate file `Makefile.S'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.S'. Trying implicit prerequisite `Makefile.S,v'. Trying pattern rule with stem `Makefile.S'. Trying implicit prerequisite `RCS/Makefile.S,v'. Trying pattern rule with stem `Makefile.S'. Trying implicit prerequisite `RCS/Makefile.S'. Trying pattern rule with stem `Makefile.S'. Trying implicit prerequisite `s.Makefile.S'. Trying pattern rule with stem `Makefile.S'. Trying implicit prerequisite `SCCS/s.Makefile.S'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.S'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.mod'. Looking for a rule with intermediate file `Makefile.mod'. Avoiding implicit rule recursion. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.mod'. Trying implicit prerequisite `Makefile.mod,v'. Trying pattern rule with stem `Makefile.mod'. Trying implicit prerequisite `RCS/Makefile.mod,v'. Trying pattern rule with stem `Makefile.mod'. Trying implicit prerequisite `RCS/Makefile.mod'. Trying pattern rule with stem `Makefile.mod'. Trying implicit prerequisite `s.Makefile.mod'. Trying pattern rule with stem `Makefile.mod'. Trying implicit prerequisite `SCCS/s.Makefile.mod'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.c'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.cc'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.C'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.cpp'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.p'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.f'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.F'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.r'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.s'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.S'. Trying pattern rule with stem `Makefile'. Rejecting impossible implicit prerequisite `Makefile.mod'. Trying pattern rule with stem `Makefile'. Trying implicit prerequisite `Makefile.sh'. Looking for a rule with intermediate file `Makefile.sh'. Avoiding implicit rule recursion. Trying pattern rule with stem `Makefile.sh'. Trying implicit prerequisite `Makefile.sh,v'. Trying pattern rule with stem `Makefile.sh'. Trying implicit prerequisite `RCS/Makefile.sh,v'. Trying pattern rule with stem `Makefile.sh'. Trying implicit prerequisite `RCS/Makefile.sh'. Trying pattern rule with stem `Makefile.sh'. Trying implicit prerequisite `s.Makefile.sh'. Trying pattern rule with stem `Makefile.sh'. Trying implicit prerequisite `SCCS/s.Makefile.sh'. No implicit rule found for `Makefile'. Finished prerequisites of target file `Makefile'. No need to remake target `Makefile'. Updating goal targets.... Considering target file `../src/gsl_sf.cc'. Looking for an implicit rule for `../src/gsl_sf.cc'. Trying pattern rule with stem `gsl_sf.cc'. Trying implicit prerequisite `../src/gsl_sf.cc,v'. Trying pattern rule with stem `gsl_sf.cc'. Trying implicit prerequisite `../src/RCS/gsl_sf.cc,v'. Trying pattern rule with stem `gsl_sf.cc'. Trying implicit prerequisite `../src/RCS/gsl_sf.cc'. Trying pattern rule with stem `gsl_sf.cc'. Trying implicit prerequisite `../src/s.gsl_sf.cc'. Trying pattern rule with stem `gsl_sf.cc'. Trying implicit prerequisite `../src/SCCS/s.gsl_sf.cc'. No implicit rule found for `../src/gsl_sf.cc'. Finished prerequisites of target file `../src/gsl_sf.cc'. No need to remake target `../src/gsl_sf.cc'. make: Nothing to be done for `../src/gsl_sf.cc'. @ gsl-1.0.8/doc/RCS/gsl.doc,v0000644000175000017500000036415111201030376013030 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @# @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @gsl_sf -*- texinfo -*- @@deftypefn {Loadable Function} {} gsl_sf () Octave bindings to the GNU Scientific Library. All GSL functions can be called with by the GSL names within octave. @@end deftypefn clausen -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} clausen (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} clausen (@@dots{}) The Clausen function is defined by the following integral, Cl_2(x) = - \\int_0^x dt \\log(2 \\sin(t/2)) It is related to the dilogarithm by Cl_2(\\theta) = \\Im Li_2(\\exp(i \\theta)). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn dawson -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} dawson (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} dawson (@@dots{}) The Dawson integral is defined by \\exp(-x^2) \\int_0^x dt \\exp(t^2). A table of Dawson integral can be found in Abramowitz & Stegun, Table 7.5. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn debye_1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} debye_1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_1 (@@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn debye_2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} debye_2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_2 (@@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn debye_3 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} debye_3 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_3 (@@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn debye_4 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} debye_4 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_4 (@@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn erf_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} erf_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erf_gsl (@@dots{}) These routines compute the error function erf(x) = (2/\\sqrt(\\pi)) \\int_0^x dt \\exp(-t^2). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn erfc_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} erfc_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erfc_gsl (@@dots{}) These routines compute the complementary error function erfc(x) = 1 - erf(x) = (2/\\sqrt(\\pi)) \\int_x^\\infty \\exp(-t^2). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn log_erfc -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} log_erfc (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} log_erfc (@@dots{}) These routines compute the logarithm of the complementary error function \\log(\\erfc(x)). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn erf_Z -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} erf_Z (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erf_Z (@@dots{}) These routines compute the Gaussian probability function Z(x) = (1/(2\\pi)) \\exp(-x^2/2). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn erf_Q -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} erf_Q (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erf_Q (@@dots{}) These routines compute the upper tail of the Gaussian probability function Q(x) = (1/(2\\pi)) \\int_x^\\infty dt \\exp(-t^2/2). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hazard -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} hazard (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} hazard (@@dots{}) The hazard function for the normal distrbution, also known as the inverse Mill\\'s ratio, is defined as h(x) = Z(x)/Q(x) = \\sqrt@@{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2)@@}. It decreases rapidly as x approaches -\\infty and asymptotes to h(x) \\sim x as x approaches +\\infty. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expm1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expm1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expm1 (@@dots{}) These routines compute the quantity \\exp(x)-1 using an algorithm that is accurate for small x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn exprel -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} exprel (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} exprel (@@dots{}) These routines compute the quantity (\\exp(x)-1)/x using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion (\\exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\dots. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn exprel_2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} exprel_2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} exprel_2 (@@dots{}) These routines compute the quantity 2(\\exp(x)-1-x)/x^2 using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion 2(\\exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\dots. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expint_E1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expint_E1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_E1 (@@dots{}) These routines compute the exponential integral E_1(x), E_1(x) := Re \\int_1^\\infty dt \\exp(-xt)/t. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expint_E2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expint_E2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_E2 (@@dots{}) These routines compute the second-order exponential integral E_2(x), E_2(x) := \\Re \\int_1^\\infty dt \\exp(-xt)/t^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expint_Ei -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expint_Ei (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_Ei (@@dots{}) These routines compute the exponential integral E_i(x), Ei(x) := - PV(\\int_@@{-x@@}^\\infty dt \\exp(-t)/t) where PV denotes the principal value of the integral. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn Shi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} Shi (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Shi (@@dots{}) These routines compute the integral Shi(x) = \\int_0^x dt \\sinh(t)/t. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn Chi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} Chi (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Chi (@@dots{}) These routines compute the integral Chi(x) := Re[ \\gamma_E + \\log(x) + \\int_0^x dt (\\cosh[t]-1)/t] , where \\gamma_E is the Euler constant. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expint_3 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expint_3 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_3 (@@dots{}) These routines compute the exponential integral Ei_3(x) = \\int_0^x dt \\exp(-t^3) for x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn Si -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} Si (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Si (@@dots{}) These routines compute the Sine integral Si(x) = \\int_0^x dt \\sin(t)/t. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn Ci -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} Ci (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Ci (@@dots{}) These routines compute the Cosine integral Ci(x) = -\\int_x^\\infty dt \\cos(t)/t for x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn atanint -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} atanint (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} atanint (@@dots{}) These routines compute the Arctangent integral AtanInt(x) = \\int_0^x dt \\arctan(t)/t. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_mhalf -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_mhalf (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_mhalf (@@dots{}) These routines compute the complete Fermi-Dirac integral F_@@{-1/2@@}(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_half -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_half (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_half (@@dots{}) These routines compute the complete Fermi-Dirac integral F_@@{1/2@@}(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_3half -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_3half (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_3half (@@dots{}) These routines compute the complete Fermi-Dirac integral F_@@{3/2@@}(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gamma_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} gamma_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} gamma_gsl (@@dots{}) These routines compute the Gamma function \\Gamma(x), subject to x not being a negative integer. The function is computed using the real Lanczos method. The maximum value of x such that \\Gamma(x) is not considered an overflow is given by the macro GSL_SF_GAMMA_XMAX and is 171.0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lngamma_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lngamma_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lngamma_gsl (@@dots{}) These routines compute the logarithm of the Gamma function, \\log(\\Gamma(x)), subject to x not a being negative integer. For x<0 the real part of \\log(\\Gamma(x)) is returned, which is equivalent to \\log(|\\Gamma(x)|). The function is computed using the real Lanczos method. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gammastar -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} gammastar (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} gammastar (@@dots{}) These routines compute the regulated Gamma Function \\Gamma^*(x) for x > 0. The regulated gamma function is given by, \\Gamma^*(x) = \\Gamma(x)/(\\sqrt@@{2\\pi@@} x^@@{(x-1/2)@@} \\exp(-x)) = (1 + (1/12x) + ...) for x \\to \\infty and is a useful suggestion of Temme. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gammainv_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} gammainv_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} gammainv_gsl (@@dots{}) These routines compute the reciprocal of the gamma function, 1/\\Gamma(x) using the real Lanczos method. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lambert_W0 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lambert_W0 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lambert_W0 (@@dots{}) These compute the principal branch of the Lambert W function, W_0(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@@{-1@@}(x) to be the other real branch, where W < -1 for x < 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lambert_Wm1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lambert_Wm1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lambert_Wm1 (@@dots{}) These compute the secondary real-valued branch of the Lambert W function, W_@@{-1@@}(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@@{-1@@}(x) to be the other real branch, where W < -1 for x < 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn log_1plusx -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} log_1plusx (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} log_1plusx (@@dots{}) These routines compute \\log(1 + x) for x > -1 using an algorithm that is accurate for small x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn log_1plusx_mx -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} log_1plusx_mx (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} log_1plusx_mx (@@dots{}) These routines compute \\log(1 + x) - x for x > -1 using an algorithm that is accurate for small x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn psi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} psi (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi (@@dots{}) These routines compute the digamma function \\psi(x) for general x, x \ e 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn psi_1piy -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} psi_1piy (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi_1piy (@@dots{}) These routines compute the real part of the digamma function on the line 1+i y, Re[\\psi(1 + i y)]. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn synchrotron_1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} synchrotron_1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} synchrotron_1 (@@dots{}) These routines compute the first synchrotron function x \\int_x^\\infty dt K_@@{5/3@@}(t) for x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn synchrotron_2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} synchrotron_2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} synchrotron_2 (@@dots{}) These routines compute the second synchrotron function x K_@@{2/3@@}(x) for x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn transport_2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} transport_2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_2 (@@dots{}) These routines compute the transport function J(2,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn transport_3 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} transport_3 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_3 (@@dots{}) These routines compute the transport function J(3,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn transport_4 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} transport_4 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_4 (@@dots{}) These routines compute the transport function J(4,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn transport_5 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} transport_5 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_5 (@@dots{}) These routines compute the transport function J(5,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn sinc_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} sinc_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} sinc_gsl (@@dots{}) These routines compute \\sinc(x) = \\sin(\\pi x) / (\\pi x) for any value of x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lnsinh -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lnsinh (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lnsinh (@@dots{}) These routines compute \\log(\\sinh(x)) for x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lncosh -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lncosh (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lncosh (@@dots{}) These routines compute \\log(\\cosh(x)) for any x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn zeta -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} zeta (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} zeta (@@dots{}) These routines compute the Riemann zeta function \\zeta(s) for arbitrary s, s \ e 1. The Riemann zeta function is defined by the infinite sum \\zeta(s) = \\sum_@@{k=1@@}^\\infty k^@@{-s@@}. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn eta -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} eta (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} eta (@@dots{}) These routines compute the eta function \\eta(s) for arbitrary s. The eta function is defined by \\eta(s) = (1-2^@@{1-s@@}) \\zeta(s). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Jn -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_Jn (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Jn (@@dots{}) These routines compute the regular cylindrical Bessel function of order n, J_n(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Yn -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_Yn (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Yn (@@dots{}) These routines compute the irregular cylindrical Bessel function of order n, Y_n(x), for x>0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_In -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_In (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_In (@@dots{}) These routines compute the regular modified cylindrical Bessel function of order n, I_n(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_In_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_In_scaled (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_In_scaled (@@dots{}) These routines compute the scaled regular modified cylindrical Bessel function of order n, \\exp(-|x|) I_n(x) @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Kn -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_Kn (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Kn (@@dots{}) These routines compute the irregular modified cylindrical Bessel function of order n, K_n(x), for x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Kn_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_Kn_scaled (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Kn_scaled (@@dots{}) @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_jl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_jl (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_jl (@@dots{}) These routines compute the regular spherical Bessel function of order l, j_l(x), for l >= 0 and x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_yl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_yl (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_yl (@@dots{}) These routines compute the irregular spherical Bessel function of order l, y_l(x), for l >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_il_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_il_scaled (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_il_scaled (@@dots{}) These routines compute the scaled regular modified spherical Bessel function of order l, \\exp(-|x|) i_l(x) @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_kl_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_kl_scaled (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_kl_scaled (@@dots{}) These routines compute the scaled irregular modified spherical Bessel function of order l, \\exp(x) k_l(x), for x>0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn exprel_n -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} exprel_n (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} exprel_n (@@dots{}) These routines compute the N-relative exponential, which is the n-th generalization of the functions gsl_sf_exprel and gsl_sf_exprel2. The N-relative exponential is given by, exprel_N(x) = N!/x^N (\\exp(x) - \\sum_@@{k=0@@}^@@{N-1@@} x^k/k!) = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ... = 1F1 (1,1+N,x) @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_int -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_int (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_int (@@dots{}) These routines compute the complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/\\Gamma(j+1)) \\int_0^\\infty dt (t^j /(\\exp(t-x)+1)). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn taylorcoeff -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} taylorcoeff (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} taylorcoeff (@@dots{}) These routines compute the Taylor coefficient x^n / n! for x >= 0, n >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn legendre_Pl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} legendre_Pl (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_Pl (@@dots{}) These functions evaluate the Legendre polynomial P_l(x) for a specific value of l, x subject to l >= 0, |x| <= 1 @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn legendre_Ql -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} legendre_Ql (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_Ql (@@dots{}) These routines compute the Legendre function Q_l(x) for x > -1, x != 1 and l >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn psi_n -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} psi_n (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi_n (@@dots{}) These routines compute the polygamma function \\psi^@@{(m)@@}(x) for m >= 0, x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Jnu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Jnu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Jnu (@@dots{}) These routines compute the regular cylindrical Bessel function of fractional order nu, J_\ u(x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Ynu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Ynu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Ynu (@@dots{}) These routines compute the irregular cylindrical Bessel function of fractional order nu, Y_\ u(x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Inu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Inu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Inu (@@dots{}) These routines compute the regular modified Bessel function of fractional order nu, I_\ u(x) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Inu_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Inu_scaled (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Inu_scaled (@@dots{}) These routines compute the scaled regular modified Bessel function of fractional order nu, \\exp(-|x|)I_\ u(x) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Knu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Knu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Knu (@@dots{}) These routines compute the irregular modified Bessel function of fractional order nu, K_\ u(x) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_lnKnu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_lnKnu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_lnKnu (@@dots{}) These routines compute the logarithm of the irregular modified Bessel function of fractional order nu, \\ln(K_\ u(x)) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Knu_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Knu_scaled (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Knu_scaled (@@dots{}) These routines compute the scaled irregular modified Bessel function of fractional order nu, \\exp(+|x|) K_\ u(x) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn exp_mult -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} exp_mult (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} exp_mult (@@dots{}) These routines exponentiate x and multiply by the factor y to return the product y \\exp(x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_inc_0 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} fermi_dirac_inc_0 (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} fermi_dirac_inc_0 (@@dots{}) These routines compute the incomplete Fermi-Dirac integral with an index of zero, F_0(x,b) = \\ln(1 + e^@@{b-x@@}) - (b-x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn poch -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} poch (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} poch (@@dots{}) These routines compute the Pochhammer symbol (a)_x := \\Gamma(a + x)/\\Gamma(a), subject to a and a+x not being negative integers. The Pochhammer symbol is also known as the Apell symbol. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lnpoch -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} lnpoch (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} lnpoch (@@dots{}) These routines compute the logarithm of the Pochhammer symbol, \\log((a)_x) = \\log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn pochrel -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} pochrel (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} pochrel (@@dots{}) These routines compute the relative Pochhammer symbol ((a,x) - 1)/x where (a,x) = (a)_x := \\Gamma(a + x)/\\Gamma(a). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gamma_inc_Q -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} gamma_inc_Q (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} gamma_inc_Q (@@dots{}) These routines compute the normalized incomplete Gamma Function Q(a,x) = 1/\\Gamma(a) \\int_x\\infty dt t^@@{a-1@@} \\exp(-t) for a > 0, x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gamma_inc_P -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} gamma_inc_P (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} gamma_inc_P (@@dots{}) These routines compute the complementary normalized incomplete Gamma Function P(a,x) = 1/\\Gamma(a) \\int_0^x dt t^@@{a-1@@} \\exp(-t) for a > 0, x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gamma_inc -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} gamma_inc (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} gamma_inc (@@dots{}) These functions compute the incomplete Gamma Function the normalization factor included in the previously defined functions: \\Gamma(a,x) = \\int_x\\infty dt t^@@{a-1@@} \\exp(-t) for a real and x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn beta_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} beta_gsl (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} beta_gsl (@@dots{}) These routines compute the Beta Function, B(a,b) = \\Gamma(a)\\Gamma(b)/\\Gamma(a+b) for a > 0, b > 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lnbeta -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} lnbeta (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} lnbeta (@@dots{}) These routines compute the logarithm of the Beta Function, \\log(B(a,b)) for a > 0, b > 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hyperg_0F1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} hyperg_0F1 (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} hyperg_0F1 (@@dots{}) These routines compute the hypergeometric function 0F1(c,x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn conicalP_half -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} conicalP_half (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_half (@@dots{}) These routines compute the irregular Spherical Conical Function P^@@{1/2@@}_@@{-1/2 + i \\lambda@@}(x) for x > -1. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn conicalP_mhalf -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} conicalP_mhalf (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_mhalf (@@dots{}) These routines compute the regular Spherical Conical Function P^@@{-1/2@@}_@@{-1/2 + i \\lambda@@}(x) for x > -1. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn conicalP_0 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} conicalP_0 (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_0 (@@dots{}) These routines compute the conical function P^0_@@{-1/2 + i \\lambda@@}(x) for x > -1. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn conicalP_1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} conicalP_1 (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_1 (@@dots{}) These routines compute the conical function P^1_@@{-1/2 + i \\lambda@@}(x) for x > -1. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hzeta -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} hzeta (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} hzeta (@@dots{}) These routines compute the Hurwitz zeta function \\zeta(s,q) for s > 1, q > 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Ai -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai (@@dots{}) These routines compute the Airy function Ai(x) with an accuracy specified by mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Bi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi (@@dots{}) These routines compute the Airy function Bi(x) with an accuracy specified by mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Ai_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai_scaled (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai_scaled (@@dots{}) These routines compute a scaled version of the Airy function S_A(x) Ai(x). For x>0 the scaling factor S_A(x) is \\exp(+(2/3) x^(3/2)), and is 1 for x<0. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Bi_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi_scaled (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi_scaled (@@dots{}) These routines compute a scaled version of the Airy function S_B(x) Bi(x). For x>0 the scaling factor S_B(x) is exp(-(2/3) x^(3/2)), and is 1 for x<0. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Ai_deriv -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai_deriv (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai_deriv (@@dots{}) These routines compute the Airy function derivative Ai'(x) with an accuracy specified by mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Bi_deriv -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi_deriv (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi_deriv (@@dots{}) These routines compute the Airy function derivative Bi'(x) with an accuracy specified by mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Ai_deriv_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai_deriv_scaled (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai_deriv_scaled (@@dots{}) These routines compute the derivative of the scaled Airy function S_A(x) Ai(x). The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Bi_deriv_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi_deriv_scaled (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi_deriv_scaled (@@dots{}) These routines compute the derivative of the scaled Airy function S_B(x) Bi(x). The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn ellint_Kcomp -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} ellint_Kcomp (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} ellint_Kcomp (@@dots{}) These routines compute the complete elliptic integral K(k) @@tex \\beforedisplay $$ \\eqalign{ K(k) &= \\int_0^{\\pi/2} {dt \\over \\sqrt{(1 - k^2 \\sin^2(t))}} \\cr } $$ \\afterdisplay @@end tex The notation used here is based on Carlson, @@cite{Numerische Mathematik} 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter @@math{m = k^2}. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn ellint_Ecomp -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} ellint_Ecomp (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} ellint_Ecomp (@@dots{}) These routines compute the complete elliptic integral E(k) to the accuracy specified by the mode variable mode. @@tex \\beforedisplay $$ \\eqalign{ E(k) &= \\int_0^{\\pi/2} \\sqrt{(1 - k^2 \\sin^2(t))} dt \\cr } $$ \\afterdisplay @@end tex The notation used here is based on Carlson, @@cite{Numerische Mathematik} 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter @@math{m = k^2}. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_zero_Ai -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Ai (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Ai (@@dots{}) These routines compute the location of the s-th zero of the Airy function Ai(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_zero_Bi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Bi (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Bi (@@dots{}) These routines compute the location of the s-th zero of the Airy function Bi(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_zero_Ai_deriv -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Ai_deriv (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Ai_deriv (@@dots{}) These routines compute the location of the s-th zero of the Airy function derivative Ai(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_zero_Bi_deriv -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Bi_deriv (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Bi_deriv (@@dots{}) These routines compute the location of the s-th zero of the Airy function derivative Bi(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_zero_J0 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_zero_J0 (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_zero_J0 (@@dots{}) These routines compute the location of the s-th positive zero of the Bessel function J_0(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_zero_J1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_zero_J1 (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_zero_J1 (@@dots{}) These routines compute the location of the s-th positive zero of the Bessel function J_1(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn psi_1_int -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} psi_1_int (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi_1_int (@@dots{}) These routines compute the Trigamma function \\psi(n) for positive integer n. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn zeta_int -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} zeta_int (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} zeta_int (@@dots{}) These routines compute the Riemann zeta function \\zeta(n) for integer n, n \ e 1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn eta_int -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} eta_int (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} eta_int (@@dots{}) These routines compute the eta function \\eta(n) for integer n. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn legendre_Plm -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} legendre_Plm (@@var{n}, @@var{m}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_Plm (@@dots{}) These routines compute the associated Legendre polynomial P_l^m(x) for m >= 0, l >= m, |x| <= 1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn legendre_sphPlm -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} legendre_sphPlm (@@var{n}, @@var{m}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_sphPlm (@@dots{}) These routines compute the normalized associated Legendre polynomial $\\sqrt@@{(2l+1)/(4\\pi)@@} \\sqrt@@{(l-m)!/(l+m)!@@} P_l^m(x)$ suitable for use in spherical harmonics. The parameters must satisfy m >= 0, l >= m, |x| <= 1. Theses routines avoid the overflows that occur for the standard normalization of P_l^m(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hyperg_U -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{out} =} hyperg_U (@@var{x0}, @@var{x1}, @@var{x2}) @@deftypefnx {Loadable Function} {[@@var{out}, @@var{err}] =} hyperg_U (@@dots{}) Secondary Confluent Hypergoemetric U function A&E 13.1.3 All input are double as is the output. @@var{err} contains an estimate of the absolute error in the value @@var{out}.a. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hyperg_1F1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{out} =} hyperg_1F1 (@@var{x0}, @@var{x1}, @@var{x2}) @@deftypefnx {Loadable Function} {[@@var{out}, @@var{err}] =} hyperg_1F1 (@@dots{}) Primary Confluent Hypergoemetric U function A&E 13.1.3 All inputs are double as is the output. @@var{err} contains an estimate of the absolute error in the value @@var{out}.a. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gsl_sf -*- texinfo -*- @@deftypefn {Loadable Function} {} gsl_sf () Octave bindings to the GNU Scientific Library. All GSL functions can be called with by the GSL names within octave. @@end deftypefn clausen -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} clausen (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} clausen (@@dots{}) The Clausen function is defined by the following integral, Cl_2(x) = - \\int_0^x dt \\log(2 \\sin(t/2)) It is related to the dilogarithm by Cl_2(\\theta) = \\Im Li_2(\\exp(i \\theta)). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn dawson -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} dawson (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} dawson (@@dots{}) The Dawson integral is defined by \\exp(-x^2) \\int_0^x dt \\exp(t^2). A table of Dawson integral can be found in Abramowitz & Stegun, Table 7.5. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn debye_1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} debye_1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_1 (@@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn debye_2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} debye_2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_2 (@@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn debye_3 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} debye_3 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_3 (@@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn debye_4 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} debye_4 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_4 (@@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn erf_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} erf_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erf_gsl (@@dots{}) These routines compute the error function erf(x) = (2/\\sqrt(\\pi)) \\int_0^x dt \\exp(-t^2). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn erfc_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} erfc_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erfc_gsl (@@dots{}) These routines compute the complementary error function erfc(x) = 1 - erf(x) = (2/\\sqrt(\\pi)) \\int_x^\\infty \\exp(-t^2). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn log_erfc -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} log_erfc (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} log_erfc (@@dots{}) These routines compute the logarithm of the complementary error function \\log(\\erfc(x)). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn erf_Z -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} erf_Z (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erf_Z (@@dots{}) These routines compute the Gaussian probability function Z(x) = (1/(2\\pi)) \\exp(-x^2/2). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn erf_Q -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} erf_Q (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erf_Q (@@dots{}) These routines compute the upper tail of the Gaussian probability function Q(x) = (1/(2\\pi)) \\int_x^\\infty dt \\exp(-t^2/2). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hazard -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} hazard (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} hazard (@@dots{}) The hazard function for the normal distrbution, also known as the inverse Mill\\'s ratio, is defined as h(x) = Z(x)/Q(x) = \\sqrt@@{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2)@@}. It decreases rapidly as x approaches -\\infty and asymptotes to h(x) \\sim x as x approaches +\\infty. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expm1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expm1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expm1 (@@dots{}) These routines compute the quantity \\exp(x)-1 using an algorithm that is accurate for small x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn exprel -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} exprel (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} exprel (@@dots{}) These routines compute the quantity (\\exp(x)-1)/x using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion (\\exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\dots. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn exprel_2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} exprel_2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} exprel_2 (@@dots{}) These routines compute the quantity 2(\\exp(x)-1-x)/x^2 using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion 2(\\exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\dots. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expint_E1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expint_E1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_E1 (@@dots{}) These routines compute the exponential integral E_1(x), E_1(x) := Re \\int_1^\\infty dt \\exp(-xt)/t. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expint_E2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expint_E2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_E2 (@@dots{}) These routines compute the second-order exponential integral E_2(x), E_2(x) := \\Re \\int_1^\\infty dt \\exp(-xt)/t^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expint_Ei -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expint_Ei (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_Ei (@@dots{}) These routines compute the exponential integral E_i(x), Ei(x) := - PV(\\int_@@{-x@@}^\\infty dt \\exp(-t)/t) where PV denotes the principal value of the integral. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn Shi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} Shi (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Shi (@@dots{}) These routines compute the integral Shi(x) = \\int_0^x dt \\sinh(t)/t. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn Chi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} Chi (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Chi (@@dots{}) These routines compute the integral Chi(x) := Re[ \\gamma_E + \\log(x) + \\int_0^x dt (\\cosh[t]-1)/t] , where \\gamma_E is the Euler constant. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expint_3 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expint_3 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_3 (@@dots{}) These routines compute the exponential integral Ei_3(x) = \\int_0^x dt \\exp(-t^3) for x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn Si -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} Si (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Si (@@dots{}) These routines compute the Sine integral Si(x) = \\int_0^x dt \\sin(t)/t. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn Ci -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} Ci (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Ci (@@dots{}) These routines compute the Cosine integral Ci(x) = -\\int_x^\\infty dt \\cos(t)/t for x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn atanint -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} atanint (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} atanint (@@dots{}) These routines compute the Arctangent integral AtanInt(x) = \\int_0^x dt \\arctan(t)/t. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_mhalf -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_mhalf (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_mhalf (@@dots{}) These routines compute the complete Fermi-Dirac integral F_@@{-1/2@@}(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_half -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_half (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_half (@@dots{}) These routines compute the complete Fermi-Dirac integral F_@@{1/2@@}(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_3half -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_3half (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_3half (@@dots{}) These routines compute the complete Fermi-Dirac integral F_@@{3/2@@}(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gamma_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} gamma_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} gamma_gsl (@@dots{}) These routines compute the Gamma function \\Gamma(x), subject to x not being a negative integer. The function is computed using the real Lanczos method. The maximum value of x such that \\Gamma(x) is not considered an overflow is given by the macro GSL_SF_GAMMA_XMAX and is 171.0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lngamma_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lngamma_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lngamma_gsl (@@dots{}) These routines compute the logarithm of the Gamma function, \\log(\\Gamma(x)), subject to x not a being negative integer. For x<0 the real part of \\log(\\Gamma(x)) is returned, which is equivalent to \\log(|\\Gamma(x)|). The function is computed using the real Lanczos method. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gammastar -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} gammastar (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} gammastar (@@dots{}) These routines compute the regulated Gamma Function \\Gamma^*(x) for x > 0. The regulated gamma function is given by, \\Gamma^*(x) = \\Gamma(x)/(\\sqrt@@{2\\pi@@} x^@@{(x-1/2)@@} \\exp(-x)) = (1 + (1/12x) + ...) for x \\to \\infty and is a useful suggestion of Temme. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gammainv_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} gammainv_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} gammainv_gsl (@@dots{}) These routines compute the reciprocal of the gamma function, 1/\\Gamma(x) using the real Lanczos method. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lambert_W0 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lambert_W0 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lambert_W0 (@@dots{}) These compute the principal branch of the Lambert W function, W_0(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@@{-1@@}(x) to be the other real branch, where W < -1 for x < 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lambert_Wm1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lambert_Wm1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lambert_Wm1 (@@dots{}) These compute the secondary real-valued branch of the Lambert W function, W_@@{-1@@}(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@@{-1@@}(x) to be the other real branch, where W < -1 for x < 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn log_1plusx -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} log_1plusx (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} log_1plusx (@@dots{}) These routines compute \\log(1 + x) for x > -1 using an algorithm that is accurate for small x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn log_1plusx_mx -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} log_1plusx_mx (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} log_1plusx_mx (@@dots{}) These routines compute \\log(1 + x) - x for x > -1 using an algorithm that is accurate for small x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn psi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} psi (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi (@@dots{}) These routines compute the digamma function \\psi(x) for general x, x \ e 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn psi_1piy -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} psi_1piy (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi_1piy (@@dots{}) These routines compute the real part of the digamma function on the line 1+i y, Re[\\psi(1 + i y)]. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn synchrotron_1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} synchrotron_1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} synchrotron_1 (@@dots{}) These routines compute the first synchrotron function x \\int_x^\\infty dt K_@@{5/3@@}(t) for x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn synchrotron_2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} synchrotron_2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} synchrotron_2 (@@dots{}) These routines compute the second synchrotron function x K_@@{2/3@@}(x) for x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn transport_2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} transport_2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_2 (@@dots{}) These routines compute the transport function J(2,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn transport_3 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} transport_3 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_3 (@@dots{}) These routines compute the transport function J(3,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn transport_4 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} transport_4 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_4 (@@dots{}) These routines compute the transport function J(4,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn transport_5 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} transport_5 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_5 (@@dots{}) These routines compute the transport function J(5,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn sinc_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} sinc_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} sinc_gsl (@@dots{}) These routines compute \\sinc(x) = \\sin(\\pi x) / (\\pi x) for any value of x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lnsinh -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lnsinh (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lnsinh (@@dots{}) These routines compute \\log(\\sinh(x)) for x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lncosh -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lncosh (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lncosh (@@dots{}) These routines compute \\log(\\cosh(x)) for any x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn zeta -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} zeta (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} zeta (@@dots{}) These routines compute the Riemann zeta function \\zeta(s) for arbitrary s, s \ e 1. The Riemann zeta function is defined by the infinite sum \\zeta(s) = \\sum_@@{k=1@@}^\\infty k^@@{-s@@}. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn eta -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} eta (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} eta (@@dots{}) These routines compute the eta function \\eta(s) for arbitrary s. The eta function is defined by \\eta(s) = (1-2^@@{1-s@@}) \\zeta(s). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Jn -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_Jn (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Jn (@@dots{}) These routines compute the regular cylindrical Bessel function of order n, J_n(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Yn -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_Yn (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Yn (@@dots{}) These routines compute the irregular cylindrical Bessel function of order n, Y_n(x), for x>0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_In -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_In (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_In (@@dots{}) These routines compute the regular modified cylindrical Bessel function of order n, I_n(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_In_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_In_scaled (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_In_scaled (@@dots{}) These routines compute the scaled regular modified cylindrical Bessel function of order n, \\exp(-|x|) I_n(x) @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Kn -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_Kn (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Kn (@@dots{}) These routines compute the irregular modified cylindrical Bessel function of order n, K_n(x), for x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Kn_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_Kn_scaled (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Kn_scaled (@@dots{}) @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_jl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_jl (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_jl (@@dots{}) These routines compute the regular spherical Bessel function of order l, j_l(x), for l >= 0 and x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_yl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_yl (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_yl (@@dots{}) These routines compute the irregular spherical Bessel function of order l, y_l(x), for l >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_il_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_il_scaled (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_il_scaled (@@dots{}) These routines compute the scaled regular modified spherical Bessel function of order l, \\exp(-|x|) i_l(x) @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_kl_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_kl_scaled (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_kl_scaled (@@dots{}) These routines compute the scaled irregular modified spherical Bessel function of order l, \\exp(x) k_l(x), for x>0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn exprel_n -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} exprel_n (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} exprel_n (@@dots{}) These routines compute the N-relative exponential, which is the n-th generalization of the functions gsl_sf_exprel and gsl_sf_exprel2. The N-relative exponential is given by, exprel_N(x) = N!/x^N (\\exp(x) - \\sum_@@{k=0@@}^@@{N-1@@} x^k/k!) = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ... = 1F1 (1,1+N,x) @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_int -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_int (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_int (@@dots{}) These routines compute the complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/\\Gamma(j+1)) \\int_0^\\infty dt (t^j /(\\exp(t-x)+1)). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn taylorcoeff -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} taylorcoeff (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} taylorcoeff (@@dots{}) These routines compute the Taylor coefficient x^n / n! for x >= 0, n >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn legendre_Pl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} legendre_Pl (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_Pl (@@dots{}) These functions evaluate the Legendre polynomial P_l(x) for a specific value of l, x subject to l >= 0, |x| <= 1 @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn legendre_Ql -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} legendre_Ql (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_Ql (@@dots{}) These routines compute the Legendre function Q_l(x) for x > -1, x != 1 and l >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn psi_n -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} psi_n (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi_n (@@dots{}) These routines compute the polygamma function \\psi^@@{(m)@@}(x) for m >= 0, x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Jnu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Jnu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Jnu (@@dots{}) These routines compute the regular cylindrical Bessel function of fractional order nu, J_\ u(x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Ynu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Ynu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Ynu (@@dots{}) These routines compute the irregular cylindrical Bessel function of fractional order nu, Y_\ u(x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Inu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Inu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Inu (@@dots{}) These routines compute the regular modified Bessel function of fractional order nu, I_\ u(x) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Inu_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Inu_scaled (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Inu_scaled (@@dots{}) These routines compute the scaled regular modified Bessel function of fractional order nu, \\exp(-|x|)I_\ u(x) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Knu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Knu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Knu (@@dots{}) These routines compute the irregular modified Bessel function of fractional order nu, K_\ u(x) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_lnKnu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_lnKnu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_lnKnu (@@dots{}) These routines compute the logarithm of the irregular modified Bessel function of fractional order nu, \\ln(K_\ u(x)) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Knu_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Knu_scaled (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Knu_scaled (@@dots{}) These routines compute the scaled irregular modified Bessel function of fractional order nu, \\exp(+|x|) K_\ u(x) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn exp_mult -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} exp_mult (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} exp_mult (@@dots{}) These routines exponentiate x and multiply by the factor y to return the product y \\exp(x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_inc_0 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} fermi_dirac_inc_0 (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} fermi_dirac_inc_0 (@@dots{}) These routines compute the incomplete Fermi-Dirac integral with an index of zero, F_0(x,b) = \\ln(1 + e^@@{b-x@@}) - (b-x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn poch -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} poch (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} poch (@@dots{}) These routines compute the Pochhammer symbol (a)_x := \\Gamma(a + x)/\\Gamma(a), subject to a and a+x not being negative integers. The Pochhammer symbol is also known as the Apell symbol. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lnpoch -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} lnpoch (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} lnpoch (@@dots{}) These routines compute the logarithm of the Pochhammer symbol, \\log((a)_x) = \\log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn pochrel -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} pochrel (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} pochrel (@@dots{}) These routines compute the relative Pochhammer symbol ((a,x) - 1)/x where (a,x) = (a)_x := \\Gamma(a + x)/\\Gamma(a). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gamma_inc_Q -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} gamma_inc_Q (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} gamma_inc_Q (@@dots{}) These routines compute the normalized incomplete Gamma Function Q(a,x) = 1/\\Gamma(a) \\int_x\\infty dt t^@@{a-1@@} \\exp(-t) for a > 0, x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gamma_inc_P -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} gamma_inc_P (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} gamma_inc_P (@@dots{}) These routines compute the complementary normalized incomplete Gamma Function P(a,x) = 1/\\Gamma(a) \\int_0^x dt t^@@{a-1@@} \\exp(-t) for a > 0, x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gamma_inc -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} gamma_inc (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} gamma_inc (@@dots{}) These functions compute the incomplete Gamma Function the normalization factor included in the previously defined functions: \\Gamma(a,x) = \\int_x\\infty dt t^@@{a-1@@} \\exp(-t) for a real and x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn beta_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} beta_gsl (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} beta_gsl (@@dots{}) These routines compute the Beta Function, B(a,b) = \\Gamma(a)\\Gamma(b)/\\Gamma(a+b) for a > 0, b > 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lnbeta -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} lnbeta (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} lnbeta (@@dots{}) These routines compute the logarithm of the Beta Function, \\log(B(a,b)) for a > 0, b > 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hyperg_0F1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} hyperg_0F1 (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} hyperg_0F1 (@@dots{}) These routines compute the hypergeometric function 0F1(c,x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn conicalP_half -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} conicalP_half (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_half (@@dots{}) These routines compute the irregular Spherical Conical Function P^@@{1/2@@}_@@{-1/2 + i \\lambda@@}(x) for x > -1. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn conicalP_mhalf -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} conicalP_mhalf (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_mhalf (@@dots{}) These routines compute the regular Spherical Conical Function P^@@{-1/2@@}_@@{-1/2 + i \\lambda@@}(x) for x > -1. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn conicalP_0 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} conicalP_0 (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_0 (@@dots{}) These routines compute the conical function P^0_@@{-1/2 + i \\lambda@@}(x) for x > -1. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn conicalP_1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} conicalP_1 (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_1 (@@dots{}) These routines compute the conical function P^1_@@{-1/2 + i \\lambda@@}(x) for x > -1. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hzeta -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} hzeta (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} hzeta (@@dots{}) These routines compute the Hurwitz zeta function \\zeta(s,q) for s > 1, q > 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Ai -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai (@@dots{}) These routines compute the Airy function Ai(x) with an accuracy specified by mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Bi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi (@@dots{}) These routines compute the Airy function Bi(x) with an accuracy specified by mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Ai_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai_scaled (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai_scaled (@@dots{}) These routines compute a scaled version of the Airy function S_A(x) Ai(x). For x>0 the scaling factor S_A(x) is \\exp(+(2/3) x^(3/2)), and is 1 for x<0. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Bi_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi_scaled (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi_scaled (@@dots{}) These routines compute a scaled version of the Airy function S_B(x) Bi(x). For x>0 the scaling factor S_B(x) is exp(-(2/3) x^(3/2)), and is 1 for x<0. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Ai_deriv -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai_deriv (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai_deriv (@@dots{}) These routines compute the Airy function derivative Ai'(x) with an accuracy specified by mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Bi_deriv -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi_deriv (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi_deriv (@@dots{}) These routines compute the Airy function derivative Bi'(x) with an accuracy specified by mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Ai_deriv_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai_deriv_scaled (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai_deriv_scaled (@@dots{}) These routines compute the derivative of the scaled Airy function S_A(x) Ai(x). The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Bi_deriv_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi_deriv_scaled (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi_deriv_scaled (@@dots{}) These routines compute the derivative of the scaled Airy function S_B(x) Bi(x). The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn ellint_Kcomp -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} ellint_Kcomp (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} ellint_Kcomp (@@dots{}) These routines compute the complete elliptic integral K(k) @@tex \\beforedisplay $$ \\eqalign{ K(k) &= \\int_0^{\\pi/2} {dt \\over \\sqrt{(1 - k^2 \\sin^2(t))}} \\cr } $$ \\afterdisplay @@end tex The notation used here is based on Carlson, @@cite{Numerische Mathematik} 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter @@math{m = k^2}. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn ellint_Ecomp -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} ellint_Ecomp (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} ellint_Ecomp (@@dots{}) These routines compute the complete elliptic integral E(k) to the accuracy specified by the mode variable mode. @@tex \\beforedisplay $$ \\eqalign{ E(k) &= \\int_0^{\\pi/2} \\sqrt{(1 - k^2 \\sin^2(t))} dt \\cr } $$ \\afterdisplay @@end tex The notation used here is based on Carlson, @@cite{Numerische Mathematik} 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter @@math{m = k^2}. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_zero_Ai -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Ai (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Ai (@@dots{}) These routines compute the location of the s-th zero of the Airy function Ai(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_zero_Bi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Bi (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Bi (@@dots{}) These routines compute the location of the s-th zero of the Airy function Bi(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_zero_Ai_deriv -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Ai_deriv (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Ai_deriv (@@dots{}) These routines compute the location of the s-th zero of the Airy function derivative Ai(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_zero_Bi_deriv -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Bi_deriv (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Bi_deriv (@@dots{}) These routines compute the location of the s-th zero of the Airy function derivative Bi(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_zero_J0 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_zero_J0 (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_zero_J0 (@@dots{}) These routines compute the location of the s-th positive zero of the Bessel function J_0(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_zero_J1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_zero_J1 (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_zero_J1 (@@dots{}) These routines compute the location of the s-th positive zero of the Bessel function J_1(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn psi_1_int -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} psi_1_int (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi_1_int (@@dots{}) These routines compute the Trigamma function \\psi(n) for positive integer n. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn zeta_int -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} zeta_int (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} zeta_int (@@dots{}) These routines compute the Riemann zeta function \\zeta(n) for integer n, n \ e 1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn eta_int -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} eta_int (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} eta_int (@@dots{}) These routines compute the eta function \\eta(n) for integer n. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn legendre_Plm -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} legendre_Plm (@@var{n}, @@var{m}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_Plm (@@dots{}) These routines compute the associated Legendre polynomial P_l^m(x) for m >= 0, l >= m, |x| <= 1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn legendre_sphPlm -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} legendre_sphPlm (@@var{n}, @@var{m}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_sphPlm (@@dots{}) These routines compute the normalized associated Legendre polynomial $\\sqrt@@{(2l+1)/(4\\pi)@@} \\sqrt@@{(l-m)!/(l+m)!@@} P_l^m(x)$ suitable for use in spherical harmonics. The parameters must satisfy m >= 0, l >= m, |x| <= 1. Theses routines avoid the overflows that occur for the standard normalization of P_l^m(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hyperg_U -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{out} =} hyperg_U (@@var{x0}, @@var{x1}, @@var{x2}) @@deftypefnx {Loadable Function} {[@@var{out}, @@var{err}] =} hyperg_U (@@dots{}) Secondary Confluent Hypergoemetric U function A&E 13.1.3 All input are double as is the output. @@var{err} contains an estimate of the absolute error in the value @@var{out}.a. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hyperg_1F1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{out} =} hyperg_1F1 (@@var{x0}, @@var{x1}, @@var{x2}) @@deftypefnx {Loadable Function} {[@@var{out}, @@var{err}] =} hyperg_1F1 (@@dots{}) Primary Confluent Hypergoemetric U function A&E 13.1.3 All inputs are double as is the output. @@var{err} contains an estimate of the absolute error in the value @@var{out}.a. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn @ gsl-1.0.8/doc/RCS/mktexi_inc,v0000755000175000017500000003106511201030376013627 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @# @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @#!/usr/bin/env perl # # David Bateman Feb 02 2003 # # Extracts the help in texinfo format for particular function for use # in documentation. Based on make_index script from octave_forge. use strict; use File::Find; use File::Basename; use Text::Wrap; use FileHandle; use IPC::Open3; use POSIX ":sys_wait_h"; my $file = shift @@ARGV; my $docfile = shift @@ARGV; my $indexfile = shift @@ARGV; my $line; print("\\input texinfo \n"); print("\@@ifnottex \n"); print("\@@node Top \n"); print("\@@top Octave gsl \n"); print("\@@end ifnottex \n"); if ( open(IN,$file) ) { $line = ; my $tex = 0; while ($line) { if ($line =~ /^\@@DOCSTRING/) { my $found = 0; my $func = $line; $func =~ s/\@@DOCSTRING\(//; $func =~ s/\)[\n\r]+//; my $func0 = $func; my $func1 = $func; $func0 =~ s/,.*$//; $func1 =~ s/^.*,//; if ( open(DOC,$docfile) ) { while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func0$/) { my $desc = ""; my $docline; my $doctex = 0; while (($docline = ) && ($docline !~ /^\037/)) { $docline =~ s/^\s*-[*]- texinfo -[*]-\s*//; if ($docline =~ /\@@tex/) { $doctex = 1; } if ($doctex) { $docline =~ s/\\\\/\\/g; } if ($docline =~ /\@@end tex/) { $doctex = 0; } $desc .= $docline; } $desc =~ s/$func0/$func1/g; $desc =~ s/\@@seealso\{(.*[^}])\}/See also: \1/g; print "$desc", "\n"; $found = 1; last; } } close (DOC); if (! $found) { print "\@@emph{Not implemented}\n"; } } else { print STDERR "Could not open file $docfile\n"; exit 1; } } elsif ($line =~ /^\@@REFERENCE_SECTION/) { my $secfound = 0; my $sec = $line; $sec =~ s/\@@REFERENCE_SECTION\(//; $sec =~ s/\)[\n\r]+//; my @@listfunc = (); my $nfunc = 0; my $seccat = 0; if ( open(IND,$indexfile) ) { while () { next unless /^[^ ]/; my $section = $_; $section =~ s/[\n\r]+//; if ($section =~ /^(.*?)\s*>>\s*(.*?)$/) { $section =~ s/.*>>(.*)/\1/; $seccat = 1; } $section =~ s/^ *//; $section =~ s/ *$//; if ($section =~ /^$sec$/) { if ($seccat) { print "\@@iftex\n"; print "\@@section Functions by Category\n"; # Get the list of categories to index my $firstcat = 1; my $category; while () { last if />>/; if (/^[^ ]/) { if (! $firstcat) { print "\@@end table\n"; } else { $firstcat = 0; } $category = $_; $category =~ s/[\n\r]+//; print "\@@subsection $category\n"; print "\@@table \@@asis\n"; } elsif (/^\s+(\S.*\S)\s*=\s*(\S.*\S)\s*$/) { my $func = $1; my $desc = $2; print "\@@item $func\n"; print "$desc\n"; print "\n"; } else { if ($firstcat) { print STDERR "Error parsing index file\n"; exit 1; } s/^\s+//; my @@funcs = split /\s+/; while ($#funcs >= 0) { my $func = shift @@funcs; $func =~ s/^ *//; $func =~ s/[\n\r]+//; push @@listfunc, $func; $nfunc = $nfunc + 1; print "\@@item $func\n"; print func_summary($func, $docfile); print "\n"; } } } if (! $firstcat) { print "\@@end table\n"; } print "\n\@@section Functions Alphabetically\n"; print "\@@end iftex\n\n"; } else { # Get the list of functions to index my $indline; while (($indline = ) && ($indline =~ /^ /)) { if ($indline =~ /^\s+(\S.*\S)\s*=\s*(\S.*\S)\s*$/) { next; } $indline =~ s/^\s+//; my @@funcs = split(/\s+/,$indline); while ($#funcs >= 0) { my $func = shift @@funcs; $func =~ s/^ *//; $func =~ s/[\n\r]+//; push @@listfunc, $func; $nfunc = $nfunc + 1; } } } $secfound = 1; last; } } close (IND); if (! $secfound) { print STDERR "Did not find section $sec\n"; } } else { print STDERR "Could not open file $indexfile\n"; exit 1; } @@listfunc = sort(@@listfunc); my @@listfunc2 = (); my $indent = 16 - 3; print "\@@menu\n"; foreach my $func (@@listfunc) { if ( open(DOC,$docfile) ) { my $found = 0; while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func$/) { $found = 1; last; } } close (DOC); if ($found) { push @@listfunc2, $func; my $func0 = "${func}::"; my $entry = sprintf("* %-*s %s",$indent,$func0,func_summary($func,$docfile)); print wrap("","\t\t","$entry"), "\n"; } } else { print STDERR "Could not open file $indexfile\n"; exit 1; } } print "\@@end menu\n"; my $up = "Function Reference"; my $next; my $prev; my $mfunc = 1; foreach my $func (@@listfunc2) { if ($mfunc == $nfunc) { $next = ""; } else { $next = @@listfunc2[$mfunc]; $mfunc = $mfunc + 1; } print "\n\@@node $func, $next, $prev, $up\n"; if ($seccat) { print "\@@subsection $func\n\n"; } else { print "\@@section $func\n\n"; } $prev = $func; my $found = 0; my $desc = ""; if ( open(DOC,$docfile) ) { while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func$/) { my $docline; my $doctex = 0; while (($docline = ) && ($docline !~ /^\037/)) { $docline =~ s/^\s*-[*]- texinfo -[*]-\s*//; if ($docline =~ /\@@tex/) { $doctex = 1; } if ($doctex) { $docline =~ s/\\\\/\\/g; } if ($docline =~ /\@@end tex/) { $doctex = 0; } $desc .= $docline; } $desc =~ s/\@@seealso\{(.*[^}])\}/See also: \1/g; print "$desc", "\n"; $found = 1; last; } } close (DOC); if (! $found) { print "\@@emph{Not implemented}\n"; } } else { print STDERR "Could not open file $docfile\n"; exit 1; } } } else { if ($line =~ /\@@tex/) { $tex = 1; } if ($tex) { $line =~ s/\\\\/\\/g; } print "$line"; if ($line =~ /\@@end tex/) { $tex = 0; } } $line = ; } } else { print STDERR "Could not open file $file\n"; exit 1; }; print("\@@bye"); sub func_summary { # {{{1 my ($func, # in function name $docfile # in DOCSTRINGS ) = @@_; my $desc = ""; my $found = 0; if ( open(DOC,$docfile) ) { while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func$/) { my $docline; my $doctex = 0; while (($docline = ) && ($docline !~ /^\037/)) { if ($docline =~ /\@@tex/) { $doctex = 1; } if ($doctex) { $docline =~ s/\\\\/\\/g; } if ($docline =~ /\@@end tex/) { $doctex = 0; } $desc .= $docline; } $desc =~ s/\@@seealso\{(.*[^}])\}/See also: \1/g; $found = 1; last; } } close (DOC); if (! $found) { $desc = "\@@emph{Not implemented}"; } } else { print STDERR "Could not open file $docfile\n"; exit 1; } return first_sentence($desc); } # 1}}} sub first_sentence { # {{{1 # grab the first real sentence from the function documentation my ($desc) = @@_; my $retval = ''; my $line; my $next; my @@lines; my $trace = 0; # $trace = 1 if $desc =~ /Levenberg/; return "" unless defined $desc; if ($desc =~ /^\s*-[*]- texinfo -[*]-/) { # help text contains texinfo. Strip the indicator and run it # through makeinfo. (XXX FIXME XXX this needs to be a function) $desc =~ s/^\s*-[*]- texinfo -[*]-\s*//; my $cmd = "makeinfo --fill-column 1600 --no-warn --no-validate --no-headers --force --ifinfo"; open3(*Writer, *Reader, *Errer, $cmd) or die "Could not run info"; print Writer "\@@macro seealso {args}\n\n\@@noindent\nSee also: \\args\\.\n\@@end macro\n"; print Writer "$desc"; close(Writer); @@lines = ; close(Reader); my @@err = ; close(Errer); waitpid(-1,&WNOHANG); # Display source and errors, if any if (@@err) { my $n = 1; foreach $line ( split(/\n/,$desc) ) { printf "%2d: %s\n",$n++,$line; } print ">>> @@err"; } # Print trace showing formatted output # print "\n"; # Skip prototype and blank lines while (1) { return "" unless @@lines; $line = shift @@lines; next if $line =~ /^\s*-/; next if $line =~ /^\s*$/; last; } } else { # print "\n"; # Skip prototype and blank lines @@lines = split(/\n/,$desc); while (1) { return "" if ($#lines < 0); $line = shift @@lines; next if $line =~ /^\s*[Uu][Ss][Aa][Gg][Ee]/; # skip " usage " $line =~ s/^\s*\w+\s*://; # chop " blah : " print "strip blah: $line\n" if $trace; $line =~ s/^\s*[Ff]unction\s+//; # chop " function " print "strip function $line\n" if $trace; $line =~ s/^\s*\[.*\]\s*=\s*//; # chop " [a,b] = " print "strip []= $line\n" if $trace; $line =~ s/^\s*\w+\s*=\s*//; # chop " a = " print "strip a= $line\n" if $trace; $line =~ s/^\s*\w+\s*\([^\)]*\)\s*//; # chop " f(x) " print "strip f(x) $line\n" if $trace; $line =~ s/^\s*[;:]\s*//; # chop " ; " print "strip ; $line\n" if $trace; $line =~ s/^\s*[[:upper:]][[:upper:]0-9_]+//; # chop " BLAH" print "strip BLAH $line\n" if $trace; $line =~ s/^\s*\w*\s*[-]+\s+//; # chop " blah --- " print "strip blah --- $line\n" if $trace; $line =~ s/^\s*\w+ *\t\s*//; # chop " blah " print "strip blah $line\n" if $trace; $line =~ s/^\s*\w+\s\s+//; # chop " blah " print "strip blah $line\n" if $trace; # next if $line =~ /^\s*\[/; # skip [a,b] = f(x) # next if $line =~ /^\s*\w+\s*(=|\()/; # skip a = f(x) OR f(x) next if $line =~ /^\s*or\s*$/; # skip blah \n or \n blah next if $line =~ /^\s*$/; # skip blank line next if $line =~ /^\s?!\//; # skip # !/usr/bin/octave # XXX FIXME XXX should be testing for unmatched () in proto # before going to the next line! last; } } # Try to make a complete sentence, including the '.' if ( "$line " !~ /[^.][.]\s/ && $#lines >= 0) { my $next = $lines[0]; $line =~ s/\s*$//; # trim trailing blanks on last $next =~ s/^\s*//; # trim leading blanks on next $line .= " $next" if "$next " =~ /[^.][.]\s/; # ends the sentence } # Tidy up the sentence. chomp $line; # trim trailing newline, if there is one $line =~ s/^\s*//; # trim leading blanks on line $line =~ s/([^.][.])\s.*$/$1/; # trim everything after the sentence print "Skipping:\n$desc---\n" if $line eq ""; # And return it. return $line; } # 1}}} __END__ This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, see . This program is granted to the public domain. THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. @ gsl-1.0.8/doc/RCS/gsl.pdf,v0000644000175000017500000062657111201030376013043 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @# @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @%PDF-1.4 3 0 obj << /Length 1665 /Filter /FlateDecode >> stream xÚíYKoÛF¾ûWðTPE¸â¾—rH“:Ha´«''5(‰²‰Jd Ñ‘Ý_ß™ÝåK¦-»vë‚X+îÌìì–4 1Iâ„“,0‹@@A(2˜ÌÏÂ1×›åùf1Š8çaôc„ VÙu^,F4,ýÆ(¢!l~šüpÆ‹µ"#Œ²¢ÎNÊt ét™9žã‘áá<*fU^Ÿy|¬X@@)I¤d¨jB%p”╱”RuõœPÊ=ÙÇXÆðŸzÂÞE#*§\ZsQkËñû¬JGÌ„_ð*«p ºåÅÜþ½Øà3V¥ÿ¼ÌÜâýo¸Åé,Ï ä®ò1À5sbNr´N×ð÷ïLFà.¾Yƒ¥—rzâhÓ«Â1S…&.6NÐ,-Ñt1]k9K—Ëlî6¶yui}÷o7E½nœÙ‚Z^pãûSXŸ¸5š®ðÔlãžXixyÇ7);v¢p<3RʾÓ1~fËôj“ý8qšXþk{DKÂÙPéÇÅ¿/Žn†‚ Ó‡+éI^"ÉdX«?r Xc˜:Z&X-ôzHŽ&JÅ´3¶L$„k ë9öy²êlHoE˜V÷Ú«GñjHeVÆ“dëõð.£,ñDŸœÙ÷[_ "yËø‚ݪ+®<丢ýJ%Ñ1“{|QP_±Ö.Ú'—>­Þ‚ÖàM&ù.±­O܃ÜQ ý<ÊQ¸¼¤áÜ@@Ò&mÒzÑ6O–ËÓo eÉË*ÖåÓÖ™tùª©p%ª\¸¼]ž34朽œ•ùºÉÍZ±ó¸õUÇè†PCk_ý9d8ŽiÖÄ»•9¯Üç²¼Àã™û¶É üV2cT‹Öö"üžö¼”Ü›m-Ó*ó֪ʞ¥àÌN³Eו±•cê–ÂÚuI„‚‹¶»e™ž÷}æX²ëÏø‘÷k*pÜμd($—¨~Rì´cM åuQ˜•Î)i^´Q“ú@@²çnª|•V>HJß®ñ6uà¤Ó:"Ë%gM ç—ë6"‹+~I Ñ„Á› ݆)F8TÁ~¸R·IhÌŒ$‰’}O.ѵŒ±pÑV0÷ Ù@@‡–+üÒš׶#Å`FŠ¦CP¯  Ÿ£öjG¿L°m€°ºä6àŠ„9Lׂí¦jè¢.¡…WýĹ-/|YUŸ·Û-¹(®H¹¾oÊEµM×Ù ÎxW-) ‘*;jíB=1F¼Þ†2Ñúë,X´ê7ò@@}N`‘Ü…©!:r+~3.êÈ™»îðàjeãѤتßÍ Øþ5@@³ÝÔµñ18SþKœùLø`žZµz‰”Ð×¥y<{áÛð4¡ä÷î6¾2ÀeÔ ÁƒX.¸î;ÃÁH‹wÝh‡ïýîâ+d’ër±Í-»å«Ya;04 Ö¾E×CM›& rÛ˜wmæ; × Ñ<¸ &æüQ€ÄZ@@àôv½PÀ€t(OÐ\ÔãÇ×+ÁÃ7î„Ê6>þ±ëŒè‚^Íq)Ñ$Ö†÷æï_ûÀ»iV·ßöe áYisk~«¡¾™®Ó•GmÕߎø·uê»1H·Ì¯Üã fjGyj"ŸŒ(ØQ¼0¢à&&Ü@@_؇(º„÷!Š†îIˆ¢¯Ö]ˆ‚=Qp­ÁTíC\iÂ8l>Q¨¢°<¾Dâ¨âœ>Z¼ÌèažMoPï¯mô ¾lq·õ¿¦ÑƒîÞ „¾@@tÆŠøRìÆŠXÇ×í@@phÁvƇžÔÕv¬Š™íŠã†wç…ïî×õ;5¯ß©‹ñ VQ Š¦îøEo2<´à½¼_&Z܉N@@®¡†=\×±´í€4ˆE«‡ß¼êLmDHëùI]5u/=‡cŸªKìâ þ\76¤X€Wi;¤ÚdÞÛ€_šùð£`ÌiKуp˜|óH†qE8¼XìE2]ÂûLC÷$$ÓWë ³¿ÊɽH …&ùÏ‘ ûF‘ ;üˆò‚H†}c?¢ÌÉÌÉüH&ëI¾ÈtèîÃ15Ù“`LO§g@@1&! 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gsl-1.0.8/doc/RCS/README~,v0000644000175000017500000000200211201030376012612 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @# @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @ README for gsl/doc .dvi, .ps,.pdf documentation generation This generation has only been brought up to a usable form. It still generates erros along the way. use ./mk_pdf_dvi gsl to update the pdf/dvi/ps documents. The gsl argument merely determines the prefixs; gsl.dvi, etc... It should probably do more. Look at the script above and make them; it simple. special files in this directory. mktexi_inc : added some headers and footers to the output .texi file. This allows more program to operate on it as an individual file. testinfo.tex: copied form the gnu gsl source file. The octave-forge original ended up replacing "_" in function names and such with a overhead period. makeinfo gsl.texi doesn't work now in this directory; but I will let the octave-forge gang continue to build it out of the src directory. @ gsl-1.0.8/doc/RCS/make_index,v0000755000175000017500000012375211201030376013606 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @# @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @#!/usr/bin/env perl # # Albert Danial Mar 21 2002 # # Creates .html files documenting all the functions in octave and # octave-forge. use strict; use File::Find; use File::Basename; use Text::Wrap; use FileHandle; use IPC::Open3; use POSIX ":sys_wait_h"; ## Local configuration; the OCTAVE directory should contain # src/DOCSTRINGS (which is a build product) and scripts/. my $OCTAVE = "../octave"; my $tmpdir = "/tmp"; # temp directory my $catdir = "doc/htdocs/doc"; # output directory ## Commands to grab the last few defs from octave ## Use the first def if you want to extract from ## a locally compiled version, or the second if you ## want to use the installed version. #my $OCTAVECMD = "LD_LIBRARY_PATH=$OCTAVE/src/:$OCTAVE/liboctave:$OCTAVE/libcruft $OCTAVE/src/octave -q"; #my $OCTAVEINIT = "path='.:$OCTAVE/src//:$OCTAVE/scripts//'; suppress_verbose_help_message = 1;"; my $OCTAVECMD = "octave -q"; my $OCTAVEINIT = "suppress_verbose_help_message(1); more off;"; # Links to octave/octave-forge web CVS/SVN my $OCTAVEHG = "http://velveeta.che.wisc.edu/cgi-bin/hgwebdir.cgi/octave/file/tip/"; my $FORGESVN = "http://octave.svn.sourceforge.net/viewvc/octave/trunk/octave-forge/"; #my $script = basename($0); my $forgebar = qq~

Home | Summary | Forums | Bugs | Support | Patches | Lists | Tasks | Docs | Surveys | News | SVN | Files
~; my $forgelink = qq~
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~; # initialize the indexing variables my %index_by_TB_cat = (); # i_TB_cat{toolbox}{category} = list of functions my %index_by_function = (); # i_function{function} =[ [toolbox_1,category_1], # [toolbox_2,category_2],..] my %TB_description = (); my %index_notes = (); # index_notes{function} = comment my %index_by_package = (); # i_package{package} = list of functions # find and load all indices my @@index_files = (); find(\&index_files, "."); sub index_files { # {{{1 populates global array @@files return unless -f and /INDEX$/; # INDEX files return if ($File::Find::dir =~ /packages$/); my $path = "$File::Find::dir/$_"; $path =~ s|^[.]/||; my $noinstall = sprintf("%s/NOINSTALL", $path); if (! -e $noinstall) { push @@index_files, $path; } } # 1}}} foreach my $f ( @@index_files ) { load_index($f, \%index_by_TB_cat, \%TB_description, \%index_by_function); } # XXX FIXME XXX should die if the index is empty # die "No INDEX in current directory" if !-e "INDEX"; my $summary = !-e "admin/make_index"; # if not in the root, just summarize my $include_octave = !$summary; # only include octave if not summarizing # locate all C++ and m-files in octave-forge, and all m-files in octave # don't need C++ files from octave because we have DOCSTRINGS my @@m_files = (); my @@C_files = (); find(\&cc_and_m_files, "$OCTAVE/scripts") if $include_octave; find(\&cc_and_m_files, "$OCTAVE/src") if $include_octave; # or just use $OCTAVE/{src,scripts}/DOCSTRINGS .... find(\&cc_and_m_files, "."); sub cc_and_m_files { # {{{1 populates global array @@files return unless -f and /\.(m|cc|l|y)$/; # .m and .cc files (lex & yacc too!) my $path = "$File::Find::dir/$_"; $path =~ s|^[.]/||; my $noinstall = sprintf("%s/NOINSTALL", $path); if (! -e $noinstall) { if (/\.m$/) { push @@m_files, $path; } else { push @@C_files, $path; } } } # 1}}} my %function_description = (); my %octave_forge_function = (); my @@uncategorized = (); my @@skipped = (); my %n_appearances = (); my $n_functions = 0; my @@shadow_paths = ('FIXES', 'extra/NaN', 'extra/Windows', 'extra/ver20'); my @@shadowed = (); my @@duplicated = (); my %n_duplicated = (); # grab help from C++ files foreach my $f ( @@C_files ) { if ( open(IN,$f) ) { while () { # skip to the next function next unless /^\s*DEF(UN[ (]|UN_MAPPER|UN_DLD|CMD|VAR|CONST)/; # print "looking at $_"; # extract function name to pattern space /\((\w*)\s*,/; # remember function name my $function = $1; # print " found function $function\n"; # skip to second , to skip default string options of DEFVAR # comment if third or higher arg # XXX FIXME XXX What about if the string arg includes , # XXX FIXME XXX What if second , is not on first line!! # Special cases # * for DEFCONST (I, Complex (0., 1.), s/\(\w*\s*,\s*Complex\s*\(\s*[0-9.]*\s*,\s*[0-9.]*\s*\),//; # * for macro containing DEFUN_DLD s/\w*\s*\(\w*\s*,\s*"/"/; # Main case s/\(\w*\s*,.*?,//; # If we have nothing but a newline, skip $_ = if /^\s*DEF(UN[ (]|UN_MAPPER|UN_DLD|CMD|VAR|CONST)\s*,*\s*\n/; # if line contains \w+_DOC_STRING we have a macro for the # help text my $desc; if (/\w+_DOC_STRING/) { my $macro = $_; $macro =~ s/^.*?\s*(\w*_DOC_STRING).*$/$1/; $macro =~ s/\n//; my $line; if ( open(IN2, $f) ) { while ($line = ) { next unless $line =~ /^\#\s*define\s+$macro\s+\"/; $desc = $line; $desc =~ s/^\#\s*define\s+$macro\s+\"(.*\n)$/$1/; while ($desc !~ /[^\\]\"/ && $desc !~ /^\"/) { $desc =~ s/\\\s*\n//; # join with the next line $desc .= ; } $desc = "" if $desc =~ /^\"/; # chop everything if it was "" $desc =~ s/\\n/\n/g; # insert fake line ends $desc =~ s/([^\"])\".*$/$1/; # chop everything after final '"' $desc =~ s/\\\"/\"/; # convert \"; XXX FIXME XXX \\" last; } close (IN2); } else { print STDERR "Could not open file ($f): $!\n"; } } else { # skip to next line if comment doesn't start on this line # XXX FIXME XXX maybe we want a loop here? $_ = unless /\"/; # skip to the beginning of the comment string by # chopping everything up to opening " $desc = $_; $desc =~ s/^[^\"]*\"//; # join lines until you get the end of the comment string # plus a bit more. You need the "plus a bit more" because # C compilers allow implicitly concatenated string constants # "A" "B" ==> "AB". while ($desc !~ /[^\\]\"\s*[\,\)]/ && $desc !~ /^\"/) { # if line ends in '\', chop it and the following '\n' $desc =~ s/\\\s*\n//; # join with the next line $desc .= ; # eliminate consecutive quotes, being careful to ignore # preceding slashes. XXX FIXME XXX what about \\" ? $desc =~ s/([^\\])\"\s*\"/$1/; } $desc = "" if $desc =~ /^\"/; # chop everything if it was "" # Now check for text included in help messages as macros # XXX FIXME XXX These macros are often compile dependent, so # how to we get the correct version of the macro in this case # without actually compiling the code??? while ($desc =~ /[^\\]\"\s*\S+\s*[^\\]\"/) { my $macro = $desc; # Deal with issues of multiple macros... # $macro =~ s/^.*[^\\]\"\s*(\S+?)\s*[^\\]\".*$/$1/; ($macro) = ($macro =~ /[^\\]\"\s*(\S+?)\s*\"/); $macro =~ s/\n//; my $macro_defn; my $line; last unless $macro =~ /\S+/; if ( open(IN2, $f) ) { while ($line = ) { if ($line =~ /^\#\s*define\s+$macro\s*\\\s*$/) { $line =~ s/\s*\\$//; $line .= ; $line =~ s/\\\s*\n/\n/; } next unless $line =~ /^\#\s*define\s+$macro\s+\"/; $macro_defn = $line; $macro_defn =~ s/^\#\s*define\s+$macro\s+\"(.*)\n$/$1/; while ($macro_defn !~ /[^\\]\"/ && $macro_defn !~ /^\"/) { $macro_defn =~ s/\\\s*\n//; # join with the next line $macro_defn .= ; } $macro_defn = "" if $macro_defn =~ /^\"/; # chop everything if it was "" $macro_defn =~ s/\\n/\n/g; # insert fake line ends $macro_defn =~ s/([^\"])\".*$/$1/; # chop everything after final '"' $macro_defn =~ s/\\\"/\"/; # convert \"; XXX FIXME XXX \\" $macro_defn =~ s/\\\\/\\/g; # convert \"; XXX FIXME XXX \\" last; } close (IN2); } else { print STDERR "Could not open file ($f): $!\n"; } $desc =~ s/\"\s*$macro\s*\"/$macro_defn/; } } $desc =~ s/\\n/\n/g; # insert fake line ends $desc =~ s/([^\"])\".*$/$1/; # chop everything after final '"' $desc =~ s/\\\"/\"/; # convert \"; XXX FIXME XXX \\" # print " description: $desc"; # register the function with a brief description register_function($function,$desc,$f,0); } close (IN); } else { print STDERR "Could not open file ($f): $!\n"; } } # grab help from m-files (octave-forge and octave) foreach my $f ( @@m_files ) { my $desc = extract_description($f); my $function = basename($f, ('.m')); die "Null function?? [$f]\n" unless $function; register_function($function,$desc,$f,0); } # grab help from octave's DOCSTRINGS if ( !$include_octave ) { # skip DOCSTRINGS if just summary } else { if (open (IN,"$OCTAVE/src/DOCSTRINGS")) { process_docstrings(); } else { print STDERR "could not open $OCTAVE/src/DOCSTRINGS !\n"; } if (open (IN,"$OCTAVE/scripts/DOCSTRINGS")) { process_docstrings(); } else { print STDERR "could not open $OCTAVE/scripts/DOCSTRINGS !\n"; } } # Desperate last measure. Try help within octave. Good for getting # keyword and operator descriptions my $octstring = ""; my @@octfiles = (); foreach my $TB ( toolbox_list()) { foreach my $cat ( cat_list($TB) ) { foreach my $func ( cat_funcs($TB,$cat) ) { if (! defined $function_description{$func}[1] && ! defined $index_notes{$func} ) { my $t =sprintf("help %s; disp(''); %s", $func, $octstring); $octstring = $t; push @@octfiles, $func; } } } } open3(*Writer, *Reader, *Errer, $OCTAVECMD) or die "Could not run octave"; print Writer $OCTAVEINIT; print Writer "$octstring"; close(Writer); my @@lines = ; close(Reader); my @@err = ; close(Errer); waitpid(-1,&WNOHANG); my $bodies = join("",@@lines); $bodies = substr($bodies,0, rindex($bodies, "")); # Display errors, if any if (@@err) { print "Help Errors:\n>>> @@err"; } else { foreach my $func (@@octfiles) { my $idx = rindex($bodies, ""); my $body; if ($idx < 0) { $body = substr($bodies, $idx); } else { $body = substr($bodies, $idx + 10); } $bodies = substr($bodies, 0, $idx); if ($body =~ /help: `(.*)' not found/ || $body =~ /help: sorry,/) { # do nothing } else { ## print "help $func\n"; my $start; if ($body =~ /^\n\*\*\*/) { # clipping assuming ops/keywords only $start = index($body,"$func") + 1 + length($func); } else { # first lines till \n\n will be octave tell us the type # of variable/funtion and where it is found $start = index($body,"\n\n") + 2; } my $stop = index($body,"ans ="); $body = substr($body,$start,$stop-$start); register_function($func,$body,$OCTAVE,0); } } } # print a summary table rather than generating the html if ( $summary ) { write_ascii("% "); } else { write_html(); } if (@@skipped) { print "skipped ", scalar(@@skipped), " functions "; my $rs = $,; $, = "\n "; print " ", sort(@@skipped); $, = $rs; print "\n"; } print_missing(); if (@@uncategorized) { print scalar(@@uncategorized), " uncategorized functions "; print "(out of ", $n_functions, " total)"; my $rs = $,; $, = "\n "; print " ", sort(@@uncategorized); $, = $rs; print "\n"; # print wrap("\t", "\t", join(" ", sort @@uncategorized)), "\n"; } if (@@shadowed) { print "unexpected shadowing of ", scalar(@@shadowed), " Octave functions"; my $rs = $,; $, = "\n "; print " ", sort(@@shadowed); $, = $rs; print "\n"; # print wrap("\t", "\t", join(" ", sort @@shadowed)), "\n"; } if (@@duplicated) { print "unexpected duplicate indexing of ", scalar(@@duplicated), " functions"; my $rs = $,; $, = "\n "; print " ", sort(@@duplicated); $, = $rs; print "\n"; } sub process_docstrings { my $function = ""; my $desc = ""; while () { if (/^\037/) { if ($n_appearances{$function} == 0) { register_function($function,$desc,$OCTAVE,1) unless $function eq ""; } $function = $_; $function =~ s/^\037//; $function =~ s/\n$//; $desc = ""; } else { $desc .= $_; } } if ($n_appearances{$function} == 0) { register_function($function,$desc,$OCTAVE,1) unless $function eq ""; } close(IN); } sub first_sentence { # {{{1 # grab the first real sentence from the function documentation my ($desc) = @@_; my $retval = ''; my $line; my $next; my @@lines; my $trace = 0; # $trace = 1 if $desc =~ /Levenberg/; return "" unless defined $desc; if ($desc =~ /^\s*-[*]- texinfo -[*]-/) { # help text contains texinfo. Strip the indicator and run it # through makeinfo. (XXX FIXME XXX this needs to be a function) $desc =~ s/^\s*-[*]- texinfo -[*]-\s*//; my $cmd = "makeinfo --fill-column 1600 --no-warn --no-validate --no-headers --force --ifinfo"; open3(*Writer, *Reader, *Errer, $cmd) or die "Could not run info"; print Writer "\@@macro seealso {args}\n\n\@@noindent\nSee also: \\args\\.\n\@@end macro\n"; print Writer "$desc"; close(Writer); @@lines = ; close(Reader); my @@err = ; close(Errer); waitpid(-1,&WNOHANG); # Display source and errors, if any if (@@err) { my $n = 1; foreach $line ( split(/\n/,$desc) ) { printf "%2d: %s\n",$n++,$line; } print ">>> @@err"; } # Print trace showing formatted output # print "\n"; # Skip prototype and blank lines while (1) { return "" unless @@lines; $line = shift @@lines; next if $line =~ /^\s*-/; next if $line =~ /^\s*$/; last; } } else { # print "\n"; # Skip prototype and blank lines @@lines = split(/\n/,$desc); while (1) { return "" if ($#lines < 0); $line = shift @@lines; next if $line =~ /^\s*[Uu][Ss][Aa][Gg][Ee]/; # skip " usage " next if $line =~ /^\s*-/; # skip " -- blah" $line =~ s/^\s*\w+\s*://; # chop " blah : " print "strip blah: $line\n" if $trace; $line =~ s/^\s*[Ff]unction\s+//; # chop " function " print "strip function $line\n" if $trace; $line =~ s/^\s*\[.*\]\s*=\s*//; # chop " [a,b] = " print "strip []= $line\n" if $trace; $line =~ s/^\s*\w+\s*=\s*//; # chop " a = " print "strip a= $line\n" if $trace; $line =~ s/^\s*\w+\s*\([^\)]*\)\s*//; # chop " f(x) " print "strip f(x) $line\n" if $trace; $line =~ s/^\s*[;:]\s*//; # chop " ; " print "strip ; $line\n" if $trace; $line =~ s/^\s*[[:upper:]][[:upper:]0-9_]+//; # chop " BLAH" print "strip BLAH $line\n" if $trace; $line =~ s/^\s*\w*\s*[-]+\s+//; # chop " blah --- " print "strip blah --- $line\n" if $trace; $line =~ s/^\s*\w+ *\t\s*//; # chop " blah " print "strip blah $line\n" if $trace; $line =~ s/^\s*\w+\s\s+//; # chop " blah " print "strip blah $line\n" if $trace; # next if $line =~ /^\s*\[/; # skip [a,b] = f(x) # next if $line =~ /^\s*\w+\s*(=|\()/; # skip a = f(x) OR f(x) next if $line =~ /^\s*or\s*$/; # skip blah \n or \n blah next if $line =~ /^\s*$/; # skip blank line next if $line =~ /^\s?!\//; # skip # !/usr/bin/octave # XXX FIXME XXX should be testing for unmatched () in proto # before going to the next line! last; } } # Try to make a complete sentence, including the '.' if ( "$line " !~ /[^.][.]\s/ && $#lines >= 0) { my $next = $lines[0]; $line =~ s/\s*$//; # trim trailing blanks on last $next =~ s/^\s*//; # trim leading blanks on next $line .= " $next" if "$next " =~ /[^.][.]\s/; # ends the sentence } # Tidy up the sentence. chomp $line; # trim trailing newline, if there is one $line =~ s/^\s*//; # trim leading blanks on line $line =~ s/([^.][.])\s.*$/$1/; # trim everything after the sentence print "Skipping:\n$desc---\n" if $line eq ""; # And return it. return $line; } # 1}}} sub shadow_path { # {{{1 # shadow_path($f) returns true if $f is on a known Octave shadow path my ($file) = @@_; $file =~ s|/[^/]*$||; my @@matches = grep(/^$file$/,@@shadow_paths); # print "looking for $file in @@shadow_paths\n"; # print "returns ",@@matches,"\n"; return scalar(@@matches) > 0 || $file =~ /alternatives$/; } # 1}}} sub register_function { # {{{1 # register the function and its one-line description my ($function, # in $index{toolbox}{category} = [functions] $desc, # in $toolbox_desc{toolbox} = description $file, $replace_shadow, ) = @@_; ++$n_appearances{$function}; if ($n_appearances{$function} > 1) { if ($replace_shadow != 0) { push @@shadowed, "$file:$function" if $file =~ /^$OCTAVE/ and !shadow_path($function_description{$function}[0]); # print "$file:$function appeared previously\n"; } } else { ++$n_functions; } if (! ($file =~ /^$OCTAVE/)) { $octave_forge_function{$function} = 1; if (defined $index_by_function{$function} || ($function !~ /__/ && $file !~ /test/ && $function !~ /^[Cc]ontents?$/ && $function !~ /pre_install/ && $function !~ /post_install/)) { my $package = $file; $package =~ s|^\s*([^/]+/[^/]+/).*$|$1|; push @@{$index_by_package{$package}}, $function; } } if (!defined $index_by_function{$function}) { my $entry = $file; $entry = "$file: $function" if $file !~ /[.]m$/; if ($function =~ /__/ || $file =~ /test/ || $function =~ /^[Cc]ontents?$/ || $function =~ /pre_install/ || $function =~ /post_install/) { push @@skipped, $entry; } else { push @@uncategorized, $entry; } } my $oneline = first_sentence($desc); #printf "%30s %s\n", $function, $oneline; if ($replace_shadow == 0 && defined @@function_description{$function}) { @@function_description{$function} = [ $function_description{$function}[0], $oneline, $desc ]; } elsif (!defined @@function_description{$function}) { @@function_description{$function} = [ $file, $oneline, $desc ]; } # push @@function_description{$function}}, "$file\n$oneline\n$desc"; #printf "%-12s %-20s %s\n", $function, # $index_by_function{$function}[0], # $index_by_function{$function}[1]; } # 1}}} sub extract_description { # {{{1 # grab the entire documentation comment from an m-file my ($file) = @@_; my $retval = ''; if( open( IN, "$file")) { # skip leading blank lines while () { last if /\S/; } if( m/\s*[%\#][\s\#%]* Copyright/) { # next block is copyright statement, skip it while () { last unless /^\s*[%\#]/; } } # Skip everything until the next comment block while ( !/^\s*[\#%]/ ) { $_ = ; last if not defined $_; } # Return the next comment block as the documentation while (/^\s*[\#%]/) { s/^[\s%\#]*//; # strip leading comment characters s/[\cM\s]*$//; # strip trailing spaces. $retval .= "$_\n"; $_ = ; last if not defined $_; } close(IN); return $retval; } else { print STDERR "Could not open file ($file): $!\n"; } } # 1}}} sub load_index { # {{{1 my ($file) = @@_; # in my $toolbox = "extra"; my $category = ""; my $description = ""; my $function = ""; open(IN, $file) or die "Cannot read $file: $!\n"; my %map; # simple macros for use in notes while () { next if /^\s*$/; # skip blank lines next if /^\s*\#/; # skip comment lines chomp; if (/^(.*?)\s*>>\s*(.*?)$/) { # toolbox lines contain "word >> description" $toolbox = $1; $description = $2; $category = ""; $TB_description{$toolbox} = $description; } elsif (/^\s*\$(\w+)\s*=\s*(\S.*\S)\s*$/) { # define a variable as "$var = expansion" $map{$1} = $2; } elsif (/^(\w.*?)\s*$/) { # category lines start in the left most column $category = $1; } elsif (/^\s+(\S.*?[^=~!><])=\s*(\S.*\S)\s*$/) { # Process "function = notes" explicit descriptions $function = $1; $description = $2; # We used ...(\S.*)=... rather than (\S.*\S)\s*= to allow for # single character function names, but that means we may have # to trim some extra spaces of the function name. Single # character descriptions get the treatment they deserve. $function =~ s/\s+$//; # expand all $var in the description my @@parts = split('\$', $description); foreach my $i ( 1 .. $#parts ) { $parts[$i] =~ /^(\w+)(\W.*)$/ or $parts[$i] =~ /^(\w+)()$/; $parts[$i] = "$map{$1}$2"; } $description = join("",@@parts); # record the function->description mapping $index_notes{$function} = $description; die "Function $function (line $.) has no category" unless $category; push @@{$index_by_TB_cat{$toolbox}{$category}}, $function; push @@{$index_by_function{$function}}, [$toolbox, $category]; ++$n_duplicated{$function}; if ($n_duplicated{$function} > 1) { push @@duplicated, "$file:$function"; } } else { s/^\s+//; my @@list = split /\s+/; while ($#list >= 0) { $function = shift @@list; die "Function $function (line $.) has no category" unless $category; push @@{$index_by_TB_cat{$toolbox}{$category}}, $function; push @@{$index_by_function{$function}}, [$toolbox, $category]; } } } close(IN); } # 1}}} sub write_html { # {{{1 # make empty html directories unlink <$catdir/*.html>; unlink <$catdir/f/*.html>; mkdir "$catdir"; mkdir "$catdir/f"; #write_main(); #write_forgebar(); write_index(); write_alphabetic_navbar(); write_TBnavbar(); foreach ( toolbox_list() ) { #write_TBnavbar($_); write_TBdetails($_); } foreach ( package_list() ) { write_package_details($_); } # Write one file for each letter. # my $Letter = chr(0); foreach my $func ( indexed_funcs() ) { # The source file my $body = long_desc($func); if ($body ne "") { # XXX FIXME XXX this will die if the punctuation is too wild open FUNC, ">$catdir/f/$func.in" or die "Could not open $func.in"; print FUNC "__DOC_HEADER__([[[Function Reference: $func]]])\n"; print FUNC "
$func\n"; # The toolboxes to which it belongs foreach my $pair ( @@{$index_by_function{$func}} ) { my ( $TB, $cat ) = @@{$pair}; print FUNC " ", cat_ref_up($TB, $cat, "[$TB]"), "\n"; } print FUNC "
\n"; print FUNC "
",download_ref($func),"
\n"; print FUNC "
\n"; print FUNC "$body\n"; print FUNC "
\n"; print FUNC "__TRAILER__"; close FUNC; } # Check if need to go to the next letter # This is particularly complicated because we # want to include all punctuation in the my $next = uc(substr($func, 0, 1)); if ($next ne $Letter) { if ($Letter =~ /[A-Y]/) { print OUT "\n__TRAILER__\n"; close OUT; } else { print OUT "\n"; } if ($Letter =~ /[\0A-Y]/) { my $head = ""; if ( $next =~ /[A-Z]/ ) { $head = $next; } elsif ( $next lt "A" ) { $head = "A"; } else { $head = "Z"; } my $file = ">$catdir/$head.in"; open(OUT, $file) or die "Cannot write $file"; print OUT "__DOC_HEADER__([[[Function Reference: $head]]])"; } $Letter = $next; print OUT "

$Letter

\n"; print OUT "
\n"; } # Function reference print OUT "
",func_ref($func,$func),"\n"; # The toolboxes to which it belongs foreach my $pair ( @@{$index_by_function{$func}} ) { my ( $TB, $cat ) = @@{$pair}; print OUT " ", cat_ref($TB, $cat, "[$TB]"), "\n"; } print OUT "
\n"; print OUT "
",download_ref($func),"
\n"; # column 3: the function description # XXX FIXME XXX multiple functions??? print OUT "
",html_desc($func),"
\n"; } print OUT "
\n__TRAILER__\n"; close(OUT); } # 1}}} sub writenav { # 1{{{ my ($cat) = @@_; } # 1}}} sub write_main { # {{{1 open(OUT,">$catdir/index.html") or die "Could not open $catdir/index.html"; print OUT < Octave-forge combined index $forgebar <H1>Octave-Forge Combined Index</H1> <ul> <li><A HREF="categorical.html">Categorical index</a> <li><A HREF="alphabetic.html">Alphabetic index</a> </ul> EOF close OUT; } # 1}}} sub write_forgebar { open(OUT,">$catdir/forgebar.html") or die "Could not open index/forgebar.html"; print OUT <Octave Forge site navigator $forgebar EOF } sub download_ref { # download_ref($func,$desc) returns a link to download $func described by $desc my ($func) = @@_; my $path = $function_description{$func}[0]; if ($path ne "" && $path !~ /^$OCTAVE/) { return "[octave-forge/$path]"; } elsif ($path =~ /^$OCTAVE/) { $path =~ s/^$OCTAVE//; return "[octave$path]"; } else { return ""; } } sub write_index { # 1{{{ open(OUT,">$catdir/index.in") or die "Could not open $catdir/index.in"; print OUT <This page contains the documentation for individual functions provided by Octave and Octave-Forge. The documentation can either be accessed by category or alphabetically. Simply use the menus at the left of the page.

__TRAILER__ EOF close OUT; } # 1}}} sub write_TBnavbar { # 1{{{ my $openTB = shift; my $file = "menu"; $file = "nav$openTB" if $openTB ne ""; open(OUT,">$catdir/$file.include") or die "Could not open $catdir/$file.include"; #print OUT "Home\n"; #print OUT "\n"; close OUT; } # 1}}} sub write_TBdetails { # 1{{{ my $TB = trim(shift); my $file = "$catdir/$TB.in"; open(OUT, ">$file") or die "Cannot write $file: $!\n"; print OUT <$TB_description{$TB} EOF # summary list of categories print OUT "
    \n"; foreach my $cat ( cat_list($TB) ) { my $anchor = cat_anchor($cat); print OUT "
  • $cat
    • \n"; } print OUT "
\n"; # Each category has a table of its functions and their descriptions. foreach my $cat ( cat_list($TB) ) { my $anchor = cat_anchor($cat); print OUT "

$cat

\n"; print OUT "
\n"; foreach my $func ( cat_funcs($TB,$cat) ) { # column 1: the function (x-ref to full description in # cvs-tree's html file) print OUT "
",func_ref($func,$func),"
\n"; print OUT "
", download_ref($func), "
\n"; # column 2: the description, if it exists # print OUT "
",html_desc($func),"
\n"; } print OUT "
\n"; } print OUT "__TRAILER__\n"; close(OUT); } # 1}}} sub write_package_details { # 1{{{ my $packdir = shift; my $package; my $title; my $desc = sprintf("%s/DESCRIPTION", $packdir); #open(IN, $desc) or die "Cannot read $desc: $!\n"; open(IN, $desc) or return; while() { if (/^[Nn]ame:/) { chomp; s/^[Nn]ame:\s*//; s/\s*$//; $package = lc($_); } elsif (/^[Tt]itle:/) { chomp; s/^[Tt]itle:\s*//; s/\s*$//; $title = $_; } } close(IN); my $file = "$catdir/funref_$package.in"; open(OUT, ">$file") or die "Cannot write $file: $!\n"; print OUT <\n"; foreach my $func ( pack_list($packdir) ) { # column 1: the function (x-ref to full description in # cvs-tree's html file) print OUT "
",func_ref($func,$func),"
\n"; print OUT "
", download_ref($func), "
\n"; # column 2: the description, if it exists # print OUT "
",html_desc($func),"
\n"; } print OUT "\n"; print OUT "__TRAILER__\n"; close(OUT); } # 1}}} sub write_alphabetic_navbar { # 1{{{ open(OUT,">$catdir/alphabetic.include") or die "Could not open $catdir/alphabetic.include"; my $A_to_Z = ""; foreach (first_letters (indexed_funcs())) { $A_to_Z .= letter_option($_) . "\\\n"; } #my $select = "\n"; print OUT $A_to_Z; close OUT; } # 1}}} sub oldnavbar { # 1{{{ my $max_TB_across_top = 7; my $all_toolboxes = "
\n"; my $n = 0; foreach my $TB (toolbox_list()) { ++$n; if ($n > $max_TB_across_top) { $n = 0; $all_toolboxes .= "$TB
"; } else { $all_toolboxes .= "$TB | "; } } $all_toolboxes =~ s/\s+\|\s*$//; # strip last pipe separator $all_toolboxes .= "

"; my $A_to_Z = ""; foreach (first_letters (indexed_funcs())) { $A_to_Z .= letter_ref($_); $A_to_Z .= " | "; } $A_to_Z =~ s/\s+\|\s*$//; # strip last pipe separator my $all_toolboxes_A_Z = $all_toolboxes . "$A_to_Z
\n"; $all_toolboxes .= "\n"; } # 1}}} sub print_missing { my $printmissing = 1; foreach my $TB ( toolbox_list() ) { my $printTB = 1; foreach my $cat ( cat_list($TB) ) { my $printcat = 1; foreach my $func ( cat_funcs($TB,$cat) ) { if (! defined $function_description{$func}[1] && ! defined $index_notes{$func} ) { print "missing functions:" if $printmissing; print "\n [$TB]" if $printTB; print "\n $cat\n >" if $printcat; print " $func"; $printTB = 0; $printcat = 0; $printmissing = 0; } } } } print "\n" unless $printmissing; } sub write_ascii { # 1{{{ # output all toolboxes as a contents.m file my ($prefix) = @@_; my $indent = 16 - 3 - length($prefix); # XXX FIXME XXX add an option to spit out contents.m # XXX FIXME XXX what if there is no toolbox? # XXX FIXME XXX preserve category order foreach my $TB ( toolbox_list() ) { print wrap($prefix,$prefix,$TB_description{$TB}),"\n$prefix\n"; foreach my $cat ( cat_list($TB) ) { print wrap($prefix,$prefix,$cat), "\n"; foreach my $func ( cat_funcs($TB,$cat) ) { my $entry = sprintf("%-*s %s",$indent,$func,ascii_desc($func)); print wrap("$prefix","$prefix\t\t"," $entry"), "\n"; } print "$prefix\n"; } } } # 1}}} sub cat_ref { # 1{{{ # cat_ref($TB,$cat,$ref) returns an html link to $cat described by $ref my ($TB,$cat,$ref) = @@_; my $anchor = cat_anchor($cat); return "$ref"; } # 1}}} sub cat_ref_up { # 1{{{ # cat_ref($TB,$cat,$ref) returns an html link to $cat described by $ref my ($TB,$cat,$ref) = @@_; my $anchor = cat_anchor($cat); return "$ref"; } # 1}}} sub cat_anchor { # 1{{{ # cat_anchor($cat) returns the anchor word generated for category $cat my ($cat) = @@_; $cat =~ s/\W+//g; return $cat; } # 1}}} sub func_ref { # 1{{{ # func_ref($func) returns an html link to $func described by $ref my ($func,$ref) = @@_; if ( defined $function_description{$func}[2] && $function_description{$func}[2] ne "") { my $ret = $ref; $ret =~ s|<|<|g; $ret =~ s|>|>|g; return "$ret"; } elsif ( $ref ne $func ) { # XXX FIXME XXX do we want "$ref ($func)"? Check how it is called. my $ret = $ref; $ret =~ s|<|<|g; $ret =~ s|>|>|g; return $ret; } else { my $ret = $ref; $ret =~ s|<|<|g; $ret =~ s|>|>|g; return $ret; } } # 1}}} sub split_long_name { # 1{{{ # html magic to break long variable/function names # XXX FIXME XXX this function is probably not used my ( $nicefunc ) = @@_; # $nicefunc =~ s/([^_])_([^_])/$1_ $2/g; return $nicefunc; } # 1}}} sub first_letters { # 1{{{ # return a list of all first letters in the arguments # The argument list must come sorted with a case-insensitive sort. my $Letter = chr(0); my @@ret = (); foreach my $name ( @@_ ) { # Check if need to go to the next letter if (uc(substr($name, 0, 1)) ne $Letter) { $Letter = uc(substr($name, 0, 1)); push @@ret, $Letter; } } return @@ret; } # 1}}} sub letter_file { # 1{{{ return "$_.html" if /[A-Z]/; return "A.html" if $_ lt "A"; return "Z.html"; } # 1}}} sub deping { # 1{{{ return "\\'" if $_ eq "'"; return "$_"; } # 1}}} sub letter_ref { # 1{{{ # letter_ref($letter) returns a link to the letter return "$_"; } # 1}}} sub letter_option { # 1{{{ # letter_option($letter) returns a link to the letter #return ""; return "" . deping($_) . "
"; } # 1}}} sub ascii_desc { # 1{{{ # ascii_desc($func) returns a decription of $func using ascii markup my ( $func ) = @@_; if (! defined $function_description{$func}[1] ) { my $notes = $index_notes{$func}; $notes = "" if $notes eq ""; # convert "desc" to "desc (link)" $notes =~ s|]*)\"?>([^<]*)|$2 ($1)|g; # strip all remaining html formatting $notes =~ s|<[^>]*>||g; return $notes; } else { my $desc = $function_description{$func}[1]; if ($desc eq "") { return ""; } else { return $desc; } } } #}}} sub html_desc { # 1{{{ # html_desc($func) returns a description of $func using html markup my ( $func ) = @@_; my $notes = $index_notes{$func}; if (! defined $function_description{$func}[1] ) { $notes = "not implemented" if $notes eq ""; # shut of the bold italics during "code" formatting $notes =~ s|||g; $notes =~ s|||g; $notes =~ s|&|&|; $notes =~ s|(\w+)|$1|g; return "$notes"; } else { print "ignoring $func = $notes\n" if $notes ne ""; my $desc = $function_description{$func}[1]; $desc =~ s|&|&|g; $desc =~ s|>|>|g; $desc =~ s|<|<|g; if ($desc eq "") { return "no description"; } else { return $desc; } } } # 1}}} sub long_desc { my ( $func ) = @@_; my $body = $function_description{$func}[2]; if ($body =~ /^\s*-[*]- texinfo -[*]-/) { $body = info2html($func, $body); } elsif ($body ne "") { $body = "
$body
"; } return $body } # 1}}} sub info2html_texi2html { # 1{{{ # run body through texi2html to produce html my ( $func, $body ) = @@_; $body =~ s/^\s*-[*]- texinfo -[*]-//; open(SRC, ">$func.texi"); print SRC "\@@macro seealso {args}\n\n\@@noindent\nSee also: \\args\\.\n\@@end macro\n"; print SRC "BEGINCUT $body ENDCUT"; close SRC; system ("texi2html -expand info $tmpdir/$func.texi"); open(SRC, "<$func.html"); my @@lines = ; close SRC; $body = join("",@@lines); my $start = index($body,"BEGINCUT") + 8; my $stop = index($body,"ENDCUT"); $body = substr($body,$start,$stop-$start); unlink "$func.texi", "$func.html"; } # 1}}} sub info2html { # 1{{{ # run body through makeinfo to produce html my ( $func, $body ) = @@_; $body =~ s/^\s*-[*]- texinfo -[*]-//; my $cmd = "makeinfo --fill-column 80 --no-warn --no-validate --force --html --ifinfo -o -"; open3(*Writer, *Reader, *Errer, $cmd) or die "Could not run info"; #SH# print Writer "\@@macro seealso {args}\n\n\@@noindent\nSee also: \\args\\.\n\@@end macro\n"; print Writer "\@@macro seealso{args}\n m4_changequote(`, ')\n seealso(\\args\\)\n m4_changequote([[[, ]]])\n\@@end macro\n"; # I have no idea why but makeinfo is introducing some weirdness with

# at the front of the document. The following works for my particular # version but I have little hope for it working in general print Writer "-CUT HERE $body"; close(Writer); my @@lines = ; close(Reader); my @@err = ; close(Errer); waitpid(-1,&WNOHANG); # strip everything before and after $body = join("",@@lines); my $start = index($body,"CUT HERE") + 8; my $stop = index($body,"$1|g; return $body; } # 1}}} sub toolbox_list { # 1{{{ # toolbox_list() returns an ordered list of toolboxes. return sort { uc($a) cmp uc($b) } keys %index_by_TB_cat; } # 1}}} sub toolbox_list_sorted_by_desc { # 1{{{ # toolbox_list_sorted_by_desc() returns an ordered list of toolboxes. return sort { uc($TB_description{$a}) cmp uc($TB_description{$b}) } keys %index_by_TB_cat; } # 1}}} sub package_list { # 1{{{ # package_list() returns an ordered list of package directories. return sort { uc($a) cmp uc($b) } keys %index_by_package; } # 1}}} sub cat_list { # 1{{{ # cat_list($TB) returns an ordered list of categories in a toolbox $TB. my ($TB) = @@_; return sort keys %{$index_by_TB_cat{$TB}}; } # 1}}} sub pack_list { # 1{{{ # pack_list($package) returns an ordered list of functions in a package directory. my ($package) = @@_; return sort @@{$index_by_package{$package}}; } # 1}}} sub cat_funcs { # 1{{{ # cat_funcs($TB,$cat) returns an ordered list of functions in $TB,$cat my ($TB,$cat) = @@_; return sort { uc($a) cmp uc($b) } @@{$index_by_TB_cat{$TB}{$cat}} } # 1}}} sub indexed_funcs { # 1{{{ # indexed_funcs() returns an ordered list of all functions in the index return sort { uc($a) cmp uc($b) } keys %index_by_function; } # 1}}} sub forge_funcs { # 1{{{ # forge_funcs() returns an ordered list of functions only found in octave forge return sort { uc($a) cmp uc($b) } keys %octave_forge_function; } # 1}}} sub scanned_funcs { # 1{{{ # scanned_funcs() returns an ordered list of all functions found in m-files and oct-files return sort { uc($a) cmp uc($b) } %function_description; } # 1}}} sub trim($) { # This functions trims spaces from the beginning and end of a string my $string = shift; $string =~ s/^\s+//; $string =~ s/\s+$//; return $string; } __END__ This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, see . This program is granted to the public domain. THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. @ gsl-1.0.8/doc/RCS/texput.log,v0000644000175000017500000000063211201030376013577 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @# @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @This is TeX, Version 3.141592 (Web2C 7.5.4) (format=tex 2008.5.11) 14 MAY 2008 14:44 **gsl.gsltexi ! Emergency stop. <*> gsl.gsltexi *** (job aborted, file error in nonstop mode) No pages of output. @ gsl-1.0.8/doc/RCS/mk_pdf_dvi,v0000755000175000017500000000055011201030376013572 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @# @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @ #!/bin/bash cp ../src/gsl*cc ./$1.cc ./mkdoc >$1.doc ./mktexi_inc $1.doc >$1.texi tex -interaction batchmode $1.texi texi2pdf -b $1.texi dvips -o $1.ps $1.dvi @ gsl-1.0.8/doc/RCS/gsl.cc,v0000644000175000017500000076024011201030376012647 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @// @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @// *** DO NOT EDIT *** this file is generated by buildgsl_sf.sh /* Copyright (C) 2004 Teemu Ikonen This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, see . */ #include #include #include #include void octave_gsl_errorhandler (const char * reason, const char * file, int line, int gsl_errno) { error("GSL error %d at %s, line %d: %s\n", gsl_errno, file, line, reason); } DEFUN_DLD (gsl_sf, args, nargout, "-*- texinfo -*-\n\ @@deftypefn {Loadable Function} {} gsl_sf ()\n\ \n\ Octave bindings to the GNU Scientific Library. All GSL functions can be\n\ called with by the GSL names within octave.\n\ @@end deftypefn") { usage("gsl_sf"); return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(clausen, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} clausen (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} clausen (@@dots{})\n\ \n\ The Clausen function is defined by the following integral,\n\ \n\ Cl_2(x) = - \\int_0^x dt \\log(2 \\sin(t/2))\n\ \n\ It is related to the dilogarithm by Cl_2(\\theta) = \\Im Li_2(\\exp(i \\theta)).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_clausen (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_clausen_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(dawson, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} dawson (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} dawson (@@dots{})\n\ \n\ The Dawson integral is defined by \\exp(-x^2) \\int_0^x dt \\exp(t^2).\n\ A table of Dawson integral can be found in Abramowitz & Stegun, Table 7.5. \n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_dawson (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_dawson_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(debye_1, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} debye_1 (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_1 (@@dots{})\n\ \n\ The Debye functions are defined by the integral \n\ \n\ D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)).\n\ \n\ For further information see Abramowitz & Stegun, Section 27.1.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_debye_1 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_debye_1_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(debye_2, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} debye_2 (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_2 (@@dots{})\n\ \n\ The Debye functions are defined by the integral\n\ \n\ D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)).\n\ \n\ For further information see Abramowitz & Stegun, Section 27.1.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_debye_2 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_debye_2_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(debye_3, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} debye_3 (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_3 (@@dots{})\n\ \n\ The Debye functions are defined by the integral\n\ \n\ D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)).\n\ \n\ For further information see Abramowitz & Stegun, Section 27.1.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_debye_3 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_debye_3_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(debye_4, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} debye_4 (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_4 (@@dots{})\n\ \n\ The Debye functions are defined by the integral\n\ \n\ D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)).\n\ \n\ For further information see Abramowitz & Stegun, Section 27.1.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_debye_4 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_debye_4_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(erf_gsl, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} erf_gsl (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erf_gsl (@@dots{})\n\ \n\ These routines compute the error function \n\ erf(x) = (2/\\sqrt(\\pi)) \\int_0^x dt \\exp(-t^2).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_erf (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_erf_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(erfc_gsl, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} erfc_gsl (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erfc_gsl (@@dots{})\n\ \n\ These routines compute the complementary error function \n\ erfc(x) = 1 - erf(x) = (2/\\sqrt(\\pi)) \\int_x^\\infty \\exp(-t^2).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_erfc (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_erfc_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(log_erfc, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} log_erfc (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} log_erfc (@@dots{})\n\ \n\ These routines compute the logarithm of the complementary error\n\ function \\log(\\erfc(x)).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_log_erfc (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_log_erfc_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(erf_Z, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} erf_Z (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erf_Z (@@dots{})\n\ \n\ These routines compute the Gaussian probability function \n\ Z(x) = (1/(2\\pi)) \\exp(-x^2/2).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_erf_Z (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_erf_Z_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(erf_Q, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} erf_Q (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erf_Q (@@dots{})\n\ \n\ These routines compute the upper tail of the Gaussian probability\n\ function Q(x) = (1/(2\\pi)) \\int_x^\\infty dt \\exp(-t^2/2).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_erf_Q (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_erf_Q_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(hazard, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} hazard (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} hazard (@@dots{})\n\ \n\ The hazard function for the normal distrbution, also known as the \n\ inverse Mill\\'s ratio, is defined as \n\ h(x) = Z(x)/Q(x) = \\sqrt@@{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2)@@}. \n\ It decreases rapidly as x approaches -\\infty and asymptotes to \n\ h(x) \\sim x as x approaches +\\infty.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_hazard (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_hazard_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(expm1, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} expm1 (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expm1 (@@dots{})\n\ \n\ These routines compute the quantity \\exp(x)-1 using an algorithm that \n\ is accurate for small x.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_expm1 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_expm1_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(exprel, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} exprel (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} exprel (@@dots{})\n\ \n\ These routines compute the quantity (\\exp(x)-1)/x using an algorithm \n\ that is accurate for small x. For small x the algorithm is based on \n\ the expansion (\\exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\dots.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_exprel (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_exprel_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(exprel_2, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} exprel_2 (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} exprel_2 (@@dots{})\n\ \n\ These routines compute the quantity 2(\\exp(x)-1-x)/x^2 using an\n\ algorithm that is accurate for small x. For small x the algorithm is \n\ based on the expansion \n\ 2(\\exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\dots.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_exprel_2 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_exprel_2_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(expint_E1, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} expint_E1 (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_E1 (@@dots{})\n\ \n\ These routines compute the exponential integral E_1(x),\n\ \n\ E_1(x) := Re \\int_1^\\infty dt \\exp(-xt)/t.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_expint_E1 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_expint_E1_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(expint_E2, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} expint_E2 (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_E2 (@@dots{})\n\ \n\ These routines compute the second-order exponential integral E_2(x),\n\ \n\ E_2(x) := \\Re \\int_1^\\infty dt \\exp(-xt)/t^2.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_expint_E2 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_expint_E2_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(expint_Ei, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} expint_Ei (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_Ei (@@dots{})\n\ \n\ These routines compute the exponential integral E_i(x),\n\ \n\ Ei(x) := - PV(\\int_@@{-x@@}^\\infty dt \\exp(-t)/t)\n\ \n\ where PV denotes the principal value of the integral.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_expint_Ei (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_expint_Ei_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(Shi, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} Shi (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Shi (@@dots{})\n\ \n\ These routines compute the integral Shi(x) = \\int_0^x dt \\sinh(t)/t.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_Shi (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_Shi_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(Chi, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} Chi (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Chi (@@dots{})\n\ \n\ These routines compute the integral \n\ \n\ Chi(x) := Re[ \\gamma_E + \\log(x) + \\int_0^x dt (\\cosh[t]-1)/t] , \n\ \n\ where \\gamma_E is the Euler constant.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_Chi (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_Chi_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(expint_3, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} expint_3 (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_3 (@@dots{})\n\ \n\ These routines compute the exponential integral \n\ Ei_3(x) = \\int_0^x dt \\exp(-t^3) for x >= 0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_expint_3 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_expint_3_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(Si, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} Si (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Si (@@dots{})\n\ \n\ These routines compute the Sine integral Si(x) = \\int_0^x dt \\sin(t)/t.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_Si (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_Si_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(Ci, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} Ci (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Ci (@@dots{})\n\ \n\ These routines compute the Cosine integral \n\ Ci(x) = -\\int_x^\\infty dt \\cos(t)/t for x > 0. \n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_Ci (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_Ci_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(atanint, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} atanint (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} atanint (@@dots{})\n\ \n\ These routines compute the Arctangent integral \n\ AtanInt(x) = \\int_0^x dt \\arctan(t)/t. \n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_atanint (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_atanint_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(fermi_dirac_mhalf, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_mhalf (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_mhalf (@@dots{})\n\ \n\ These routines compute the complete Fermi-Dirac integral F_@@{-1/2@@}(x).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_fermi_dirac_mhalf (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_fermi_dirac_mhalf_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(fermi_dirac_half, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_half (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_half (@@dots{})\n\ \n\ These routines compute the complete Fermi-Dirac integral F_@@{1/2@@}(x).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_fermi_dirac_half (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_fermi_dirac_half_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(fermi_dirac_3half, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_3half (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_3half (@@dots{})\n\ \n\ These routines compute the complete Fermi-Dirac integral F_@@{3/2@@}(x).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_fermi_dirac_3half (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_fermi_dirac_3half_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(gamma_gsl, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} gamma_gsl (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} gamma_gsl (@@dots{})\n\ \n\ These routines compute the Gamma function \\Gamma(x), subject to x not \n\ being a negative integer. The function is computed using the real \n\ Lanczos method. The maximum value of x such that \\Gamma(x) is not \n\ considered an overflow is given by the macro GSL_SF_GAMMA_XMAX and is 171.0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_gamma (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_gamma_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(lngamma_gsl, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} lngamma_gsl (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lngamma_gsl (@@dots{})\n\ \n\ These routines compute the logarithm of the Gamma function, \n\ \\log(\\Gamma(x)), subject to x not a being negative integer. \n\ For x<0 the real part of \\log(\\Gamma(x)) is returned, which is \n\ equivalent to \\log(|\\Gamma(x)|). The function is computed using \n\ the real Lanczos method.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_lngamma (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_lngamma_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(gammastar, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} gammastar (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} gammastar (@@dots{})\n\ \n\ These routines compute the regulated Gamma Function \\Gamma^*(x) \n\ for x > 0. The regulated gamma function is given by,\n\ \n\ \\Gamma^*(x) = \\Gamma(x)/(\\sqrt@@{2\\pi@@} x^@@{(x-1/2)@@} \\exp(-x))\n\ = (1 + (1/12x) + ...) for x \\to \\infty\n\ \n\ and is a useful suggestion of Temme. \n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_gammastar (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_gammastar_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(gammainv_gsl, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} gammainv_gsl (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} gammainv_gsl (@@dots{})\n\ \n\ These routines compute the reciprocal of the gamma function, 1/\\Gamma(x) using the real Lanczos method.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_gammainv (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_gammainv_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(lambert_W0, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} lambert_W0 (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lambert_W0 (@@dots{})\n\ \n\ These compute the principal branch of the Lambert W function, W_0(x).\n\ \n\ Lambert\\'s W functions, W(x), are defined to be solutions of the\n\ equation W(x) \\exp(W(x)) = x. This function has multiple branches \n\ for x < 0; however, it has only two real-valued branches. \n\ We define W_0(x) to be the principal branch, where W > -1 for x < 0, \n\ and W_@@{-1@@}(x) to be the other real branch, where W < -1 for x < 0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_lambert_W0 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_lambert_W0_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(lambert_Wm1, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} lambert_Wm1 (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lambert_Wm1 (@@dots{})\n\ \n\ These compute the secondary real-valued branch of the Lambert \n\ W function, W_@@{-1@@}(x).\n\ \n\ Lambert\\'s W functions, W(x), are defined to be solutions of the\n\ equation W(x) \\exp(W(x)) = x. This function has multiple branches \n\ for x < 0; however, it has only two real-valued branches. \n\ We define W_0(x) to be the principal branch, where W > -1 for x < 0, \n\ and W_@@{-1@@}(x) to be the other real branch, where W < -1 for x < 0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_lambert_Wm1 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_lambert_Wm1_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(log_1plusx, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} log_1plusx (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} log_1plusx (@@dots{})\n\ \n\ These routines compute \\log(1 + x) for x > -1 using an algorithm that\n\ is accurate for small x.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_log_1plusx (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_log_1plusx_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(log_1plusx_mx, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} log_1plusx_mx (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} log_1plusx_mx (@@dots{})\n\ \n\ These routines compute \\log(1 + x) - x for x > -1 using an algorithm \n\ that is accurate for small x.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_log_1plusx_mx (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_log_1plusx_mx_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(psi, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} psi (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi (@@dots{})\n\ \n\ These routines compute the digamma function \\psi(x) for general x, \n\ x \\ne 0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_psi (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_psi_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(psi_1piy, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} psi_1piy (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi_1piy (@@dots{})\n\ \n\ These routines compute the real part of the digamma function on \n\ the line 1+i y, Re[\\psi(1 + i y)].\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_psi_1piy (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_psi_1piy_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(synchrotron_1, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} synchrotron_1 (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} synchrotron_1 (@@dots{})\n\ \n\ These routines compute the first synchrotron function \n\ x \\int_x^\\infty dt K_@@{5/3@@}(t) for x >= 0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_synchrotron_1 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_synchrotron_1_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(synchrotron_2, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} synchrotron_2 (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} synchrotron_2 (@@dots{})\n\ \n\ These routines compute the second synchrotron function \n\ x K_@@{2/3@@}(x) for x >= 0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_synchrotron_2 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_synchrotron_2_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(transport_2, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} transport_2 (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_2 (@@dots{})\n\ \n\ These routines compute the transport function J(2,x).\n\ \n\ The transport functions J(n,x) are defined by the integral\n\ representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_transport_2 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_transport_2_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(transport_3, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} transport_3 (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_3 (@@dots{})\n\ \n\ These routines compute the transport function J(3,x).\n\ \n\ The transport functions J(n,x) are defined by the integral\n\ representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_transport_3 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_transport_3_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(transport_4, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} transport_4 (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_4 (@@dots{})\n\ \n\ These routines compute the transport function J(4,x).\n\ \n\ The transport functions J(n,x) are defined by the integral\n\ representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_transport_4 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_transport_4_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(transport_5, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} transport_5 (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_5 (@@dots{})\n\ \n\ These routines compute the transport function J(5,x).\n\ \n\ The transport functions J(n,x) are defined by the integral\n\ representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_transport_5 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_transport_5_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(sinc_gsl, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} sinc_gsl (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} sinc_gsl (@@dots{})\n\ \n\ These routines compute \\sinc(x) = \\sin(\\pi x) / (\\pi x) for any value of x.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_sinc (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_sinc_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(lnsinh, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} lnsinh (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lnsinh (@@dots{})\n\ \n\ These routines compute \\log(\\sinh(x)) for x > 0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_lnsinh (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_lnsinh_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(lncosh, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} lncosh (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lncosh (@@dots{})\n\ \n\ These routines compute \\log(\\cosh(x)) for any x.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_lncosh (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_lncosh_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(zeta, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} zeta (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} zeta (@@dots{})\n\ \n\ These routines compute the Riemann zeta function \\zeta(s) for \n\ arbitrary s, s \\ne 1.\n\ \n\ The Riemann zeta function is defined by the infinite sum \n\ \\zeta(s) = \\sum_@@{k=1@@}^\\infty k^@@{-s@@}. \n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_zeta (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_zeta_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(eta, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} eta (@@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} eta (@@dots{})\n\ \n\ These routines compute the eta function \\eta(s) for arbitrary s.\n\ \n\ The eta function is defined by \\eta(s) = (1-2^@@{1-s@@}) \\zeta(s).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_eta (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_eta_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_Jn, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} bessel_Jn (@@var{n}, @@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Jn (@@dots{})\n\ \n\ These routines compute the regular cylindrical Bessel function of\n\ order n, J_n(x).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Jn (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Jn_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Jn (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Jn_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Jn (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Jn_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_Yn, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} bessel_Yn (@@var{n}, @@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Yn (@@dots{})\n\ \n\ These routines compute the irregular cylindrical Bessel function of \n\ order n, Y_n(x), for x>0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Yn (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Yn_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Yn (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Yn_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Yn (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Yn_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_In, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} bessel_In (@@var{n}, @@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_In (@@dots{})\n\ \n\ These routines compute the regular modified cylindrical Bessel\n\ function of order n, I_n(x).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_In (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_In_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_In (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_In_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_In (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_In_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_In_scaled, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} bessel_In_scaled (@@var{n}, @@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_In_scaled (@@dots{})\n\ \n\ These routines compute the scaled regular modified cylindrical Bessel\n\ function of order n, \\exp(-|x|) I_n(x)\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_In_scaled (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_In_scaled_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_In_scaled (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_In_scaled_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_In_scaled (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_In_scaled_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_Kn, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} bessel_Kn (@@var{n}, @@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Kn (@@dots{})\n\ \n\ These routines compute the irregular modified cylindrical Bessel\n\ function of order n, K_n(x), for x > 0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Kn (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Kn_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Kn (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Kn_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Kn (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Kn_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_Kn_scaled, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} bessel_Kn_scaled (@@var{n}, @@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Kn_scaled (@@dots{})\n\ \n\ \n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Kn_scaled (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Kn_scaled_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Kn_scaled (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Kn_scaled_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Kn_scaled (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Kn_scaled_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_jl, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} bessel_jl (@@var{n}, @@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_jl (@@dots{})\n\ \n\ These routines compute the regular spherical Bessel function of \n\ order l, j_l(x), for l >= 0 and x >= 0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_jl (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_jl_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_jl (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_jl_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_jl (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_jl_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_yl, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} bessel_yl (@@var{n}, @@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_yl (@@dots{})\n\ \n\ These routines compute the irregular spherical Bessel function of\n\ order l, y_l(x), for l >= 0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_yl (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_yl_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_yl (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_yl_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_yl (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_yl_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_il_scaled, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} bessel_il_scaled (@@var{n}, @@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_il_scaled (@@dots{})\n\ \n\ These routines compute the scaled regular modified spherical Bessel\n\ function of order l, \\exp(-|x|) i_l(x)\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_il_scaled (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_il_scaled_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_il_scaled (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_il_scaled_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_il_scaled (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_il_scaled_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_kl_scaled, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} bessel_kl_scaled (@@var{n}, @@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_kl_scaled (@@dots{})\n\ \n\ These routines compute the scaled irregular modified spherical Bessel\n\ function of order l, \\exp(x) k_l(x), for x>0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_kl_scaled (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_kl_scaled_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_kl_scaled (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_kl_scaled_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_kl_scaled (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_kl_scaled_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(exprel_n, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} exprel_n (@@var{n}, @@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} exprel_n (@@dots{})\n\ \n\ These routines compute the N-relative exponential, which is the n-th\n\ generalization of the functions gsl_sf_exprel and gsl_sf_exprel2. The\n\ N-relative exponential is given by,\n\ \n\ exprel_N(x) = N!/x^N (\\exp(x) - \\sum_@@{k=0@@}^@@{N-1@@} x^k/k!)\n\ = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ...\n\ = 1F1 (1,1+N,x)\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_exprel_n (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_exprel_n_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_exprel_n (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_exprel_n_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_exprel_n (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_exprel_n_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(fermi_dirac_int, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_int (@@var{n}, @@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_int (@@dots{})\n\ \n\ These routines compute the complete Fermi-Dirac integral with an\n\ integer index of j, F_j(x) = (1/\\Gamma(j+1)) \\int_0^\\infty dt (t^j\n\ /(\\exp(t-x)+1)).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_fermi_dirac_int (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_fermi_dirac_int_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_fermi_dirac_int (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_fermi_dirac_int_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_fermi_dirac_int (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_fermi_dirac_int_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(taylorcoeff, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} taylorcoeff (@@var{n}, @@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} taylorcoeff (@@dots{})\n\ \n\ These routines compute the Taylor coefficient x^n / n! \n\ for x >= 0, n >= 0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_taylorcoeff (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_taylorcoeff_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_taylorcoeff (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_taylorcoeff_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_taylorcoeff (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_taylorcoeff_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(legendre_Pl, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} legendre_Pl (@@var{n}, @@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_Pl (@@dots{})\n\ \n\ These functions evaluate the Legendre polynomial P_l(x) for a specific\n\ value of l, x subject to l >= 0, |x| <= 1\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_Pl (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_Pl_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_Pl (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_Pl_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_Pl (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_Pl_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(legendre_Ql, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} legendre_Ql (@@var{n}, @@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_Ql (@@dots{})\n\ \n\ These routines compute the Legendre function Q_l(x) for x > -1, x != 1\n\ and l >= 0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_Ql (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_Ql_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_Ql (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_Ql_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_Ql (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_Ql_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(psi_n, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} psi_n (@@var{n}, @@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi_n (@@dots{})\n\ \n\ These routines compute the polygamma function \\psi^@@{(m)@@}(x) \n\ for m >= 0, x > 0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_psi_n (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_psi_n_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_psi_n (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_psi_n_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_psi_n (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_psi_n_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_Jnu, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} bessel_Jnu (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Jnu (@@dots{})\n\ \n\ These routines compute the regular cylindrical Bessel function of\n\ fractional order nu, J_\\nu(x).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Jnu (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Jnu_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Jnu (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Jnu_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Jnu (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Jnu_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_Ynu, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} bessel_Ynu (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Ynu (@@dots{})\n\ \n\ These routines compute the irregular cylindrical Bessel function of\n\ fractional order nu, Y_\\nu(x).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Ynu (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Ynu_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Ynu (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Ynu_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Ynu (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Ynu_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_Inu, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} bessel_Inu (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Inu (@@dots{})\n\ \n\ These routines compute the regular modified Bessel function of\n\ fractional order nu, I_\\nu(x) for x>0, \\nu>0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Inu (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Inu_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Inu (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Inu_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Inu (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Inu_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_Inu_scaled, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} bessel_Inu_scaled (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Inu_scaled (@@dots{})\n\ \n\ These routines compute the scaled regular modified Bessel function of\n\ fractional order nu, \\exp(-|x|)I_\\nu(x) for x>0, \\nu>0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Inu_scaled (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Inu_scaled_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Inu_scaled (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Inu_scaled_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Inu_scaled (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Inu_scaled_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_Knu, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} bessel_Knu (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Knu (@@dots{})\n\ \n\ These routines compute the irregular modified Bessel function of\n\ fractional order nu, K_\\nu(x) for x>0, \\nu>0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Knu (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Knu_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Knu (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Knu_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Knu (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Knu_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_lnKnu, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} bessel_lnKnu (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_lnKnu (@@dots{})\n\ \n\ These routines compute the logarithm of the irregular modified Bessel\n\ function of fractional order nu, \\ln(K_\\nu(x)) for x>0, \\nu>0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_lnKnu (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_lnKnu_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_lnKnu (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_lnKnu_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_lnKnu (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_lnKnu_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_Knu_scaled, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} bessel_Knu_scaled (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Knu_scaled (@@dots{})\n\ \n\ These routines compute the scaled irregular modified Bessel function\n\ of fractional order nu, \\exp(+|x|) K_\\nu(x) for x>0, \\nu>0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Knu_scaled (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Knu_scaled_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Knu_scaled (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Knu_scaled_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Knu_scaled (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Knu_scaled_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(exp_mult, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} exp_mult (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} exp_mult (@@dots{})\n\ \n\ These routines exponentiate x and multiply by the factor y to return\n\ the product y \\exp(x).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_exp_mult (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_exp_mult_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_exp_mult (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_exp_mult_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_exp_mult (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_exp_mult_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(fermi_dirac_inc_0, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} fermi_dirac_inc_0 (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} fermi_dirac_inc_0 (@@dots{})\n\ \n\ These routines compute the incomplete Fermi-Dirac integral with an\n\ index of zero, F_0(x,b) = \\ln(1 + e^@@{b-x@@}) - (b-x).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_fermi_dirac_inc_0 (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_fermi_dirac_inc_0_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_fermi_dirac_inc_0 (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_fermi_dirac_inc_0_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_fermi_dirac_inc_0 (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_fermi_dirac_inc_0_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(poch, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} poch (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} poch (@@dots{})\n\ \n\ These routines compute the Pochhammer symbol \n\ \n\ (a)_x := \\Gamma(a + x)/\\Gamma(a), \n\ \n\ subject to a and a+x not being negative integers. The Pochhammer\n\ symbol is also known as the Apell symbol.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_poch (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_poch_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_poch (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_poch_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_poch (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_poch_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(lnpoch, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} lnpoch (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} lnpoch (@@dots{})\n\ \n\ These routines compute the logarithm of the Pochhammer symbol,\n\ \\log((a)_x) = \\log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_lnpoch (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_lnpoch_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_lnpoch (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_lnpoch_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_lnpoch (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_lnpoch_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(pochrel, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} pochrel (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} pochrel (@@dots{})\n\ \n\ These routines compute the relative Pochhammer symbol ((a,x) - 1)/x\n\ where (a,x) = (a)_x := \\Gamma(a + x)/\\Gamma(a).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_pochrel (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_pochrel_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_pochrel (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_pochrel_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_pochrel (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_pochrel_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(gamma_inc_Q, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} gamma_inc_Q (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} gamma_inc_Q (@@dots{})\n\ \n\ These routines compute the normalized incomplete Gamma Function \n\ Q(a,x) = 1/\\Gamma(a) \\int_x\\infty dt t^@@{a-1@@} \\exp(-t) for a > 0, x >= 0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_gamma_inc_Q (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_gamma_inc_Q_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_gamma_inc_Q (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_gamma_inc_Q_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_gamma_inc_Q (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_gamma_inc_Q_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(gamma_inc_P, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} gamma_inc_P (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} gamma_inc_P (@@dots{})\n\ \n\ These routines compute the complementary normalized incomplete Gamma\n\ Function P(a,x) = 1/\\Gamma(a) \\int_0^x dt t^@@{a-1@@} \\exp(-t) \n\ for a > 0, x >= 0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_gamma_inc_P (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_gamma_inc_P_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_gamma_inc_P (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_gamma_inc_P_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_gamma_inc_P (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_gamma_inc_P_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(gamma_inc, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} gamma_inc (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} gamma_inc (@@dots{})\n\ \n\ These functions compute the incomplete Gamma Function the\n\ normalization factor included in the previously defined functions:\n\ \\Gamma(a,x) = \\int_x\\infty dt t^@@{a-1@@} \\exp(-t) for a real and x >= 0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_gamma_inc (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_gamma_inc_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_gamma_inc (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_gamma_inc_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_gamma_inc (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_gamma_inc_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(beta_gsl, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} beta_gsl (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} beta_gsl (@@dots{})\n\ \n\ These routines compute the Beta Function, \n\ B(a,b) = \\Gamma(a)\\Gamma(b)/\\Gamma(a+b) for a > 0, b > 0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_beta (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_beta_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_beta (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_beta_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_beta (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_beta_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(lnbeta, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} lnbeta (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} lnbeta (@@dots{})\n\ \n\ These routines compute the logarithm of the Beta Function,\n\ \\log(B(a,b)) for a > 0, b > 0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_lnbeta (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_lnbeta_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_lnbeta (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_lnbeta_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_lnbeta (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_lnbeta_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(hyperg_0F1, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} hyperg_0F1 (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} hyperg_0F1 (@@dots{})\n\ \n\ These routines compute the hypergeometric function 0F1(c,x).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_hyperg_0F1 (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_0F1_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_hyperg_0F1 (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_0F1_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_hyperg_0F1 (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_0F1_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(conicalP_half, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} conicalP_half (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_half (@@dots{})\n\ \n\ These routines compute the irregular Spherical Conical Function\n\ P^@@{1/2@@}_@@{-1/2 + i \\lambda@@}(x) for x > -1.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_half (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_half_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_half (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_half_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_half (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_half_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(conicalP_mhalf, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} conicalP_mhalf (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_mhalf (@@dots{})\n\ \n\ These routines compute the regular Spherical Conical Function\n\ P^@@{-1/2@@}_@@{-1/2 + i \\lambda@@}(x) for x > -1.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_mhalf (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_mhalf_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_mhalf (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_mhalf_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_mhalf (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_mhalf_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(conicalP_0, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} conicalP_0 (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_0 (@@dots{})\n\ \n\ These routines compute the conical function P^0_@@{-1/2 + i \\lambda@@}(x)\n\ for x > -1.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_0 (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_0_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_0 (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_0_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_0 (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_0_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(conicalP_1, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} conicalP_1 (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_1 (@@dots{})\n\ \n\ These routines compute the conical function P^1_@@{-1/2 + i \\lambda@@}(x)\n\ for x > -1.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_1 (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_1_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_1 (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_1_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_1 (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_1_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(hzeta, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{z} =} hzeta (@@var{x}, @@var{y})\n\ @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} hzeta (@@dots{})\n\ \n\ These routines compute the Hurwitz zeta function \\zeta(s,q) \n\ for s > 1, q > 0.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_hzeta (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hzeta_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_hzeta (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hzeta_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_hzeta (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hzeta_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_Ai, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai (@@var{x}, @@var{mode})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai (@@dots{})\n\ \n\ These routines compute the Airy function Ai(x) with an accuracy\n\ specified by mode.\n\ \n\ The second argument @@var{mode} must be an integer corresponding to\n\ \n\ @@table @@asis\n\ @@item 0 = GSL_PREC_DOUBLE\n\ Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}.\n\ @@item 1 = GSL_PREC_SINGLE\n\ Single-precision, a relative accuracy of approximately @@code{10^-7}.\n\ @@item 2 = GSL_PREC_APPROX\n\ Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}.\n\ @@end table\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } if(!args(1).is_scalar_type()) { error("The mode must be scalar."); print_usage (); return octave_value(); } int mode = static_cast((args(1).array_value())(0)); if(mode < 0) mode = 0; else if(mode > 2) mode = 2; NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_Ai (x.xelem(i), mode); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_Ai_e (x.xelem(i), mode, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_Bi, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi (@@var{x}, @@var{mode})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi (@@dots{})\n\ \n\ These routines compute the Airy function Bi(x) with an accuracy\n\ specified by mode.\n\ \n\ The second argument @@var{mode} must be an integer corresponding to\n\ \n\ @@table @@asis\n\ @@item 0 = GSL_PREC_DOUBLE\n\ Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}.\n\ @@item 1 = GSL_PREC_SINGLE\n\ Single-precision, a relative accuracy of approximately @@code{10^-7}.\n\ @@item 2 = GSL_PREC_APPROX\n\ Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}.\n\ @@end table\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } if(!args(1).is_scalar_type()) { error("The mode must be scalar."); print_usage (); return octave_value(); } int mode = static_cast((args(1).array_value())(0)); if(mode < 0) mode = 0; else if(mode > 2) mode = 2; NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_Bi (x.xelem(i), mode); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_Bi_e (x.xelem(i), mode, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_Ai_scaled, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai_scaled (@@var{x}, @@var{mode})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai_scaled (@@dots{})\n\ \n\ These routines compute a scaled version of the Airy function \n\ S_A(x) Ai(x). For x>0 the scaling factor S_A(x) is \\exp(+(2/3) x^(3/2)), and\n\ is 1 for x<0.\n\ \n\ The second argument @@var{mode} must be an integer corresponding to\n\ \n\ @@table @@asis\n\ @@item 0 = GSL_PREC_DOUBLE\n\ Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}.\n\ @@item 1 = GSL_PREC_SINGLE\n\ Single-precision, a relative accuracy of approximately @@code{10^-7}.\n\ @@item 2 = GSL_PREC_APPROX\n\ Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}.\n\ @@end table\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } if(!args(1).is_scalar_type()) { error("The mode must be scalar."); print_usage (); return octave_value(); } int mode = static_cast((args(1).array_value())(0)); if(mode < 0) mode = 0; else if(mode > 2) mode = 2; NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_Ai_scaled (x.xelem(i), mode); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_Ai_scaled_e (x.xelem(i), mode, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_Bi_scaled, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi_scaled (@@var{x}, @@var{mode})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi_scaled (@@dots{})\n\ \n\ These routines compute a scaled version of the Airy function \n\ S_B(x) Bi(x). For x>0 the scaling factor S_B(x) is exp(-(2/3) x^(3/2)), and\n\ is 1 for x<0.\n\ \n\ The second argument @@var{mode} must be an integer corresponding to\n\ \n\ @@table @@asis\n\ @@item 0 = GSL_PREC_DOUBLE\n\ Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}.\n\ @@item 1 = GSL_PREC_SINGLE\n\ Single-precision, a relative accuracy of approximately @@code{10^-7}.\n\ @@item 2 = GSL_PREC_APPROX\n\ Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}.\n\ @@end table\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } if(!args(1).is_scalar_type()) { error("The mode must be scalar."); print_usage (); return octave_value(); } int mode = static_cast((args(1).array_value())(0)); if(mode < 0) mode = 0; else if(mode > 2) mode = 2; NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_Bi_scaled (x.xelem(i), mode); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_Bi_scaled_e (x.xelem(i), mode, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_Ai_deriv, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai_deriv (@@var{x}, @@var{mode})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai_deriv (@@dots{})\n\ \n\ These routines compute the Airy function derivative Ai'(x) with an\n\ accuracy specified by mode.\n\ \n\ The second argument @@var{mode} must be an integer corresponding to\n\ \n\ @@table @@asis\n\ @@item 0 = GSL_PREC_DOUBLE\n\ Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}.\n\ @@item 1 = GSL_PREC_SINGLE\n\ Single-precision, a relative accuracy of approximately @@code{10^-7}.\n\ @@item 2 = GSL_PREC_APPROX\n\ Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}.\n\ @@end table\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } if(!args(1).is_scalar_type()) { error("The mode must be scalar."); print_usage (); return octave_value(); } int mode = static_cast((args(1).array_value())(0)); if(mode < 0) mode = 0; else if(mode > 2) mode = 2; NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_Ai_deriv (x.xelem(i), mode); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_Ai_deriv_e (x.xelem(i), mode, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_Bi_deriv, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi_deriv (@@var{x}, @@var{mode})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi_deriv (@@dots{})\n\ \n\ These routines compute the Airy function derivative Bi'(x) with an\n\ accuracy specified by mode.\n\ \n\ The second argument @@var{mode} must be an integer corresponding to\n\ \n\ @@table @@asis\n\ @@item 0 = GSL_PREC_DOUBLE\n\ Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}.\n\ @@item 1 = GSL_PREC_SINGLE\n\ Single-precision, a relative accuracy of approximately @@code{10^-7}.\n\ @@item 2 = GSL_PREC_APPROX\n\ Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}.\n\ @@end table\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } if(!args(1).is_scalar_type()) { error("The mode must be scalar."); print_usage (); return octave_value(); } int mode = static_cast((args(1).array_value())(0)); if(mode < 0) mode = 0; else if(mode > 2) mode = 2; NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_Bi_deriv (x.xelem(i), mode); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_Bi_deriv_e (x.xelem(i), mode, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_Ai_deriv_scaled, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai_deriv_scaled (@@var{x}, @@var{mode})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai_deriv_scaled (@@dots{})\n\ \n\ These routines compute the derivative of the scaled Airy function\n\ S_A(x) Ai(x).\n\ \n\ The second argument @@var{mode} must be an integer corresponding to\n\ \n\ @@table @@asis\n\ @@item 0 = GSL_PREC_DOUBLE\n\ Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}.\n\ @@item 1 = GSL_PREC_SINGLE\n\ Single-precision, a relative accuracy of approximately @@code{10^-7}.\n\ @@item 2 = GSL_PREC_APPROX\n\ Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}.\n\ @@end table\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } if(!args(1).is_scalar_type()) { error("The mode must be scalar."); print_usage (); return octave_value(); } int mode = static_cast((args(1).array_value())(0)); if(mode < 0) mode = 0; else if(mode > 2) mode = 2; NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_Ai_deriv_scaled (x.xelem(i), mode); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_Ai_deriv_scaled_e (x.xelem(i), mode, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_Bi_deriv_scaled, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi_deriv_scaled (@@var{x}, @@var{mode})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi_deriv_scaled (@@dots{})\n\ \n\ These routines compute the derivative of the scaled Airy function\n\ S_B(x) Bi(x).\n\ \n\ The second argument @@var{mode} must be an integer corresponding to\n\ \n\ @@table @@asis\n\ @@item 0 = GSL_PREC_DOUBLE\n\ Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}.\n\ @@item 1 = GSL_PREC_SINGLE\n\ Single-precision, a relative accuracy of approximately @@code{10^-7}.\n\ @@item 2 = GSL_PREC_APPROX\n\ Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}.\n\ @@end table\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } if(!args(1).is_scalar_type()) { error("The mode must be scalar."); print_usage (); return octave_value(); } int mode = static_cast((args(1).array_value())(0)); if(mode < 0) mode = 0; else if(mode > 2) mode = 2; NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_Bi_deriv_scaled (x.xelem(i), mode); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_Bi_deriv_scaled_e (x.xelem(i), mode, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(ellint_Kcomp, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} ellint_Kcomp (@@var{x}, @@var{mode})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} ellint_Kcomp (@@dots{})\n\ \n\ These routines compute the complete elliptic integral K(k) \n\ @@tex\n\ \\beforedisplay\n\ $$\n\ \\eqalign{\n\ K(k) &= \\int_0^{\\pi/2} {dt \\over \\sqrt{(1 - k^2 \\sin^2(t))}} \\cr\n\ }\n\ $$\n\ \\afterdisplay\n\ @@end tex\n\ \n\ The notation used here is based on Carlson, @@cite{Numerische\n\ Mathematik} 33 (1979) and differs slightly from that used by\n\ Abramowitz & Stegun, where the functions are given in terms of the\n\ parameter @@math{m = k^2}.\n\ \n\ \n\ The second argument @@var{mode} must be an integer corresponding to\n\ \n\ @@table @@asis\n\ @@item 0 = GSL_PREC_DOUBLE\n\ Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}.\n\ @@item 1 = GSL_PREC_SINGLE\n\ Single-precision, a relative accuracy of approximately @@code{10^-7}.\n\ @@item 2 = GSL_PREC_APPROX\n\ Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}.\n\ @@end table\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } if(!args(1).is_scalar_type()) { error("The mode must be scalar."); print_usage (); return octave_value(); } int mode = static_cast((args(1).array_value())(0)); if(mode < 0) mode = 0; else if(mode > 2) mode = 2; NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_ellint_Kcomp (x.xelem(i), mode); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_ellint_Kcomp_e (x.xelem(i), mode, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(ellint_Ecomp, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} ellint_Ecomp (@@var{x}, @@var{mode})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} ellint_Ecomp (@@dots{})\n\ \n\ These routines compute the complete elliptic integral E(k) to the\n\ accuracy specified by the mode variable mode.\n\ \n\ @@tex\n\ \\beforedisplay\n\ $$\n\ \\eqalign{\n\ E(k) &= \\int_0^{\\pi/2} \\sqrt{(1 - k^2 \\sin^2(t))} dt \\cr\n\ }\n\ $$\n\ \\afterdisplay\n\ \n\ @@end tex\n\ \n\ The notation used here is based on Carlson, @@cite{Numerische\n\ Mathematik} 33 (1979) and differs slightly from that used by\n\ Abramowitz & Stegun, where the functions are given in terms of the\n\ parameter @@math{m = k^2}.\n\ \n\ The second argument @@var{mode} must be an integer corresponding to\n\ \n\ @@table @@asis\n\ @@item 0 = GSL_PREC_DOUBLE\n\ Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}.\n\ @@item 1 = GSL_PREC_SINGLE\n\ Single-precision, a relative accuracy of approximately @@code{10^-7}.\n\ @@item 2 = GSL_PREC_APPROX\n\ Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}.\n\ @@end table\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } if(!args(1).is_scalar_type()) { error("The mode must be scalar."); print_usage (); return octave_value(); } int mode = static_cast((args(1).array_value())(0)); if(mode < 0) mode = 0; else if(mode > 2) mode = 2; NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_ellint_Ecomp (x.xelem(i), mode); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_ellint_Ecomp_e (x.xelem(i), mode, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_zero_Ai, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Ai (@@var{n})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Ai (@@dots{})\n\ \n\ These routines compute the location of the s-th zero of the Airy\n\ function Ai(x).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_zero_Ai (static_cast(x.xelem(i))); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_zero_Ai_e (static_cast(x.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value_list(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_zero_Bi, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Bi (@@var{n})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Bi (@@dots{})\n\ \n\ These routines compute the location of the s-th zero of the Airy\n\ function Bi(x).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_zero_Bi (static_cast(x.xelem(i))); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_zero_Bi_e (static_cast(x.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value_list(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_zero_Ai_deriv, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Ai_deriv (@@var{n})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Ai_deriv (@@dots{})\n\ \n\ These routines compute the location of the s-th zero of the Airy\n\ function derivative Ai(x).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_zero_Ai_deriv (static_cast(x.xelem(i))); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_zero_Ai_deriv_e (static_cast(x.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value_list(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_zero_Bi_deriv, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Bi_deriv (@@var{n})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Bi_deriv (@@dots{})\n\ \n\ These routines compute the location of the s-th zero of the Airy\n\ function derivative Bi(x).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_zero_Bi_deriv (static_cast(x.xelem(i))); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_zero_Bi_deriv_e (static_cast(x.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value_list(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_zero_J0, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} bessel_zero_J0 (@@var{n})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_zero_J0 (@@dots{})\n\ \n\ These routines compute the location of the s-th positive zero of the\n\ Bessel function J_0(x).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_bessel_zero_J0 (static_cast(x.xelem(i))); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_bessel_zero_J0_e (static_cast(x.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value_list(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_zero_J1, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} bessel_zero_J1 (@@var{n})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_zero_J1 (@@dots{})\n\ \n\ These routines compute the location of the s-th positive zero of the\n\ Bessel function J_1(x).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_bessel_zero_J1 (static_cast(x.xelem(i))); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_bessel_zero_J1_e (static_cast(x.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value_list(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(psi_1_int, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} psi_1_int (@@var{n})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi_1_int (@@dots{})\n\ \n\ These routines compute the Trigamma function \\psi(n) for positive\n\ integer n.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_psi_1_int (static_cast(x.xelem(i))); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_psi_1_int_e (static_cast(x.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value_list(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(zeta_int, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} zeta_int (@@var{n})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} zeta_int (@@dots{})\n\ \n\ These routines compute the Riemann zeta function \\zeta(n) for \n\ integer n, n \\ne 1.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_zeta_int (static_cast(x.xelem(i))); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_zeta_int_e (static_cast(x.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value_list(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(eta_int, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} eta_int (@@var{n})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} eta_int (@@dots{})\n\ \n\ These routines compute the eta function \\eta(n) for integer n.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_eta_int (static_cast(x.xelem(i))); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_eta_int_e (static_cast(x.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value_list(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(legendre_Plm, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} legendre_Plm (@@var{n}, @@var{m}, @@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_Plm (@@dots{})\n\ \n\ These routines compute the associated Legendre polynomial P_l^m(x) \n\ for m >= 0, l >= m, |x| <= 1.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 3) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type() || !args(2).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray m = args(1).array_value(); if(n.length() != m.length()) { error("Two first arguments must have the same size."); print_usage (); return octave_value(); } NDArray x = args(2).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_Plm (static_cast(n.xelem(i)), static_cast(m.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_Plm_e (static_cast(n.xelem(i)), static_cast(m.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); int mint = static_cast(m.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_Plm (nint, mint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_Plm_e (nint, mint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_Plm (static_cast(n.xelem(i)), static_cast(m.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_Plm_e (static_cast(n.xelem(i)), static_cast(m.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("The two first and the third argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(legendre_sphPlm, args, nargout, "\ -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{y} =} legendre_sphPlm (@@var{n}, @@var{m}, @@var{x})\n\ @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_sphPlm (@@dots{})\n\ \n\ These routines compute the normalized associated Legendre polynomial\n\ $\\sqrt@@{(2l+1)/(4\\pi)@@} \\sqrt@@{(l-m)!/(l+m)!@@} P_l^m(x)$ suitable for use\n\ in spherical harmonics. The parameters must satisfy m >= 0, l >= m,\n\ |x| <= 1. Theses routines avoid the overflows that occur for the\n\ standard normalization of P_l^m(x).\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 3) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type() || !args(2).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray m = args(1).array_value(); if(n.length() != m.length()) { error("Two first arguments must have the same size."); print_usage (); return octave_value(); } NDArray x = args(2).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_sphPlm (static_cast(n.xelem(i)), static_cast(m.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_sphPlm_e (static_cast(n.xelem(i)), static_cast(m.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); int mint = static_cast(m.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_sphPlm (nint, mint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_sphPlm_e (nint, mint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_sphPlm (static_cast(n.xelem(i)), static_cast(m.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_sphPlm_e (static_cast(n.xelem(i)), static_cast(m.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("The two first and the third argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(hyperg_U, args, nargout, " -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{out} =} hyperg_U (@@var{x0}, @@var{x1}, @@var{x2})\n\ @@deftypefnx {Loadable Function} {[@@var{out}, @@var{err}] =} hyperg_U (@@dots{})\n\ \n\ Secondary Confluent Hypergoemetric U function A&E 13.1.3 \n\ All input are double as is the output.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{out}.a.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") // // // Generated R. Rogers 4/21/2008 // Version 1 Expanded to three argument input and added maintainence hints // { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); // Check number of arguments here if((args.length() != 3 )|| (nargout > 2)) { print_usage (); return octave_value(); } // Check argument types here if(!args(0).is_real_type() || !args(1).is_real_type()|| !args(2).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here // Generate internal variables NDArray x0 = args(0).array_value(); NDArray x1 = args(1).array_value(); NDArray x2 = args(2).array_value(); // // Case one; all inputs the same length A A A if((x0.length() == x1.length() )&& (x0.length()==x2.length())) { dv = x0.dims(); NDArray out(dv); int len = x0.length(); // One output argument if(nargout < 2) { for(i = 0; i < len; i++) { out.xelem(i) = gsl_sf_hyperg_U (x0.xelem(i), x1.xelem(i),x2.xelem(i)); } return octave_value(out); // Two arguments } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_U_e (x0.xelem(i), x1.xelem(i), x2.xelem(i), &result); out.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(out); return retval; } // // Now we start on having only one array and two scalars, A S S } else if(( x0.length() != 1)&& (x1.length() == 1) && (x2.length()==1)) { dv = x0.dims(); NDArray out(dv); int len = x0.length(); // int x1_int = static_cast(x1.xelem(0)); // int x2_int = static_cast(x2.xelem(0)); double x1_real = x1.xelem(0); double x2_real = x2.xelem(0); // One output argument if(nargout < 2) { for(i = 0; i < len; i++) { out.xelem(i) = gsl_sf_hyperg_U (x0.xelem(i),x1_real,x2_real); } return octave_value(out); // Two output argument } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_U_e (x0.xelem(i),x1_real,x2_real, &result); out.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(out); return retval; } // S A S input form } else if((x0.length() == 1)&& ( x1.length() != 1) && (x2.length()==1)) { dv = x1.dims(); NDArray out(dv); int len = x1.length(); // int x0_int = static_cast(x0.xelem(0)); // int x2_int = static_cast(x2.xelem(0)); double x0_real = x0.xelem(0); double x2_real = x2.xelem(0); // One output argument if(nargout < 2) { for(i = 0; i < len; i++) { out.xelem(i) = gsl_sf_hyperg_U (x0_real,x1.xelem(i),x2_real); } return octave_value(out); // Two output argument } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_U_e (x0_real,x1.xelem(i),x2_real, &result); out.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(out); return retval; } // S S A input form } else if((x0.length() == 1)&& ( x1.length() == 1) && ( x2.length()!=1)) { dv = x2.dims(); NDArray out(dv); int len = x2.length(); // int x0_int = static_cast(x0.xelem(0)); // int x1_int = static_cast(x1.xelem(0)); double x0_real = x0.xelem(0); double x1_real = x1.xelem(0); // One output argument if(nargout < 2) { for(i = 0; i < len; i++) { out.xelem(i) = gsl_sf_hyperg_U (x0_real,x1_real,x2.xelem(i)); } return octave_value(out); // Two output argument } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_U_e (x0_real,x1_real,x2.xelem(i), &result); out.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(out); return retval; } } else { error("First, second, and third argument must either have the same size, or two of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(hyperg_1F1, args, nargout, " -*- texinfo -*-\n\ @@deftypefn {Loadable Function} {@@var{out} =} hyperg_1F1 (@@var{x0}, @@var{x1}, @@var{x2})\n\ @@deftypefnx {Loadable Function} {[@@var{out}, @@var{err}] =} hyperg_1F1 (@@dots{})\n\ \n\ Primary Confluent Hypergoemetric U function A&E 13.1.3 \n\ All inputs are double as is the output.\n\ \n\ @@var{err} contains an estimate of the absolute error in the value @@var{out}.a.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @@url{http://www.gnu.org/software/gsl/} for documentation.\n\ @@end deftypefn\n\ ") // // // Generated R. Rogers 4/21/2008 // Version 1 Expanded to three argument input and added maintainence hints // { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); // Check number of arguments here if((args.length() != 3 )|| (nargout > 2)) { print_usage (); return octave_value(); } // Check argument types here if(!args(0).is_real_type() || !args(1).is_real_type()|| !args(2).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here // Generate internal variables NDArray x0 = args(0).array_value(); NDArray x1 = args(1).array_value(); NDArray x2 = args(2).array_value(); // // Case one; all inputs the same length A A A if((x0.length() == x1.length() )&& (x0.length()==x2.length())) { dv = x0.dims(); NDArray out(dv); int len = x0.length(); // One output argument if(nargout < 2) { for(i = 0; i < len; i++) { out.xelem(i) = gsl_sf_hyperg_1F1 (x0.xelem(i), x1.xelem(i),x2.xelem(i)); } return octave_value(out); // Two arguments } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_1F1_e (x0.xelem(i), x1.xelem(i), x2.xelem(i), &result); out.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(out); return retval; } // // Now we start on having only one array and two scalars, A S S } else if(( x0.length() != 1)&& (x1.length() == 1) && (x2.length()==1)) { dv = x0.dims(); NDArray out(dv); int len = x0.length(); // int x1_int = static_cast(x1.xelem(0)); // int x2_int = static_cast(x2.xelem(0)); double x1_real = x1.xelem(0); double x2_real = x2.xelem(0); // One output argument if(nargout < 2) { for(i = 0; i < len; i++) { out.xelem(i) = gsl_sf_hyperg_1F1 (x0.xelem(i),x1_real,x2_real); } return octave_value(out); // Two output argument } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_1F1_e (x0.xelem(i),x1_real,x2_real, &result); out.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(out); return retval; } // S A S input form } else if((x0.length() == 1)&& ( x1.length() != 1) && (x2.length()==1)) { dv = x1.dims(); NDArray out(dv); int len = x1.length(); // int x0_int = static_cast(x0.xelem(0)); // int x2_int = static_cast(x2.xelem(0)); double x0_real = x0.xelem(0); double x2_real = x2.xelem(0); // One output argument if(nargout < 2) { for(i = 0; i < len; i++) { out.xelem(i) = gsl_sf_hyperg_1F1 (x0_real,x1.xelem(i),x2_real); } return octave_value(out); // Two output argument } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_1F1_e (x0_real,x1.xelem(i),x2_real, &result); out.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(out); return retval; } // S S A input form } else if((x0.length() == 1)&& ( x1.length() == 1) && ( x2.length()!=1)) { dv = x2.dims(); NDArray out(dv); int len = x2.length(); // int x0_int = static_cast(x0.xelem(0)); // int x1_int = static_cast(x1.xelem(0)); double x0_real = x0.xelem(0); double x1_real = x1.xelem(0); // One output argument if(nargout < 2) { for(i = 0; i < len; i++) { out.xelem(i) = gsl_sf_hyperg_1F1 (x0_real,x1_real,x2.xelem(i)); } return octave_value(out); // Two output argument } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_1F1_e (x0_real,x1_real,x2.xelem(i), &result); out.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(out); return retval; } } else { error("First, second, and third argument must either have the same size, or two of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ @ gsl-1.0.8/doc/RCS/texinfo.tex.max,v0000755000175000017500000061065411201030376014543 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @# @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @% texinfo.tex -- TeX macros to handle Texinfo files. % % Load plain if necessary, i.e., if running under initex. \expandafter\ifx\csname fmtname\endcsname\relax\input plain\fi % \def\texinfoversion{1999-09-25.10} % % Copyright (C) 1985, 86, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99 % Free Software Foundation, Inc. % % This texinfo.tex file is free software; you can redistribute it and/or % modify it under the terms of the GNU General Public License as % published by the Free Software Foundation; either version 2, or (at % your option) any later version. % % This texinfo.tex file is distributed in the hope that it will be % useful, but WITHOUT ANY WARRANTY; without even the implied warranty % of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU % General Public License for more details. % % You should have received a copy of the GNU General Public License % along with this texinfo.tex file; see the file COPYING. If not, see % . % % In other words, you are welcome to use, share and improve this program. % You are forbidden to forbid anyone else to use, share and improve % what you give them. Help stamp out software-hoarding! % % Please try the latest version of texinfo.tex before submitting bug % reports; you can get the latest version from: % ftp://ftp.gnu.org/gnu/texinfo.tex % (and all GNU mirrors, see http://www.gnu.org/order/ftp.html) % ftp://texinfo.org/tex/texinfo.tex % ftp://us.ctan.org/macros/texinfo/texinfo.tex % (and all CTAN mirrors, finger ctan@@us.ctan.org for a list). % /home/gd/gnu/doc/texinfo.tex on the GNU machines. % The texinfo.tex in any given Texinfo distribution could well be out % of date, so if that's what you're using, please check. % Texinfo has a small home page at http://texinfo.org/. % % Send bug reports to bug-texinfo@@gnu.org. Please include including a % complete document in each bug report with which we can reproduce the % problem. Patches are, of course, greatly appreciated. % % To process a Texinfo manual with TeX, it's most reliable to use the % texi2dvi shell script that comes with the distribution. For a simple % manual foo.texi, however, you can get away with this: % tex foo.texi % texindex foo.?? % tex foo.texi % tex foo.texi % dvips foo.dvi -o # or whatever, to process the dvi file; this makes foo.ps. % The extra runs of TeX get the cross-reference information correct. % Sometimes one run after texindex suffices, and sometimes you need more % than two; texi2dvi does it as many times as necessary. % % It is possible to adapt texinfo.tex for other languages. You can get % the existing language-specific files from ftp://ftp.gnu.org/gnu/texinfo/. \message{Loading texinfo [version \texinfoversion]:} % If in a .fmt file, print the version number % and turn on active characters that we couldn't do earlier because % they might have appeared in the input file name. \everyjob{\message{[Texinfo version \texinfoversion]}% \catcode`+=\active \catcode`\_=\active} % Save some parts of plain tex whose names we will redefine. \let\ptexb=\b \let\ptexbullet=\bullet \let\ptexc=\c \let\ptexcomma=\, \let\ptexdot=\. \let\ptexdots=\dots \let\ptexend=\end \let\ptexequiv=\equiv \let\ptexexclam=\! \let\ptexi=\i \let\ptexlbrace=\{ \let\ptexrbrace=\} \let\ptexstar=\* \let\ptext=\t % We never want plain's outer \+ definition in Texinfo. % For @@tex, we can use \tabalign. \let\+ = \relax \message{Basics,} \chardef\other=12 % If this character appears in an error message or help string, it % starts a new line in the output. \newlinechar = `^^J % Set up fixed words for English if not already set. \ifx\putwordAppendix\undefined \gdef\putwordAppendix{Appendix}\fi \ifx\putwordChapter\undefined \gdef\putwordChapter{Chapter}\fi \ifx\putwordfile\undefined \gdef\putwordfile{file}\fi \ifx\putwordin\undefined \gdef\putwordin{in}\fi \ifx\putwordIndexIsEmpty\undefined \gdef\putwordIndexIsEmpty{(Index is empty)}\fi \ifx\putwordIndexNonexistent\undefined \gdef\putwordIndexNonexistent{(Index is nonexistent)}\fi \ifx\putwordInfo\undefined \gdef\putwordInfo{Info}\fi \ifx\putwordInstanceVariableof\undefined \gdef\putwordInstanceVariableof{Instance Variable of}\fi \ifx\putwordMethodon\undefined \gdef\putwordMethodon{Method on}\fi \ifx\putwordNoTitle\undefined \gdef\putwordNoTitle{No Title}\fi \ifx\putwordof\undefined \gdef\putwordof{of}\fi \ifx\putwordon\undefined \gdef\putwordon{on}\fi \ifx\putwordpage\undefined \gdef\putwordpage{page}\fi \ifx\putwordsection\undefined \gdef\putwordsection{section}\fi \ifx\putwordSection\undefined \gdef\putwordSection{Section}\fi \ifx\putwordsee\undefined \gdef\putwordsee{see}\fi \ifx\putwordSee\undefined \gdef\putwordSee{See}\fi \ifx\putwordShortTOC\undefined \gdef\putwordShortTOC{Short Contents}\fi \ifx\putwordTOC\undefined \gdef\putwordTOC{Table of Contents}\fi % \ifx\putwordMJan\undefined \gdef\putwordMJan{January}\fi \ifx\putwordMFeb\undefined \gdef\putwordMFeb{February}\fi \ifx\putwordMMar\undefined \gdef\putwordMMar{March}\fi \ifx\putwordMApr\undefined \gdef\putwordMApr{April}\fi \ifx\putwordMMay\undefined \gdef\putwordMMay{May}\fi \ifx\putwordMJun\undefined \gdef\putwordMJun{June}\fi \ifx\putwordMJul\undefined \gdef\putwordMJul{July}\fi \ifx\putwordMAug\undefined \gdef\putwordMAug{August}\fi \ifx\putwordMSep\undefined \gdef\putwordMSep{September}\fi \ifx\putwordMOct\undefined \gdef\putwordMOct{October}\fi \ifx\putwordMNov\undefined \gdef\putwordMNov{November}\fi \ifx\putwordMDec\undefined \gdef\putwordMDec{December}\fi % \ifx\putwordDefmac\undefined \gdef\putwordDefmac{Macro}\fi \ifx\putwordDefspec\undefined \gdef\putwordDefspec{Special Form}\fi \ifx\putwordDefvar\undefined \gdef\putwordDefvar{Variable}\fi \ifx\putwordDefopt\undefined \gdef\putwordDefopt{User Option}\fi \ifx\putwordDeftypevar\undefined\gdef\putwordDeftypevar{Variable}\fi \ifx\putwordDeffunc\undefined \gdef\putwordDeffunc{Function}\fi \ifx\putwordDeftypefun\undefined\gdef\putwordDeftypefun{Function}\fi % Ignore a token. % \def\gobble#1{} \hyphenation{ap-pen-dix} \hyphenation{mini-buf-fer mini-buf-fers} \hyphenation{eshell} \hyphenation{white-space} % Margin to add to right of even pages, to left of odd pages. \newdimen \bindingoffset \newdimen \normaloffset \newdimen\pagewidth \newdimen\pageheight % Sometimes it is convenient to have everything in the transcript file % and nothing on the terminal. We don't just call \tracingall here, % since that produces some useless output on the terminal. % \def\gloggingall{\begingroup \globaldefs = 1 \loggingall \endgroup}% \ifx\eTeXversion\undefined \def\loggingall{\tracingcommands2 \tracingstats2 \tracingpages1 \tracingoutput1 \tracinglostchars1 \tracingmacros2 \tracingparagraphs1 \tracingrestores1 \showboxbreadth\maxdimen\showboxdepth\maxdimen }% \else \def\loggingall{\tracingcommands3 \tracingstats2 \tracingpages1 \tracingoutput1 \tracinglostchars1 \tracingmacros2 \tracingparagraphs1 \tracingrestores1 \tracingscantokens1 \tracingassigns1 \tracingifs1 \tracinggroups1 \tracingnesting2 \showboxbreadth\maxdimen\showboxdepth\maxdimen }% \fi % For @@cropmarks command. % Do @@cropmarks to get crop marks. % \newif\ifcropmarks \let\cropmarks = \cropmarkstrue % % Dimensions to add cropmarks at corners. % Added by P. A. MacKay, 12 Nov. 1986 % \newdimen\outerhsize \newdimen\outervsize % set by the paper size routines \newdimen\cornerlong \cornerlong=1pc \newdimen\cornerthick \cornerthick=.3pt \newdimen\topandbottommargin \topandbottommargin=.75in % Main output routine. \chardef\PAGE = 255 \output = {\onepageout{\pagecontents\PAGE}} \newbox\headlinebox \newbox\footlinebox % \onepageout takes a vbox as an argument. Note that \pagecontents % does insertions, but you have to call it yourself. \def\onepageout#1{% \ifcropmarks \hoffset=0pt \else \hoffset=\normaloffset \fi % \ifodd\pageno \advance\hoffset by \bindingoffset \else \advance\hoffset by -\bindingoffset\fi % % Do this outside of the \shipout so @@code etc. will be expanded in % the headline as they should be, not taken literally (outputting ''code). \setbox\headlinebox = \vbox{\let\hsize=\pagewidth \makeheadline}% \setbox\footlinebox = \vbox{\let\hsize=\pagewidth \makefootline}% % {% % Have to do this stuff outside the \shipout because we want it to % take effect in \write's, yet the group defined by the \vbox ends % before the \shipout runs. % \escapechar = `\\ % use backslash in output files. \indexdummies % don't expand commands in the output. \normalturnoffactive % \ in index entries must not stay \, e.g., if % the page break happens to be in the middle of an example. \shipout\vbox{% \ifcropmarks \vbox to \outervsize\bgroup \hsize = \outerhsize \vskip-\topandbottommargin \vtop to0pt{% \line{\ewtop\hfil\ewtop}% \nointerlineskip \line{% \vbox{\moveleft\cornerthick\nstop}% \hfill \vbox{\moveright\cornerthick\nstop}% }% \vss}% \vskip\topandbottommargin \line\bgroup \hfil % center the page within the outer (page) hsize. \ifodd\pageno\hskip\bindingoffset\fi \vbox\bgroup \fi % \unvbox\headlinebox \pagebody{#1}% \ifdim\ht\footlinebox > 0pt % Only leave this space if the footline is nonempty. % (We lessened \vsize for it in \oddfootingxxx.) % The \baselineskip=24pt in plain's \makefootline has no effect. \vskip 2\baselineskip \unvbox\footlinebox \fi % \ifpdfmakepagedest \pdfmkdest{\the\pageno} \fi % \ifcropmarks \egroup % end of \vbox\bgroup \hfil\egroup % end of (centering) \line\bgroup \vskip\topandbottommargin plus1fill minus1fill \boxmaxdepth = \cornerthick \vbox to0pt{\vss \line{% \vbox{\moveleft\cornerthick\nsbot}% \hfill \vbox{\moveright\cornerthick\nsbot}% }% \nointerlineskip \line{\ewbot\hfil\ewbot}% }% \egroup % \vbox from first cropmarks clause \fi }% end of \shipout\vbox }% end of group with \turnoffactive \advancepageno \ifnum\outputpenalty>-20000 \else\dosupereject\fi } \newinsert\margin \dimen\margin=\maxdimen \def\pagebody#1{\vbox to\pageheight{\boxmaxdepth=\maxdepth #1}} {\catcode`\@@ =11 \gdef\pagecontents#1{\ifvoid\topins\else\unvbox\topins\fi % marginal hacks, juha@@viisa.uucp (Juha Takala) \ifvoid\margin\else % marginal info is present \rlap{\kern\hsize\vbox to\z@@{\kern1pt\box\margin \vss}}\fi \dimen@@=\dp#1 \unvbox#1 \ifvoid\footins\else\vskip\skip\footins\footnoterule \unvbox\footins\fi \ifr@@ggedbottom \kern-\dimen@@ \vfil \fi} } % Here are the rules for the cropmarks. Note that they are % offset so that the space between them is truly \outerhsize or \outervsize % (P. A. MacKay, 12 November, 1986) % \def\ewtop{\vrule height\cornerthick depth0pt width\cornerlong} \def\nstop{\vbox {\hrule height\cornerthick depth\cornerlong width\cornerthick}} \def\ewbot{\vrule height0pt depth\cornerthick width\cornerlong} \def\nsbot{\vbox {\hrule height\cornerlong depth\cornerthick width\cornerthick}} % Parse an argument, then pass it to #1. The argument is the rest of % the input line (except we remove a trailing comment). #1 should be a % macro which expects an ordinary undelimited TeX argument. % \def\parsearg#1{% \let\next = #1% \begingroup \obeylines \futurelet\temp\parseargx } % If the next token is an obeyed space (from an @@example environment or % the like), remove it and recurse. Otherwise, we're done. \def\parseargx{% % \obeyedspace is defined far below, after the definition of \sepspaces. \ifx\obeyedspace\temp \expandafter\parseargdiscardspace \else \expandafter\parseargline \fi } % Remove a single space (as the delimiter token to the macro call). {\obeyspaces % \gdef\parseargdiscardspace {\futurelet\temp\parseargx}} {\obeylines % \gdef\parseargline#1^^M{% \endgroup % End of the group started in \parsearg. % % First remove any @@c comment, then any @@comment. % Result of each macro is put in \toks0. \argremovec #1\c\relax % \expandafter\argremovecomment \the\toks0 \comment\relax % % % Call the caller's macro, saved as \next in \parsearg. \expandafter\next\expandafter{\the\toks0}% }% } % Since all \c{,omment} does is throw away the argument, we can let TeX % do that for us. The \relax here is matched by the \relax in the call % in \parseargline; it could be more or less anything, its purpose is % just to delimit the argument to the \c. \def\argremovec#1\c#2\relax{\toks0 = {#1}} \def\argremovecomment#1\comment#2\relax{\toks0 = {#1}} % \argremovec{,omment} might leave us with trailing spaces, though; e.g., % @@end itemize @@c foo % will have two active spaces as part of the argument with the % `itemize'. Here we remove all active spaces from #1, and assign the % result to \toks0. % % This loses if there are any *other* active characters besides spaces % in the argument -- _ ^ +, for example -- since they get expanded. % Fortunately, Texinfo does not define any such commands. (If it ever % does, the catcode of the characters in questionwill have to be changed % here.) But this means we cannot call \removeactivespaces as part of % \argremovec{,omment}, since @@c uses \parsearg, and thus the argument % that \parsearg gets might well have any character at all in it. % \def\removeactivespaces#1{% \begingroup \ignoreactivespaces \edef\temp{#1}% \global\toks0 = \expandafter{\temp}% \endgroup } % Change the active space to expand to nothing. % \begingroup \obeyspaces \gdef\ignoreactivespaces{\obeyspaces\let =\empty} \endgroup \def\flushcr{\ifx\par\lisppar \def\next##1{}\else \let\next=\relax \fi \next} %% These are used to keep @@begin/@@end levels from running away %% Call \inENV within environments (after a \begingroup) \newif\ifENV \ENVfalse \def\inENV{\ifENV\relax\else\ENVtrue\fi} \def\ENVcheck{% \ifENV\errmessage{Still within an environment; press RETURN to continue} \endgroup\fi} % This is not perfect, but it should reduce lossage % @@begin foo is the same as @@foo, for now. \newhelp\EMsimple{Press RETURN to continue.} \outer\def\begin{\parsearg\beginxxx} \def\beginxxx #1{% \expandafter\ifx\csname #1\endcsname\relax {\errhelp=\EMsimple \errmessage{Undefined command @@begin #1}}\else \csname #1\endcsname\fi} % @@end foo executes the definition of \Efoo. % \def\end{\parsearg\endxxx} \def\endxxx #1{% \removeactivespaces{#1}% \edef\endthing{\the\toks0}% % \expandafter\ifx\csname E\endthing\endcsname\relax \expandafter\ifx\csname \endthing\endcsname\relax % There's no \foo, i.e., no ``environment'' foo. \errhelp = \EMsimple \errmessage{Undefined command `@@end \endthing'}% \else \unmatchedenderror\endthing \fi \else % Everything's ok; the right environment has been started. \csname E\endthing\endcsname \fi } % There is an environment #1, but it hasn't been started. Give an error. % \def\unmatchedenderror#1{% \errhelp = \EMsimple \errmessage{This `@@end #1' doesn't have a matching `@@#1'}% } % Define the control sequence \E#1 to give an unmatched @@end error. % \def\defineunmatchedend#1{% \expandafter\def\csname E#1\endcsname{\unmatchedenderror{#1}}% } % Single-spacing is done by various environments (specifically, in % \nonfillstart and \quotations). \newskip\singlespaceskip \singlespaceskip = 12.5pt \def\singlespace{% % Why was this kern here? It messes up equalizing space above and below % environments. --karl, 6may93 %{\advance \baselineskip by -\singlespaceskip %\kern \baselineskip}% \setleading \singlespaceskip } %% Simple single-character @@ commands % @@@@ prints an @@ % Kludge this until the fonts are right (grr). \def\@@{{\tt\char64}} % This is turned off because it was never documented % and you can use @@w{...} around a quote to suppress ligatures. %% Define @@` and @@' to be the same as ` and ' %% but suppressing ligatures. %\def\`{{`}} %\def\'{{'}} % Used to generate quoted braces. \def\mylbrace {{\tt\char123}} \def\myrbrace {{\tt\char125}} \let\{=\mylbrace \let\}=\myrbrace \begingroup % Definitions to produce actual \{ & \} command in an index. \catcode`\{ = 12 \catcode`\} = 12 \catcode`\[ = 1 \catcode`\] = 2 \catcode`\@@ = 0 \catcode`\\ = 12 @@gdef@@lbracecmd[\{]% @@gdef@@rbracecmd[\}]% @@endgroup % Accents: @@, @@dotaccent @@ringaccent @@ubaraccent @@udotaccent % Others are defined by plain TeX: @@` @@' @@" @@^ @@~ @@= @@v @@H. \let\, = \c \let\dotaccent = \. \def\ringaccent#1{{\accent23 #1}} \let\tieaccent = \t \let\ubaraccent = \b \let\udotaccent = \d % Other special characters: @@questiondown @@exclamdown % Plain TeX defines: @@AA @@AE @@O @@OE @@L (and lowercase versions) @@ss. \def\questiondown{?`} \def\exclamdown{!`} % Dotless i and dotless j, used for accents. \def\imacro{i} \def\jmacro{j} \def\dotless#1{% \def\temp{#1}% \ifx\temp\imacro \ptexi \else\ifx\temp\jmacro \j \else \errmessage{@@dotless can be used only with i or j}% \fi\fi } % Be sure we're in horizontal mode when doing a tie, since we make space % equivalent to this in @@example-like environments. Otherwise, a space % at the beginning of a line will start with \penalty -- and % since \penalty is valid in vertical mode, we'd end up putting the % penalty on the vertical list instead of in the new paragraph. {\catcode`@@ = 11 % Avoid using \@@M directly, because that causes trouble % if the definition is written into an index file. \global\let\tiepenalty = \@@M \gdef\tie{\leavevmode\penalty\tiepenalty\ } } % @@: forces normal size whitespace following. \def\:{\spacefactor=1000 } % @@* forces a line break. \def\*{\hfil\break\hbox{}\ignorespaces} % @@. is an end-of-sentence period. \def\.{.\spacefactor=3000 } % @@! is an end-of-sentence bang. \def\!{!\spacefactor=3000 } % @@? is an end-of-sentence query. \def\?{?\spacefactor=3000 } % @@w prevents a word break. Without the \leavevmode, @@w at the % beginning of a paragraph, when TeX is still in vertical mode, would % produce a whole line of output instead of starting the paragraph. \def\w#1{\leavevmode\hbox{#1}} % @@group ... @@end group forces ... to be all on one page, by enclosing % it in a TeX vbox. We use \vtop instead of \vbox to construct the box % to keep its height that of a normal line. According to the rules for % \topskip (p.114 of the TeXbook), the glue inserted is % max (\topskip - \ht (first item), 0). If that height is large, % therefore, no glue is inserted, and the space between the headline and % the text is small, which looks bad. % \def\group{\begingroup \ifnum\catcode13=\active \else \errhelp = \groupinvalidhelp \errmessage{@@group invalid in context where filling is enabled}% \fi % % The \vtop we start below produces a box with normal height and large % depth; thus, TeX puts \baselineskip glue before it, and (when the % next line of text is done) \lineskip glue after it. (See p.82 of % the TeXbook.) Thus, space below is not quite equal to space % above. But it's pretty close. \def\Egroup{% \egroup % End the \vtop. \endgroup % End the \group. }% % \vtop\bgroup % We have to put a strut on the last line in case the @@group is in % the midst of an example, rather than completely enclosing it. % Otherwise, the interline space between the last line of the group % and the first line afterwards is too small. But we can't put the % strut in \Egroup, since there it would be on a line by itself. % Hence this just inserts a strut at the beginning of each line. \everypar = {\strut}% % % Since we have a strut on every line, we don't need any of TeX's % normal interline spacing. \offinterlineskip % % OK, but now we have to do something about blank % lines in the input in @@example-like environments, which normally % just turn into \lisppar, which will insert no space now that we've % turned off the interline space. Simplest is to make them be an % empty paragraph. \ifx\par\lisppar \edef\par{\leavevmode \par}% % % Reset ^^M's definition to new definition of \par. \obeylines \fi % % Do @@comment since we are called inside an environment such as % @@example, where each end-of-line in the input causes an % end-of-line in the output. We don't want the end-of-line after % the `@@group' to put extra space in the output. Since @@group % should appear on a line by itself (according to the Texinfo % manual), we don't worry about eating any user text. \comment } % % TeX puts in an \escapechar (i.e., `@@') at the beginning of the help % message, so this ends up printing `@@group can only ...'. % \newhelp\groupinvalidhelp{% group can only be used in environments such as @@example,^^J% where each line of input produces a line of output.} % @@need space-in-mils % forces a page break if there is not space-in-mils remaining. \newdimen\mil \mil=0.001in \def\need{\parsearg\needx} % Old definition--didn't work. %\def\needx #1{\par % %% This method tries to make TeX break the page naturally %% if the depth of the box does not fit. %{\baselineskip=0pt% %\vtop to #1\mil{\vfil}\kern -#1\mil\nobreak %\prevdepth=-1000pt %}} \def\needx#1{% % Ensure vertical mode, so we don't make a big box in the middle of a % paragraph. \par % % If the @@need value is less than one line space, it's useless. \dimen0 = #1\mil \dimen2 = \ht\strutbox \advance\dimen2 by \dp\strutbox \ifdim\dimen0 > \dimen2 % % Do a \strut just to make the height of this box be normal, so the % normal leading is inserted relative to the preceding line. % And a page break here is fine. \vtop to #1\mil{\strut\vfil}% % % TeX does not even consider page breaks if a penalty added to the % main vertical list is 10000 or more. But in order to see if the % empty box we just added fits on the page, we must make it consider % page breaks. On the other hand, we don't want to actually break the % page after the empty box. So we use a penalty of 9999. % % There is an extremely small chance that TeX will actually break the % page at this \penalty, if there are no other feasible breakpoints in % sight. (If the user is using lots of big @@group commands, which % almost-but-not-quite fill up a page, TeX will have a hard time doing % good page breaking, for example.) However, I could not construct an % example where a page broke at this \penalty; if it happens in a real % document, then we can reconsider our strategy. \penalty9999 % % Back up by the size of the box, whether we did a page break or not. \kern -#1\mil % % Do not allow a page break right after this kern. \nobreak \fi } % @@br forces paragraph break \let\br = \par % @@dots{} output an ellipsis using the current font. % We do .5em per period so that it has the same spacing in a typewriter % font as three actual period characters. % \def\dots{% \leavevmode \hbox to 1.5em{% \hskip 0pt plus 0.25fil minus 0.25fil .\hss.\hss.% \hskip 0pt plus 0.5fil minus 0.5fil }% } % @@enddots{} is an end-of-sentence ellipsis. % \def\enddots{% \leavevmode \hbox to 2em{% \hskip 0pt plus 0.25fil minus 0.25fil .\hss.\hss.\hss.% \hskip 0pt plus 0.5fil minus 0.5fil }% \spacefactor=3000 } % @@page forces the start of a new page % \def\page{\par\vfill\supereject} % @@exdent text.... % outputs text on separate line in roman font, starting at standard page margin % This records the amount of indent in the innermost environment. % That's how much \exdent should take out. \newskip\exdentamount % This defn is used inside fill environments such as @@defun. \def\exdent{\parsearg\exdentyyy} \def\exdentyyy #1{{\hfil\break\hbox{\kern -\exdentamount{\rm#1}}\hfil\break}} % This defn is used inside nofill environments such as @@example. \def\nofillexdent{\parsearg\nofillexdentyyy} \def\nofillexdentyyy #1{{\advance \leftskip by -\exdentamount \leftline{\hskip\leftskip{\rm#1}}}} % @@inmargin{TEXT} puts TEXT in the margin next to the current paragraph. \def\inmargin#1{% \strut\vadjust{\nobreak\kern-\strutdepth \vtop to \strutdepth{\baselineskip\strutdepth\vss \llap{\rightskip=\inmarginspacing \vbox{\noindent #1}}\null}}} \newskip\inmarginspacing \inmarginspacing=1cm \def\strutdepth{\dp\strutbox} %\hbox{{\rm#1}}\hfil\break}} % @@include file insert text of that file as input. % Allow normal characters that we make active in the argument (a file name). \def\include{\begingroup \catcode`\\=12 \catcode`~=12 \catcode`^=12 \catcode`_=12 \catcode`|=12 \catcode`<=12 \catcode`>=12 \catcode`+=12 \parsearg\includezzz} % Restore active chars for included file. \def\includezzz#1{\endgroup\begingroup % Read the included file in a group so nested @@include's work. \def\thisfile{#1}% \input\thisfile \endgroup} \def\thisfile{} % @@center line outputs that line, centered \def\center{\parsearg\centerzzz} \def\centerzzz #1{{\advance\hsize by -\leftskip \advance\hsize by -\rightskip \centerline{#1}}} % @@sp n outputs n lines of vertical space \def\sp{\parsearg\spxxx} \def\spxxx #1{\vskip #1\baselineskip} % @@comment ...line which is ignored... % @@c is the same as @@comment % @@ignore ... @@end ignore is another way to write a comment \def\comment{\begingroup \catcode`\^^M=\other% \catcode`\@@=\other \catcode`\{=\other \catcode`\}=\other% \commentxxx} {\catcode`\^^M=\other \gdef\commentxxx#1^^M{\endgroup}} \let\c=\comment % @@paragraphindent NCHARS % We'll use ems for NCHARS, close enough. % We cannot implement @@paragraphindent asis, though. % \def\asisword{asis} % no translation, these are keywords \def\noneword{none} % \def\paragraphindent{\parsearg\doparagraphindent} \def\doparagraphindent#1{% \def\temp{#1}% \ifx\temp\asisword \else \ifx\temp\noneword \defaultparindent = 0pt \else \defaultparindent = #1em \fi \fi \parindent = \defaultparindent } % @@exampleindent NCHARS % We'll use ems for NCHARS like @@paragraphindent. % It seems @@exampleindent asis isn't necessary, but % I preserve it to make it similar to @@paragraphindent. \def\exampleindent{\parsearg\doexampleindent} \def\doexampleindent#1{% \def\temp{#1}% \ifx\temp\asisword \else \ifx\temp\noneword \lispnarrowing = 0pt \else \lispnarrowing = #1em \fi \fi } % @@asis just yields its argument. Used with @@table, for example. % \def\asis#1{#1} % @@math means output in math mode. % We don't use $'s directly in the definition of \math because control % sequences like \math are expanded when the toc file is written. Then, % we read the toc file back, the $'s will be normal characters (as they % should be, according to the definition of Texinfo). So we must use a % control sequence to switch into and out of math mode. % % This isn't quite enough for @@math to work properly in indices, but it % seems unlikely it will ever be needed there. % \let\implicitmath = $ \def\math#1{\implicitmath #1\implicitmath} % @@bullet and @@minus need the same treatment as @@math, just above. \def\bullet{\implicitmath\ptexbullet\implicitmath} \def\minus{\implicitmath-\implicitmath} % @@refill is a no-op. \let\refill=\relax % If working on a large document in chapters, it is convenient to % be able to disable indexing, cross-referencing, and contents, for test runs. % This is done with @@novalidate (before @@setfilename). % \newif\iflinks \linkstrue % by default we want the aux files. \let\novalidate = \linksfalse % @@setfilename is done at the beginning of every texinfo file. % So open here the files we need to have open while reading the input. % This makes it possible to make a .fmt file for texinfo. \def\setfilename{% \iflinks \readauxfile \fi % \openindices needs to do some work in any case. \openindices \fixbackslash % Turn off hack to swallow `\input texinfo'. \global\let\setfilename=\comment % Ignore extra @@setfilename cmds. % % If texinfo.cnf is present on the system, read it. % Useful for site-wide @@afourpaper, etc. % Just to be on the safe side, close the input stream before the \input. \openin 1 texinfo.cnf \ifeof1 \let\temp=\relax \else \def\temp{\input texinfo.cnf }\fi \closein1 \temp % \comment % Ignore the actual filename. } % Called from \setfilename. % \def\openindices{% \newindex{cp}% \newcodeindex{fn}% \newcodeindex{vr}% \newcodeindex{tp}% \newcodeindex{ky}% \newcodeindex{pg}% } % @@bye. \outer\def\bye{\pagealignmacro\tracingstats=1\ptexend} \message{pdf,} % adobe `portable' document format \newcount\tempnum \newcount\lnkcount \newtoks\filename \newcount\filenamelength \newcount\pgn \newtoks\toksA \newtoks\toksB \newtoks\toksC \newtoks\toksD \newbox\boxA \newcount\countA \newif\ifpdf \newif\ifpdfmakepagedest \ifx\pdfoutput\undefined \pdffalse \let\pdfmkdest = \gobble \let\pdfurl = \gobble \let\endlink = \relax \let\linkcolor = \relax \let\pdfmakeoutlines = \relax \else \pdftrue \pdfoutput = 1 \input pdfcolor \def\dopdfimage#1#2#3{% \def\imagewidth{#2}% \def\imageheight{#3}% \ifnum\pdftexversion < 14 \pdfimage \else \pdfximage \fi \ifx\empty\imagewidth\else width \imagewidth \fi \ifx\empty\imageheight\else height \imageheight \fi {#1.pdf}% \ifnum\pdftexversion < 14 \else \pdfrefximage \pdflastximage \fi} \def\pdfmkdest#1{\pdfdest name{#1@@} xyz} \def\pdfmkpgn#1{#1@@} \let\linkcolor = \Cyan \def\endlink{\Black\pdfendlink} % Adding outlines to PDF; macros for calculating structure of outlines % come from Petr Olsak \def\expnumber#1{\expandafter\ifx\csname#1\endcsname\relax 0% \else \csname#1\endcsname \fi} \def\advancenumber#1{\tempnum=\expnumber{#1}\relax \advance\tempnum by1 \expandafter\xdef\csname#1\endcsname{\the\tempnum}} \def\pdfmakeoutlines{{% \openin 1 \jobname.toc \ifeof 1\else\bgroup \closein 1 \indexnofonts \def\tt{} % thanh's hack / proper braces in bookmarks \edef\mylbrace{\iftrue \string{\else}\fi}\let\{=\mylbrace \edef\myrbrace{\iffalse{\else\string}\fi}\let\}=\myrbrace % \def\chapentry ##1##2##3{} \def\unnumbchapentry ##1##2{} \def\secentry ##1##2##3##4{\advancenumber{chap##2}} \def\unnumbsecentry ##1##2{} \def\subsecentry ##1##2##3##4##5{\advancenumber{sec##2.##3}} \def\unnumbsubsecentry ##1##2{} \def\subsubsecentry ##1##2##3##4##5##6{\advancenumber{subsec##2.##3.##4}} \def\unnumbsubsubsecentry ##1##2{} \input \jobname.toc \def\chapentry ##1##2##3{% \pdfoutline goto name{\pdfmkpgn{##3}}count-\expnumber{chap##2}{##1}} \def\unnumbchapentry ##1##2{% \pdfoutline goto name{\pdfmkpgn{##2}}{##1}} \def\secentry ##1##2##3##4{% \pdfoutline goto name{\pdfmkpgn{##4}}count-\expnumber{sec##2.##3}{##1}} \def\unnumbsecentry ##1##2{% \pdfoutline goto name{\pdfmkpgn{##2}}{##1}} \def\subsecentry ##1##2##3##4##5{% \pdfoutline goto name{\pdfmkpgn{##5}}count-\expnumber{subsec##2.##3.##4}{##1}} \def\unnumbsubsecentry ##1##2{% \pdfoutline goto name{\pdfmkpgn{##2}}{##1}} \def\subsubsecentry ##1##2##3##4##5##6{% \pdfoutline goto name{\pdfmkpgn{##6}}{##1}} \def\unnumbsubsubsecentry ##1##2{% \pdfoutline goto name{\pdfmkpgn{##2}}{##1}} \input \jobname.toc \egroup\fi }} \def\makelinks #1,{% \def\params{#1}\def\E{END}% \ifx\params\E \let\nextmakelinks=\relax \else \let\nextmakelinks=\makelinks \ifnum\lnkcount>0,\fi \picknum{#1}% \startlink attr{/Border [0 0 0]} goto name{\pdfmkpgn{\the\pgn}}% \linkcolor #1% \advance\lnkcount by 1% \endlink \fi \nextmakelinks } \def\picknum#1{\expandafter\pn#1} \def\pn#1{% \def\p{#1}% \ifx\p\lbrace \let\nextpn=\ppn \else \let\nextpn=\ppnn \def\first{#1} \fi \nextpn } \def\ppn#1{\pgn=#1\gobble} \def\ppnn{\pgn=\first} \def\pdfmklnk#1{\lnkcount=0\makelinks #1,END,} \def\addtokens#1#2{\edef\addtoks{\noexpand#1={\the#1#2}}\addtoks} \def\skipspaces#1{\def\PP{#1}\def\D{|}% \ifx\PP\D\let\nextsp\relax \else\let\nextsp\skipspaces \ifx\p\space\else\addtokens{\filename}{\PP}% \advance\filenamelength by 1 \fi \fi \nextsp} \def\getfilename#1{\filenamelength=0\expandafter\skipspaces#1|\relax} \ifnum\pdftexversion < 14 \let \startlink \pdfannotlink \else \let \startlink \pdfstartlink \fi \def\pdfurl#1{% \begingroup \normalturnoffactive\def\@@{@@}% \leavevmode\Red \startlink attr{/Border [0 0 0]}% user{/Subtype /Link /A << /S /URI /URI (#1) >>}% % #1 \endgroup} \def\pdfgettoks#1.{\setbox\boxA=\hbox{\toksA={#1.}\toksB={}\maketoks}} \def\addtokens#1#2{\edef\addtoks{\noexpand#1={\the#1#2}}\addtoks} \def\adn#1{\addtokens{\toksC}{#1}\global\countA=1\let\next=\maketoks} \def\poptoks#1#2|ENDTOKS|{\let\first=#1\toksD={#1}\toksA={#2}} \def\maketoks{% \expandafter\poptoks\the\toksA|ENDTOKS| \ifx\first0\adn0 \else\ifx\first1\adn1 \else\ifx\first2\adn2 \else\ifx\first3\adn3 \else\ifx\first4\adn4 \else\ifx\first5\adn5 \else\ifx\first6\adn6 \else\ifx\first7\adn7 \else\ifx\first8\adn8 \else\ifx\first9\adn9 \else \ifnum0=\countA\else\makelink\fi \ifx\first.\let\next=\done\else \let\next=\maketoks \addtokens{\toksB}{\the\toksD} \ifx\first,\addtokens{\toksB}{\space}\fi \fi \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi \next} \def\makelink{\addtokens{\toksB}% {\noexpand\pdflink{\the\toksC}}\toksC={}\global\countA=0} \def\pdflink#1{% \startlink attr{/Border [0 0 0]} goto name{\mkpgn{#1}} \linkcolor #1\endlink} \def\mkpgn#1{#1@@} \def\done{\edef\st{\global\noexpand\toksA={\the\toksB}}\st} \fi % \ifx\pdfoutput \message{fonts,} % Font-change commands. % Texinfo sort of supports the sans serif font style, which plain TeX does not. % So we set up a \sf analogous to plain's \rm, etc. \newfam\sffam \def\sf{\fam=\sffam \tensf} \let\li = \sf % Sometimes we call it \li, not \sf. % We don't need math for this one. \def\ttsl{\tenttsl} % Use Computer Modern fonts at \magstephalf (11pt). \newcount\mainmagstep \mainmagstep=\magstephalf % Set the font macro #1 to the font named #2, adding on the % specified font prefix (normally `cm'). % #3 is the font's design size, #4 is a scale factor \def\setfont#1#2#3#4{\font#1=\fontprefix#2#3 scaled #4} % Use cm as the default font prefix. % To specify the font prefix, you must define \fontprefix % before you read in texinfo.tex. \ifx\fontprefix\undefined \def\fontprefix{cm} \fi % Support font families that don't use the same naming scheme as CM. \def\rmshape{r} \def\rmbshape{bx} %where the normal face is bold \def\bfshape{b} \def\bxshape{bx} \def\ttshape{tt} \def\ttbshape{tt} \def\ttslshape{sltt} \def\itshape{ti} \def\itbshape{bxti} \def\slshape{sl} \def\slbshape{bxsl} \def\sfshape{ss} \def\sfbshape{ss} \def\scshape{csc} \def\scbshape{csc} \ifx\bigger\relax \let\mainmagstep=\magstep1 \setfont\textrm\rmshape{12}{1000} \setfont\texttt\ttshape{12}{1000} \else \setfont\textrm\rmshape{10}{\mainmagstep} \setfont\texttt\ttshape{10}{\mainmagstep} \fi % Instead of cmb10, you many want to use cmbx10. % cmbx10 is a prettier font on its own, but cmb10 % looks better when embedded in a line with cmr10. \setfont\textbf\bfshape{10}{\mainmagstep} \setfont\textit\itshape{10}{\mainmagstep} \setfont\textsl\slshape{10}{\mainmagstep} \setfont\textsf\sfshape{10}{\mainmagstep} \setfont\textsc\scshape{10}{\mainmagstep} \setfont\textttsl\ttslshape{10}{\mainmagstep} \font\texti=cmmi10 scaled \mainmagstep \font\textsy=cmsy10 scaled \mainmagstep % A few fonts for @@defun, etc. \setfont\defbf\bxshape{10}{\magstep1} %was 1314 \setfont\deftt\ttshape{10}{\magstep1} \def\df{\let\tentt=\deftt \let\tenbf = \defbf \bf} % Fonts for indices, footnotes, small examples (9pt). \setfont\smallrm\rmshape{9}{1000} \setfont\smalltt\ttshape{9}{1000} \setfont\smallbf\bfshape{10}{900} \setfont\smallit\itshape{9}{1000} \setfont\smallsl\slshape{9}{1000} \setfont\smallsf\sfshape{9}{1000} \setfont\smallsc\scshape{10}{900} \setfont\smallttsl\ttslshape{10}{900} \font\smalli=cmmi9 \font\smallsy=cmsy9 % Fonts for title page: \setfont\titlerm\rmbshape{12}{\magstep3} \setfont\titleit\itbshape{10}{\magstep4} \setfont\titlesl\slbshape{10}{\magstep4} \setfont\titlett\ttbshape{12}{\magstep3} \setfont\titlettsl\ttslshape{10}{\magstep4} \setfont\titlesf\sfbshape{17}{\magstep1} \let\titlebf=\titlerm \setfont\titlesc\scbshape{10}{\magstep4} \font\titlei=cmmi12 scaled \magstep3 \font\titlesy=cmsy10 scaled \magstep4 \def\authorrm{\secrm} % Chapter (and unnumbered) fonts (17.28pt). \setfont\chaprm\rmbshape{12}{\magstep2} \setfont\chapit\itbshape{10}{\magstep3} \setfont\chapsl\slbshape{10}{\magstep3} \setfont\chaptt\ttbshape{12}{\magstep2} \setfont\chapttsl\ttslshape{10}{\magstep3} \setfont\chapsf\sfbshape{17}{1000} \let\chapbf=\chaprm \setfont\chapsc\scbshape{10}{\magstep3} \font\chapi=cmmi12 scaled \magstep2 \font\chapsy=cmsy10 scaled \magstep3 % Section fonts (14.4pt). \setfont\secrm\rmbshape{12}{\magstep1} \setfont\secit\itbshape{10}{\magstep2} \setfont\secsl\slbshape{10}{\magstep2} \setfont\sectt\ttbshape{12}{\magstep1} \setfont\secttsl\ttslshape{10}{\magstep2} \setfont\secsf\sfbshape{12}{\magstep1} \let\secbf\secrm \setfont\secsc\scbshape{10}{\magstep2} \font\seci=cmmi12 scaled \magstep1 \font\secsy=cmsy10 scaled \magstep2 % \setfont\ssecrm\bxshape{10}{\magstep1} % This size an font looked bad. % \setfont\ssecit\itshape{10}{\magstep1} % The letters were too crowded. % \setfont\ssecsl\slshape{10}{\magstep1} % \setfont\ssectt\ttshape{10}{\magstep1} % \setfont\ssecsf\sfshape{10}{\magstep1} %\setfont\ssecrm\bfshape{10}{1315} % Note the use of cmb rather than cmbx. %\setfont\ssecit\itshape{10}{1315} % Also, the size is a little larger than %\setfont\ssecsl\slshape{10}{1315} % being scaled magstep1. %\setfont\ssectt\ttshape{10}{1315} %\setfont\ssecsf\sfshape{10}{1315} %\let\ssecbf=\ssecrm % Subsection fonts (13.15pt). \setfont\ssecrm\rmbshape{12}{\magstephalf} \setfont\ssecit\itbshape{10}{1315} \setfont\ssecsl\slbshape{10}{1315} \setfont\ssectt\ttbshape{12}{\magstephalf} \setfont\ssecttsl\ttslshape{10}{1315} \setfont\ssecsf\sfbshape{12}{\magstephalf} \let\ssecbf\ssecrm \setfont\ssecsc\scbshape{10}{\magstep1} \font\sseci=cmmi12 scaled \magstephalf \font\ssecsy=cmsy10 scaled 1315 % The smallcaps and symbol fonts should actually be scaled \magstep1.5, % but that is not a standard magnification. % In order for the font changes to affect most math symbols and letters, % we have to define the \textfont of the standard families. Since % texinfo doesn't allow for producing subscripts and superscripts, we % don't bother to reset \scriptfont and \scriptscriptfont (which would % also require loading a lot more fonts). % \def\resetmathfonts{% \textfont0 = \tenrm \textfont1 = \teni \textfont2 = \tensy \textfont\itfam = \tenit \textfont\slfam = \tensl \textfont\bffam = \tenbf \textfont\ttfam = \tentt \textfont\sffam = \tensf } % The font-changing commands redefine the meanings of \tenSTYLE, instead % of just \STYLE. We do this so that font changes will continue to work % in math mode, where it is the current \fam that is relevant in most % cases, not the current font. Plain TeX does \def\bf{\fam=\bffam % \tenbf}, for example. By redefining \tenbf, we obviate the need to % redefine \bf itself. \def\textfonts{% \let\tenrm=\textrm \let\tenit=\textit \let\tensl=\textsl \let\tenbf=\textbf \let\tentt=\texttt \let\smallcaps=\textsc \let\tensf=\textsf \let\teni=\texti \let\tensy=\textsy \let\tenttsl=\textttsl \resetmathfonts} \def\titlefonts{% \let\tenrm=\titlerm \let\tenit=\titleit \let\tensl=\titlesl \let\tenbf=\titlebf \let\tentt=\titlett \let\smallcaps=\titlesc \let\tensf=\titlesf \let\teni=\titlei \let\tensy=\titlesy \let\tenttsl=\titlettsl \resetmathfonts \setleading{25pt}} \def\titlefont#1{{\titlefonts\rm #1}} \def\chapfonts{% \let\tenrm=\chaprm \let\tenit=\chapit \let\tensl=\chapsl \let\tenbf=\chapbf \let\tentt=\chaptt \let\smallcaps=\chapsc \let\tensf=\chapsf \let\teni=\chapi \let\tensy=\chapsy \let\tenttsl=\chapttsl \resetmathfonts \setleading{19pt}} \def\secfonts{% \let\tenrm=\secrm \let\tenit=\secit \let\tensl=\secsl \let\tenbf=\secbf \let\tentt=\sectt \let\smallcaps=\secsc \let\tensf=\secsf \let\teni=\seci \let\tensy=\secsy \let\tenttsl=\secttsl \resetmathfonts \setleading{16pt}} \def\subsecfonts{% \let\tenrm=\ssecrm \let\tenit=\ssecit \let\tensl=\ssecsl \let\tenbf=\ssecbf \let\tentt=\ssectt \let\smallcaps=\ssecsc \let\tensf=\ssecsf \let\teni=\sseci \let\tensy=\ssecsy \let\tenttsl=\ssecttsl \resetmathfonts \setleading{15pt}} \let\subsubsecfonts = \subsecfonts % Maybe make sssec fonts scaled magstephalf? \def\smallfonts{% \let\tenrm=\smallrm \let\tenit=\smallit \let\tensl=\smallsl \let\tenbf=\smallbf \let\tentt=\smalltt \let\smallcaps=\smallsc \let\tensf=\smallsf \let\teni=\smalli \let\tensy=\smallsy \let\tenttsl=\smallttsl \resetmathfonts \setleading{11pt}} % Set up the default fonts, so we can use them for creating boxes. % \textfonts % Define these so they can be easily changed for other fonts. \def\angleleft{$\langle$} \def\angleright{$\rangle$} % Count depth in font-changes, for error checks \newcount\fontdepth \fontdepth=0 % Fonts for short table of contents. \setfont\shortcontrm\rmshape{12}{1000} \setfont\shortcontbf\bxshape{12}{1000} \setfont\shortcontsl\slshape{12}{1000} %% Add scribe-like font environments, plus @@l for inline lisp (usually sans %% serif) and @@ii for TeX italic % \smartitalic{ARG} outputs arg in italics, followed by an italic correction % unless the following character is such as not to need one. \def\smartitalicx{\ifx\next,\else\ifx\next-\else\ifx\next.\else\/\fi\fi\fi} \def\smartslanted#1{{\sl #1}\futurelet\next\smartitalicx} \def\smartitalic#1{{\it #1}\futurelet\next\smartitalicx} \let\i=\smartitalic \let\var=\smartslanted \let\dfn=\smartslanted \let\emph=\smartitalic \let\cite=\smartslanted \def\b#1{{\bf #1}} \let\strong=\b % We can't just use \exhyphenpenalty, because that only has effect at % the end of a paragraph. Restore normal hyphenation at the end of the % group within which \nohyphenation is presumably called. % \def\nohyphenation{\hyphenchar\font = -1 \aftergroup\restorehyphenation} \def\restorehyphenation{\hyphenchar\font = `- } \def\t#1{% {\tt \rawbackslash \frenchspacing #1}% \null } \let\ttfont=\t \def\samp#1{`\tclose{#1}'\null} \setfont\keyrm\rmshape{8}{1000} \font\keysy=cmsy9 \def\key#1{{\keyrm\textfont2=\keysy \leavevmode\hbox{% \raise0.4pt\hbox{\angleleft}\kern-.08em\vtop{% \vbox{\hrule\kern-0.4pt \hbox{\raise0.4pt\hbox{\vphantom{\angleleft}}#1}}% \kern-0.4pt\hrule}% \kern-.06em\raise0.4pt\hbox{\angleright}}}} % The old definition, with no lozenge: %\def\key #1{{\ttsl \nohyphenation \uppercase{#1}}\null} \def\ctrl #1{{\tt \rawbackslash \hat}#1} % @@file, @@option are the same as @@samp. \let\file=\samp \let\option=\samp % @@code is a modification of @@t, % which makes spaces the same size as normal in the surrounding text. \def\tclose#1{% {% % Change normal interword space to be same as for the current font. \spaceskip = \fontdimen2\font % % Switch to typewriter. \tt % % But `\ ' produces the large typewriter interword space. \def\ {{\spaceskip = 0pt{} }}% % % Turn off hyphenation. \nohyphenation % \rawbackslash \frenchspacing #1% }% \null } % We *must* turn on hyphenation at `-' and `_' in \code. % Otherwise, it is too hard to avoid overfull hboxes % in the Emacs manual, the Library manual, etc. % Unfortunately, TeX uses one parameter (\hyphenchar) to control % both hyphenation at - and hyphenation within words. % We must therefore turn them both off (\tclose does that) % and arrange explicitly to hyphenate at a dash. % -- rms. { \catcode`\-=\active \catcode`\_=\active % \global\def\code{\begingroup \catcode`\-=\active \let-\codedash \catcode`\_=\active \let_\codeunder \codex } % % If we end up with any active - characters when handling the index, % just treat them as a normal -. \global\def\indexbreaks{\catcode`\-=\active \let-\realdash} } \def\realdash{-} \def\codedash{-\discretionary{}{}{}} \def\codeunder{\ifusingtt{\normalunderscore\discretionary{}{}{}}{\_}} \def\codex #1{\tclose{#1}\endgroup} %\let\exp=\tclose %Was temporary % @@kbd is like @@code, except that if the argument is just one @@key command, % then @@kbd has no effect. % @@kbdinputstyle -- arg is `distinct' (@@kbd uses slanted tty font always), % `example' (@@kbd uses ttsl only inside of @@example and friends), % or `code' (@@kbd uses normal tty font always). \def\kbdinputstyle{\parsearg\kbdinputstylexxx} \def\kbdinputstylexxx#1{% \def\arg{#1}% \ifx\arg\worddistinct \gdef\kbdexamplefont{\ttsl}\gdef\kbdfont{\ttsl}% \else\ifx\arg\wordexample \gdef\kbdexamplefont{\ttsl}\gdef\kbdfont{\tt}% \else\ifx\arg\wordcode \gdef\kbdexamplefont{\tt}\gdef\kbdfont{\tt}% \fi\fi\fi } \def\worddistinct{distinct} \def\wordexample{example} \def\wordcode{code} % Default is kbdinputdistinct. (Too much of a hassle to call the macro, % the catcodes are wrong for parsearg to work.) \gdef\kbdexamplefont{\ttsl}\gdef\kbdfont{\ttsl} \def\xkey{\key} \def\kbdfoo#1#2#3\par{\def\one{#1}\def\three{#3}\def\threex{??}% \ifx\one\xkey\ifx\threex\three \key{#2}% \else{\tclose{\kbdfont\look}}\fi \else{\tclose{\kbdfont\look}}\fi} % For @@url, @@env, @@command quotes seem unnecessary, so use \code. \let\url=\code \let\env=\code \let\command=\code % @@uref (abbreviation for `urlref') takes an optional (comma-separated) % second argument specifying the text to display and an optional third % arg as text to display instead of (rather than in addition to) the url % itself. First (mandatory) arg is the url. Perhaps eventually put in % a hypertex \special here. % \def\uref#1{\douref #1,,,\finish} \def\douref#1,#2,#3,#4\finish{\begingroup \unsepspaces \pdfurl{#1}% \setbox0 = \hbox{\ignorespaces #3}% \ifdim\wd0 > 0pt \unhbox0 % third arg given, show only that \else \setbox0 = \hbox{\ignorespaces #2}% \ifdim\wd0 > 0pt \ifpdf \unhbox0 % PDF: 2nd arg given, show only it \else \unhbox0\ (\code{#1})% DVI: 2nd arg given, show both it and url \fi \else \code{#1}% only url given, so show it \fi \fi \endlink \endgroup} % rms does not like angle brackets --karl, 17may97. % So now @@email is just like @@uref, unless we are pdf. % %\def\email#1{\angleleft{\tt #1}\angleright} \ifpdf \def\email#1{\doemail#1,,\finish} \def\doemail#1,#2,#3\finish{\begingroup \unsepspaces \pdfurl{mailto:#1}% \setbox0 = \hbox{\ignorespaces #2}% \ifdim\wd0>0pt\unhbox0\else\code{#1}\fi \endlink \endgroup} \else \let\email=\uref \fi % Check if we are currently using a typewriter font. Since all the % Computer Modern typewriter fonts have zero interword stretch (and % shrink), and it is reasonable to expect all typewriter fonts to have % this property, we can check that font parameter. % \def\ifmonospace{\ifdim\fontdimen3\font=0pt } % Typeset a dimension, e.g., `in' or `pt'. The only reason for the % argument is to make the input look right: @@dmn{pt} instead of @@dmn{}pt. % \def\dmn#1{\thinspace #1} \def\kbd#1{\def\look{#1}\expandafter\kbdfoo\look??\par} % @@l was never documented to mean ``switch to the Lisp font'', % and it is not used as such in any manual I can find. We need it for % Polish suppressed-l. --karl, 22sep96. %\def\l#1{{\li #1}\null} % Explicit font changes: @@r, @@sc, undocumented @@ii. \def\r#1{{\rm #1}} % roman font \def\sc#1{{\smallcaps#1}} % smallcaps font \def\ii#1{{\it #1}} % italic font % @@acronym downcases the argument and prints in smallcaps. \def\acronym#1{{\smallcaps \lowercase{#1}}} % @@pounds{} is a sterling sign. \def\pounds{{\it\$}} \message{page headings,} \newskip\titlepagetopglue \titlepagetopglue = 1.5in \newskip\titlepagebottomglue \titlepagebottomglue = 2pc % First the title page. Must do @@settitle before @@titlepage. \newif\ifseenauthor \newif\iffinishedtitlepage % Do an implicit @@contents or @@shortcontents after @@end titlepage if the % user says @@setcontentsaftertitlepage or @@setshortcontentsaftertitlepage. % \newif\ifsetcontentsaftertitlepage \let\setcontentsaftertitlepage = \setcontentsaftertitlepagetrue \newif\ifsetshortcontentsaftertitlepage \let\setshortcontentsaftertitlepage = \setshortcontentsaftertitlepagetrue \def\shorttitlepage{\parsearg\shorttitlepagezzz} \def\shorttitlepagezzz #1{\begingroup\hbox{}\vskip 1.5in \chaprm \centerline{#1}% \endgroup\page\hbox{}\page} \def\titlepage{\begingroup \parindent=0pt \textfonts \let\subtitlerm=\tenrm \def\subtitlefont{\subtitlerm \normalbaselineskip = 13pt \normalbaselines}% % \def\authorfont{\authorrm \normalbaselineskip = 16pt \normalbaselines}% % % Leave some space at the very top of the page. \vglue\titlepagetopglue % % Now you can print the title using @@title. \def\title{\parsearg\titlezzz}% \def\titlezzz##1{\leftline{\titlefonts\rm ##1} % print a rule at the page bottom also. \finishedtitlepagefalse \vskip4pt \hrule height 4pt width \hsize \vskip4pt}% % No rule at page bottom unless we print one at the top with @@title. \finishedtitlepagetrue % % Now you can put text using @@subtitle. \def\subtitle{\parsearg\subtitlezzz}% \def\subtitlezzz##1{{\subtitlefont \rightline{##1}}}% % % @@author should come last, but may come many times. \def\author{\parsearg\authorzzz}% \def\authorzzz##1{\ifseenauthor\else\vskip 0pt plus 1filll\seenauthortrue\fi {\authorfont \leftline{##1}}}% % % Most title ``pages'' are actually two pages long, with space % at the top of the second. We don't want the ragged left on the second. \let\oldpage = \page \def\page{% \iffinishedtitlepage\else \finishtitlepage \fi \oldpage \let\page = \oldpage \hbox{}}% % \def\page{\oldpage \hbox{}} } \def\Etitlepage{% \iffinishedtitlepage\else \finishtitlepage \fi % It is important to do the page break before ending the group, % because the headline and footline are only empty inside the group. % If we use the new definition of \page, we always get a blank page % after the title page, which we certainly don't want. \oldpage \endgroup % % If they want short, they certainly want long too. \ifsetshortcontentsaftertitlepage \shortcontents \contents \global\let\shortcontents = \relax \global\let\contents = \relax \fi % \ifsetcontentsaftertitlepage \contents \global\let\contents = \relax \global\let\shortcontents = \relax \fi % \ifpdf \pdfmakepagedesttrue \fi % \HEADINGSon } \def\finishtitlepage{% \vskip4pt \hrule height 2pt width \hsize \vskip\titlepagebottomglue \finishedtitlepagetrue } %%% Set up page headings and footings. \let\thispage=\folio \newtoks\evenheadline % headline on even pages \newtoks\oddheadline % headline on odd pages \newtoks\evenfootline % footline on even pages \newtoks\oddfootline % footline on odd pages % Now make Tex use those variables \headline={{\textfonts\rm \ifodd\pageno \the\oddheadline \else \the\evenheadline \fi}} \footline={{\textfonts\rm \ifodd\pageno \the\oddfootline \else \the\evenfootline \fi}\HEADINGShook} \let\HEADINGShook=\relax % Commands to set those variables. % For example, this is what @@headings on does % @@evenheading @@thistitle|@@thispage|@@thischapter % @@oddheading @@thischapter|@@thispage|@@thistitle % @@evenfooting @@thisfile|| % @@oddfooting ||@@thisfile \def\evenheading{\parsearg\evenheadingxxx} \def\oddheading{\parsearg\oddheadingxxx} \def\everyheading{\parsearg\everyheadingxxx} \def\evenfooting{\parsearg\evenfootingxxx} \def\oddfooting{\parsearg\oddfootingxxx} \def\everyfooting{\parsearg\everyfootingxxx} {\catcode`\@@=0 % \gdef\evenheadingxxx #1{\evenheadingyyy #1@@|@@|@@|@@|\finish} \gdef\evenheadingyyy #1@@|#2@@|#3@@|#4\finish{% \global\evenheadline={\rlap{\centerline{#2}}\line{#1\hfil#3}}} \gdef\oddheadingxxx #1{\oddheadingyyy #1@@|@@|@@|@@|\finish} \gdef\oddheadingyyy #1@@|#2@@|#3@@|#4\finish{% \global\oddheadline={\rlap{\centerline{#2}}\line{#1\hfil#3}}} \gdef\everyheadingxxx#1{\oddheadingxxx{#1}\evenheadingxxx{#1}}% \gdef\evenfootingxxx #1{\evenfootingyyy #1@@|@@|@@|@@|\finish} \gdef\evenfootingyyy #1@@|#2@@|#3@@|#4\finish{% \global\evenfootline={\rlap{\centerline{#2}}\line{#1\hfil#3}}} \gdef\oddfootingxxx #1{\oddfootingyyy #1@@|@@|@@|@@|\finish} \gdef\oddfootingyyy #1@@|#2@@|#3@@|#4\finish{% \global\oddfootline = {\rlap{\centerline{#2}}\line{#1\hfil#3}}% % % Leave some space for the footline. Hopefully ok to assume % @@evenfooting will not be used by itself. \global\advance\pageheight by -\baselineskip \global\advance\vsize by -\baselineskip } \gdef\everyfootingxxx#1{\oddfootingxxx{#1}\evenfootingxxx{#1}} % }% unbind the catcode of @@. % @@headings double turns headings on for double-sided printing. % @@headings single turns headings on for single-sided printing. % @@headings off turns them off. % @@headings on same as @@headings double, retained for compatibility. % @@headings after turns on double-sided headings after this page. % @@headings doubleafter turns on double-sided headings after this page. % @@headings singleafter turns on single-sided headings after this page. % By default, they are off at the start of a document, % and turned `on' after @@end titlepage. \def\headings #1 {\csname HEADINGS#1\endcsname} \def\HEADINGSoff{ \global\evenheadline={\hfil} \global\evenfootline={\hfil} \global\oddheadline={\hfil} \global\oddfootline={\hfil}} \HEADINGSoff % When we turn headings on, set the page number to 1. % For double-sided printing, put current file name in lower left corner, % chapter name on inside top of right hand pages, document % title on inside top of left hand pages, and page numbers on outside top % edge of all pages. \def\HEADINGSdouble{ \global\pageno=1 \global\evenfootline={\hfil} \global\oddfootline={\hfil} \global\evenheadline={\line{\folio\hfil\thistitle}} \global\oddheadline={\line{\thischapter\hfil\folio}} \global\let\contentsalignmacro = \chapoddpage } \let\contentsalignmacro = \chappager % For single-sided printing, chapter title goes across top left of page, % page number on top right. \def\HEADINGSsingle{ \global\pageno=1 \global\evenfootline={\hfil} \global\oddfootline={\hfil} \global\evenheadline={\line{\thischapter\hfil\folio}} \global\oddheadline={\line{\thischapter\hfil\folio}} \global\let\contentsalignmacro = \chappager } \def\HEADINGSon{\HEADINGSdouble} \def\HEADINGSafter{\let\HEADINGShook=\HEADINGSdoublex} \let\HEADINGSdoubleafter=\HEADINGSafter \def\HEADINGSdoublex{% \global\evenfootline={\hfil} \global\oddfootline={\hfil} \global\evenheadline={\line{\folio\hfil\thistitle}} \global\oddheadline={\line{\thischapter\hfil\folio}} \global\let\contentsalignmacro = \chapoddpage } \def\HEADINGSsingleafter{\let\HEADINGShook=\HEADINGSsinglex} \def\HEADINGSsinglex{% \global\evenfootline={\hfil} \global\oddfootline={\hfil} \global\evenheadline={\line{\thischapter\hfil\folio}} \global\oddheadline={\line{\thischapter\hfil\folio}} \global\let\contentsalignmacro = \chappager } % Subroutines used in generating headings % Produces Day Month Year style of output. \def\today{% \number\day\space \ifcase\month \or\putwordMJan\or\putwordMFeb\or\putwordMMar\or\putwordMApr \or\putwordMMay\or\putwordMJun\or\putwordMJul\or\putwordMAug \or\putwordMSep\or\putwordMOct\or\putwordMNov\or\putwordMDec \fi \space\number\year} % @@settitle line... specifies the title of the document, for headings. % It generates no output of its own. \def\thistitle{\putwordNoTitle} \def\settitle{\parsearg\settitlezzz} \def\settitlezzz #1{\gdef\thistitle{#1}} \message{tables,} % Tables -- @@table, @@ftable, @@vtable, @@item(x), @@kitem(x), @@xitem(x). % default indentation of table text \newdimen\tableindent \tableindent=.8in % default indentation of @@itemize and @@enumerate text \newdimen\itemindent \itemindent=.3in % margin between end of table item and start of table text. \newdimen\itemmargin \itemmargin=.1in % used internally for \itemindent minus \itemmargin \newdimen\itemmax % Note @@table, @@vtable, and @@vtable define @@item, @@itemx, etc., with % these defs. % They also define \itemindex % to index the item name in whatever manner is desired (perhaps none). \newif\ifitemxneedsnegativevskip \def\itemxpar{\par\ifitemxneedsnegativevskip\nobreak\vskip-\parskip\nobreak\fi} \def\internalBitem{\smallbreak \parsearg\itemzzz} \def\internalBitemx{\itemxpar \parsearg\itemzzz} \def\internalBxitem "#1"{\def\xitemsubtopix{#1} \smallbreak \parsearg\xitemzzz} \def\internalBxitemx "#1"{\def\xitemsubtopix{#1} \itemxpar \parsearg\xitemzzz} \def\internalBkitem{\smallbreak \parsearg\kitemzzz} \def\internalBkitemx{\itemxpar \parsearg\kitemzzz} \def\kitemzzz #1{\dosubind {kw}{\code{#1}}{for {\bf \lastfunction}}% \itemzzz {#1}} \def\xitemzzz #1{\dosubind {kw}{\code{#1}}{for {\bf \xitemsubtopic}}% \itemzzz {#1}} \def\itemzzz #1{\begingroup % \advance\hsize by -\rightskip \advance\hsize by -\tableindent \setbox0=\hbox{\itemfont{#1}}% \itemindex{#1}% \nobreak % This prevents a break before @@itemx. % % If the item text does not fit in the space we have, put it on a line % by itself, and do not allow a page break either before or after that % line. We do not start a paragraph here because then if the next % command is, e.g., @@kindex, the whatsit would get put into the % horizontal list on a line by itself, resulting in extra blank space. \ifdim \wd0>\itemmax % % Make this a paragraph so we get the \parskip glue and wrapping, % but leave it ragged-right. \begingroup \advance\leftskip by-\tableindent \advance\hsize by\tableindent \advance\rightskip by0pt plus1fil \leavevmode\unhbox0\par \endgroup % % We're going to be starting a paragraph, but we don't want the % \parskip glue -- logically it's part of the @@item we just started. \nobreak \vskip-\parskip % % Stop a page break at the \parskip glue coming up. Unfortunately % we can't prevent a possible page break at the following % \baselineskip glue. \nobreak \endgroup \itemxneedsnegativevskipfalse \else % The item text fits into the space. Start a paragraph, so that the % following text (if any) will end up on the same line. \noindent % Do this with kerns and \unhbox so that if there is a footnote in % the item text, it can migrate to the main vertical list and % eventually be printed. \nobreak\kern-\tableindent \dimen0 = \itemmax \advance\dimen0 by \itemmargin \advance\dimen0 by -\wd0 \unhbox0 \nobreak\kern\dimen0 \endgroup \itemxneedsnegativevskiptrue \fi } \def\item{\errmessage{@@item while not in a table}} \def\itemx{\errmessage{@@itemx while not in a table}} \def\kitem{\errmessage{@@kitem while not in a table}} \def\kitemx{\errmessage{@@kitemx while not in a table}} \def\xitem{\errmessage{@@xitem while not in a table}} \def\xitemx{\errmessage{@@xitemx while not in a table}} % Contains a kludge to get @@end[description] to work. \def\description{\tablez{\dontindex}{1}{}{}{}{}} % @@table, @@ftable, @@vtable. \def\table{\begingroup\inENV\obeylines\obeyspaces\tablex} {\obeylines\obeyspaces% \gdef\tablex #1^^M{% \tabley\dontindex#1 \endtabley}} \def\ftable{\begingroup\inENV\obeylines\obeyspaces\ftablex} {\obeylines\obeyspaces% \gdef\ftablex #1^^M{% \tabley\fnitemindex#1 \endtabley \def\Eftable{\endgraf\afterenvbreak\endgroup}% \let\Etable=\relax}} \def\vtable{\begingroup\inENV\obeylines\obeyspaces\vtablex} {\obeylines\obeyspaces% \gdef\vtablex #1^^M{% \tabley\vritemindex#1 \endtabley \def\Evtable{\endgraf\afterenvbreak\endgroup}% \let\Etable=\relax}} \def\dontindex #1{} \def\fnitemindex #1{\doind {fn}{\code{#1}}}% \def\vritemindex #1{\doind {vr}{\code{#1}}}% {\obeyspaces % \gdef\tabley#1#2 #3 #4 #5 #6 #7\endtabley{\endgroup% \tablez{#1}{#2}{#3}{#4}{#5}{#6}}} \def\tablez #1#2#3#4#5#6{% \aboveenvbreak % \begingroup % \def\Edescription{\Etable}% Necessary kludge. \let\itemindex=#1% \ifnum 0#3>0 \advance \leftskip by #3\mil \fi % \ifnum 0#4>0 \tableindent=#4\mil \fi % \ifnum 0#5>0 \advance \rightskip by #5\mil \fi % \def\itemfont{#2}% \itemmax=\tableindent % \advance \itemmax by -\itemmargin % \advance \leftskip by \tableindent % \exdentamount=\tableindent \parindent = 0pt \parskip = \smallskipamount \ifdim \parskip=0pt \parskip=2pt \fi% \def\Etable{\endgraf\afterenvbreak\endgroup}% \let\item = \internalBitem % \let\itemx = \internalBitemx % \let\kitem = \internalBkitem % \let\kitemx = \internalBkitemx % \let\xitem = \internalBxitem % \let\xitemx = \internalBxitemx % } % This is the counter used by @@enumerate, which is really @@itemize \newcount \itemno \def\itemize{\parsearg\itemizezzz} \def\itemizezzz #1{% \begingroup % ended by the @@end itemize \itemizey {#1}{\Eitemize} } \def\itemizey #1#2{% \aboveenvbreak % \itemmax=\itemindent % \advance \itemmax by -\itemmargin % \advance \leftskip by \itemindent % \exdentamount=\itemindent \parindent = 0pt % \parskip = \smallskipamount % \ifdim \parskip=0pt \parskip=2pt \fi% \def#2{\endgraf\afterenvbreak\endgroup}% \def\itemcontents{#1}% \let\item=\itemizeitem} % Set sfcode to normal for the chars that usually have another value. % These are `.?!:;,' \def\frenchspacing{\sfcode46=1000 \sfcode63=1000 \sfcode33=1000 \sfcode58=1000 \sfcode59=1000 \sfcode44=1000 } % \splitoff TOKENS\endmark defines \first to be the first token in % TOKENS, and \rest to be the remainder. % \def\splitoff#1#2\endmark{\def\first{#1}\def\rest{#2}}% % Allow an optional argument of an uppercase letter, lowercase letter, % or number, to specify the first label in the enumerated list. No % argument is the same as `1'. % \def\enumerate{\parsearg\enumeratezzz} \def\enumeratezzz #1{\enumeratey #1 \endenumeratey} \def\enumeratey #1 #2\endenumeratey{% \begingroup % ended by the @@end enumerate % % If we were given no argument, pretend we were given `1'. \def\thearg{#1}% \ifx\thearg\empty \def\thearg{1}\fi % % Detect if the argument is a single token. If so, it might be a % letter. Otherwise, the only valid thing it can be is a number. % (We will always have one token, because of the test we just made. % This is a good thing, since \splitoff doesn't work given nothing at % all -- the first parameter is undelimited.) \expandafter\splitoff\thearg\endmark \ifx\rest\empty % Only one token in the argument. It could still be anything. % A ``lowercase letter'' is one whose \lccode is nonzero. % An ``uppercase letter'' is one whose \lccode is both nonzero, and % not equal to itself. % Otherwise, we assume it's a number. % % We need the \relax at the end of the \ifnum lines to stop TeX from % continuing to look for a . % \ifnum\lccode\expandafter`\thearg=0\relax \numericenumerate % a number (we hope) \else % It's a letter. \ifnum\lccode\expandafter`\thearg=\expandafter`\thearg\relax \lowercaseenumerate % lowercase letter \else \uppercaseenumerate % uppercase letter \fi \fi \else % Multiple tokens in the argument. We hope it's a number. \numericenumerate \fi } % An @@enumerate whose labels are integers. The starting integer is % given in \thearg. % \def\numericenumerate{% \itemno = \thearg \startenumeration{\the\itemno}% } % The starting (lowercase) letter is in \thearg. \def\lowercaseenumerate{% \itemno = \expandafter`\thearg \startenumeration{% % Be sure we're not beyond the end of the alphabet. \ifnum\itemno=0 \errmessage{No more lowercase letters in @@enumerate; get a bigger alphabet}% \fi \char\lccode\itemno }% } % The starting (uppercase) letter is in \thearg. \def\uppercaseenumerate{% \itemno = \expandafter`\thearg \startenumeration{% % Be sure we're not beyond the end of the alphabet. \ifnum\itemno=0 \errmessage{No more uppercase letters in @@enumerate; get a bigger alphabet} \fi \char\uccode\itemno }% } % Call itemizey, adding a period to the first argument and supplying the % common last two arguments. Also subtract one from the initial value in % \itemno, since @@item increments \itemno. % \def\startenumeration#1{% \advance\itemno by -1 \itemizey{#1.}\Eenumerate\flushcr } % @@alphaenumerate and @@capsenumerate are abbreviations for giving an arg % to @@enumerate. % \def\alphaenumerate{\enumerate{a}} \def\capsenumerate{\enumerate{A}} \def\Ealphaenumerate{\Eenumerate} \def\Ecapsenumerate{\Eenumerate} % Definition of @@item while inside @@itemize. \def\itemizeitem{% \advance\itemno by 1 {\let\par=\endgraf \smallbreak}% \ifhmode \errmessage{In hmode at itemizeitem}\fi {\parskip=0in \hskip 0pt \hbox to 0pt{\hss \itemcontents\hskip \itemmargin}% \vadjust{\penalty 1200}}% \flushcr} % @@multitable macros % Amy Hendrickson, 8/18/94, 3/6/96 % % @@multitable ... @@end multitable will make as many columns as desired. % Contents of each column will wrap at width given in preamble. Width % can be specified either with sample text given in a template line, % or in percent of \hsize, the current width of text on page. % Table can continue over pages but will only break between lines. % To make preamble: % % Either define widths of columns in terms of percent of \hsize: % @@multitable @@columnfractions .25 .3 .45 % @@item ... % % Numbers following @@columnfractions are the percent of the total % current hsize to be used for each column. You may use as many % columns as desired. % Or use a template: % @@multitable {Column 1 template} {Column 2 template} {Column 3 template} % @@item ... % using the widest term desired in each column. % % For those who want to use more than one line's worth of words in % the preamble, break the line within one argument and it % will parse correctly, i.e., % % @@multitable {Column 1 template} {Column 2 template} {Column 3 % template} % Not: % @@multitable {Column 1 template} {Column 2 template} % {Column 3 template} % Each new table line starts with @@item, each subsequent new column % starts with @@tab. Empty columns may be produced by supplying @@tab's % with nothing between them for as many times as empty columns are needed, % ie, @@tab@@tab@@tab will produce two empty columns. % @@item, @@tab, @@multitable or @@end multitable do not need to be on their % own lines, but it will not hurt if they are. % Sample multitable: % @@multitable {Column 1 template} {Column 2 template} {Column 3 template} % @@item first col stuff @@tab second col stuff @@tab third col % @@item % first col stuff % @@tab % second col stuff % @@tab % third col % @@item first col stuff @@tab second col stuff % @@tab Many paragraphs of text may be used in any column. % % They will wrap at the width determined by the template. % @@item@@tab@@tab This will be in third column. % @@end multitable % Default dimensions may be reset by user. % @@multitableparskip is vertical space between paragraphs in table. % @@multitableparindent is paragraph indent in table. % @@multitablecolmargin is horizontal space to be left between columns. % @@multitablelinespace is space to leave between table items, baseline % to baseline. % 0pt means it depends on current normal line spacing. % \newskip\multitableparskip \newskip\multitableparindent \newdimen\multitablecolspace \newskip\multitablelinespace \multitableparskip=0pt \multitableparindent=6pt \multitablecolspace=12pt \multitablelinespace=0pt % Macros used to set up halign preamble: % \let\endsetuptable\relax \def\xendsetuptable{\endsetuptable} \let\columnfractions\relax \def\xcolumnfractions{\columnfractions} \newif\ifsetpercent % #1 is the part of the @@columnfraction before the decimal point, which % is presumably either 0 or the empty string (but we don't check, we % just throw it away). #2 is the decimal part, which we use as the % percent of \hsize for this column. \def\pickupwholefraction#1.#2 {% \global\advance\colcount by 1 \expandafter\xdef\csname col\the\colcount\endcsname{.#2\hsize}% \setuptable } \newcount\colcount \def\setuptable#1{% \def\firstarg{#1}% \ifx\firstarg\xendsetuptable \let\go = \relax \else \ifx\firstarg\xcolumnfractions \global\setpercenttrue \else \ifsetpercent \let\go\pickupwholefraction \else \global\advance\colcount by 1 \setbox0=\hbox{#1\unskip }% Add a normal word space as a separator; % typically that is always in the input, anyway. \expandafter\xdef\csname col\the\colcount\endcsname{\the\wd0}% \fi \fi \ifx\go\pickupwholefraction % Put the argument back for the \pickupwholefraction call, so % we'll always have a period there to be parsed. \def\go{\pickupwholefraction#1}% \else \let\go = \setuptable \fi% \fi \go } % This used to have \hskip1sp. But then the space in a template line is % not enough. That is bad. So let's go back to just & until we % encounter the problem it was intended to solve again. % --karl, nathan@@acm.org, 20apr99. \def\tab{&} % @@multitable ... @@end multitable definitions: % \def\multitable{\parsearg\dotable} \def\dotable#1{\bgroup \vskip\parskip \let\item\crcr \tolerance=9500 \hbadness=9500 \setmultitablespacing \parskip=\multitableparskip \parindent=\multitableparindent \overfullrule=0pt \global\colcount=0 \def\Emultitable{\global\setpercentfalse\cr\egroup\egroup}% % % To parse everything between @@multitable and @@item: \setuptable#1 \endsetuptable % % \everycr will reset column counter, \colcount, at the end of % each line. Every column entry will cause \colcount to advance by one. % The table preamble % looks at the current \colcount to find the correct column width. \everycr{\noalign{% % % \filbreak%% keeps underfull box messages off when table breaks over pages. % Maybe so, but it also creates really weird page breaks when the table % breaks over pages. Wouldn't \vfil be better? Wait until the problem % manifests itself, so it can be fixed for real --karl. \global\colcount=0\relax}}% % % This preamble sets up a generic column definition, which will % be used as many times as user calls for columns. % \vtop will set a single line and will also let text wrap and % continue for many paragraphs if desired. \halign\bgroup&\global\advance\colcount by 1\relax \multistrut\vtop{\hsize=\expandafter\csname col\the\colcount\endcsname % % In order to keep entries from bumping into each other % we will add a \leftskip of \multitablecolspace to all columns after % the first one. % % If a template has been used, we will add \multitablecolspace % to the width of each template entry. % % If the user has set preamble in terms of percent of \hsize we will % use that dimension as the width of the column, and the \leftskip % will keep entries from bumping into each other. Table will start at % left margin and final column will justify at right margin. % % Make sure we don't inherit \rightskip from the outer environment. \rightskip=0pt \ifnum\colcount=1 % The first column will be indented with the surrounding text. \advance\hsize by\leftskip \else \ifsetpercent \else % If user has not set preamble in terms of percent of \hsize % we will advance \hsize by \multitablecolspace. \advance\hsize by \multitablecolspace \fi % In either case we will make \leftskip=\multitablecolspace: \leftskip=\multitablecolspace \fi % Ignoring space at the beginning and end avoids an occasional spurious % blank line, when TeX decides to break the line at the space before the % box from the multistrut, so the strut ends up on a line by itself. % For example: % @@multitable @@columnfractions .11 .89 % @@item @@code{#} % @@tab Legal holiday which is valid in major parts of the whole country. % Is automatically provided with highlighting sequences respectively marking % characters. \noindent\ignorespaces##\unskip\multistrut}\cr } \def\setmultitablespacing{% test to see if user has set \multitablelinespace. % If so, do nothing. If not, give it an appropriate dimension based on % current baselineskip. \ifdim\multitablelinespace=0pt \setbox0=\vbox{X}\global\multitablelinespace=\the\baselineskip \global\advance\multitablelinespace by-\ht0 %% strut to put in table in case some entry doesn't have descenders, %% to keep lines equally spaced \let\multistrut = \strut \else %% FIXME: what is \box0 supposed to be? \gdef\multistrut{\vrule height\multitablelinespace depth\dp0 width0pt\relax} \fi %% Test to see if parskip is larger than space between lines of %% table. If not, do nothing. %% If so, set to same dimension as multitablelinespace. \ifdim\multitableparskip>\multitablelinespace \global\multitableparskip=\multitablelinespace \global\advance\multitableparskip-7pt %% to keep parskip somewhat smaller %% than skip between lines in the table. \fi% \ifdim\multitableparskip=0pt \global\multitableparskip=\multitablelinespace \global\advance\multitableparskip-7pt %% to keep parskip somewhat smaller %% than skip between lines in the table. \fi} \message{conditionals,} % Prevent errors for section commands. % Used in @@ignore and in failing conditionals. \def\ignoresections{% \let\chapter=\relax \let\unnumbered=\relax \let\top=\relax \let\unnumberedsec=\relax \let\unnumberedsection=\relax \let\unnumberedsubsec=\relax \let\unnumberedsubsection=\relax \let\unnumberedsubsubsec=\relax \let\unnumberedsubsubsection=\relax \let\section=\relax \let\subsec=\relax \let\subsubsec=\relax \let\subsection=\relax \let\subsubsection=\relax \let\appendix=\relax \let\appendixsec=\relax \let\appendixsection=\relax \let\appendixsubsec=\relax \let\appendixsubsection=\relax \let\appendixsubsubsec=\relax \let\appendixsubsubsection=\relax \let\contents=\relax \let\smallbook=\relax \let\titlepage=\relax } % Used in nested conditionals, where we have to parse the Texinfo source % and so want to turn off most commands, in case they are used % incorrectly. % \def\ignoremorecommands{% \let\defcodeindex = \relax \let\defcv = \relax \let\deffn = \relax \let\deffnx = \relax \let\defindex = \relax \let\defivar = \relax \let\defmac = \relax \let\defmethod = \relax \let\defop = \relax \let\defopt = \relax \let\defspec = \relax \let\deftp = \relax \let\deftypefn = \relax \let\deftypefun = \relax \let\deftypeivar = \relax \let\deftypeop = \relax \let\deftypevar = \relax \let\deftypevr = \relax \let\defun = \relax \let\defvar = \relax \let\defvr = \relax \let\ref = \relax \let\xref = \relax \let\printindex = \relax \let\pxref = \relax \let\settitle = \relax \let\setchapternewpage = \relax \let\setchapterstyle = \relax \let\everyheading = \relax \let\evenheading = \relax \let\oddheading = \relax \let\everyfooting = \relax \let\evenfooting = \relax \let\oddfooting = \relax \let\headings = \relax \let\include = \relax \let\lowersections = \relax \let\down = \relax \let\raisesections = \relax \let\up = \relax \let\set = \relax \let\clear = \relax \let\item = \relax } % Ignore @@ignore ... @@end ignore. % \def\ignore{\doignore{ignore}} % Ignore @@ifinfo, @@ifhtml, @@ifnottex, @@html, @@menu, and @@direntry text. % \def\ifinfo{\doignore{ifinfo}} \def\ifhtml{\doignore{ifhtml}} \def\ifnottex{\doignore{ifnottex}} \def\html{\doignore{html}} \def\menu{\doignore{menu}} \def\direntry{\doignore{direntry}} % @@dircategory CATEGORY -- specify a category of the dir file % which this file should belong to. Ignore this in TeX. \let\dircategory = \comment % Ignore text until a line `@@end #1'. % \def\doignore#1{\begingroup % Don't complain about control sequences we have declared \outer. \ignoresections % % Define a command to swallow text until we reach `@@end #1'. % This @@ is a catcode 12 token (that is the normal catcode of @@ in % this texinfo.tex file). We change the catcode of @@ below to match. \long\def\doignoretext##1@@end #1{\enddoignore}% % % Make sure that spaces turn into tokens that match what \doignoretext wants. \catcode32 = 10 % % Ignore braces, too, so mismatched braces don't cause trouble. \catcode`\{ = 9 \catcode`\} = 9 % % We must not have @@c interpreted as a control sequence. \catcode`\@@ = 12 % % Make the letter c a comment character so that the rest of the line % will be ignored. This way, the document can have (for example) % @@c @@end ifinfo % and the @@end ifinfo will be properly ignored. % (We've just changed @@ to catcode 12.) \catcode`\c = 14 % % And now expand that command. \doignoretext } % What we do to finish off ignored text. % \def\enddoignore{\endgroup\ignorespaces}% \newif\ifwarnedobs\warnedobsfalse \def\obstexwarn{% \ifwarnedobs\relax\else % We need to warn folks that they may have trouble with TeX 3.0. % This uses \immediate\write16 rather than \message to get newlines. \immediate\write16{} \immediate\write16{WARNING: for users of Unix TeX 3.0!} \immediate\write16{This manual trips a bug in TeX version 3.0 (tex hangs).} \immediate\write16{If you are running another version of TeX, relax.} \immediate\write16{If you are running Unix TeX 3.0, kill this TeX process.} \immediate\write16{ Then upgrade your TeX installation if you can.} \immediate\write16{ (See ftp://ftp.gnu.org/pub/gnu/TeX.README.)} \immediate\write16{If you are stuck with version 3.0, run the} \immediate\write16{ script ``tex3patch'' from the Texinfo distribution} \immediate\write16{ to use a workaround.} \immediate\write16{} \global\warnedobstrue \fi } % **In TeX 3.0, setting text in \nullfont hangs tex. For a % workaround (which requires the file ``dummy.tfm'' to be installed), % uncomment the following line: %%%%%\font\nullfont=dummy\let\obstexwarn=\relax % Ignore text, except that we keep track of conditional commands for % purposes of nesting, up to an `@@end #1' command. % \def\nestedignore#1{% \obstexwarn % We must actually expand the ignored text to look for the @@end % command, so that nested ignore constructs work. Thus, we put the % text into a \vbox and then do nothing with the result. To minimize % the change of memory overflow, we follow the approach outlined on % page 401 of the TeXbook: make the current font be a dummy font. % \setbox0 = \vbox\bgroup % Don't complain about control sequences we have declared \outer. \ignoresections % % Define `@@end #1' to end the box, which will in turn undefine the % @@end command again. \expandafter\def\csname E#1\endcsname{\egroup\ignorespaces}% % % We are going to be parsing Texinfo commands. Most cause no % trouble when they are used incorrectly, but some commands do % complicated argument parsing or otherwise get confused, so we % undefine them. % % We can't do anything about stray @@-signs, unfortunately; % they'll produce `undefined control sequence' errors. \ignoremorecommands % % Set the current font to be \nullfont, a TeX primitive, and define % all the font commands to also use \nullfont. We don't use % dummy.tfm, as suggested in the TeXbook, because not all sites % might have that installed. Therefore, math mode will still % produce output, but that should be an extremely small amount of % stuff compared to the main input. % \nullfont \let\tenrm=\nullfont \let\tenit=\nullfont \let\tensl=\nullfont \let\tenbf=\nullfont \let\tentt=\nullfont \let\smallcaps=\nullfont \let\tensf=\nullfont % Similarly for index fonts (mostly for their use in smallexample). \let\smallrm=\nullfont \let\smallit=\nullfont \let\smallsl=\nullfont \let\smallbf=\nullfont \let\smalltt=\nullfont \let\smallsc=\nullfont \let\smallsf=\nullfont % % Don't complain when characters are missing from the fonts. \tracinglostchars = 0 % % Don't bother to do space factor calculations. \frenchspacing % % Don't report underfull hboxes. \hbadness = 10000 % % Do minimal line-breaking. \pretolerance = 10000 % % Do not execute instructions in @@tex \def\tex{\doignore{tex}}% % Do not execute macro definitions. % `c' is a comment character, so the word `macro' will get cut off. \def\macro{\doignore{ma}}% } % @@set VAR sets the variable VAR to an empty value. % @@set VAR REST-OF-LINE sets VAR to the value REST-OF-LINE. % % Since we want to separate VAR from REST-OF-LINE (which might be % empty), we can't just use \parsearg; we have to insert a space of our % own to delimit the rest of the line, and then take it out again if we % didn't need it. Make sure the catcode of space is correct to avoid % losing inside @@example, for instance. % \def\set{\begingroup\catcode` =10 \catcode`\-=12 \catcode`\_=12 % Allow - and _ in VAR. \parsearg\setxxx} \def\setxxx#1{\setyyy#1 \endsetyyy} \def\setyyy#1 #2\endsetyyy{% \def\temp{#2}% \ifx\temp\empty \global\expandafter\let\csname SET#1\endcsname = \empty \else \setzzz{#1}#2\endsetzzz % Remove the trailing space \setxxx inserted. \fi \endgroup } % Can't use \xdef to pre-expand #2 and save some time, since \temp or % \next or other control sequences that we've defined might get us into % an infinite loop. Consider `@@set foo @@cite{bar}'. \def\setzzz#1#2 \endsetzzz{\expandafter\gdef\csname SET#1\endcsname{#2}} % @@clear VAR clears (i.e., unsets) the variable VAR. % \def\clear{\parsearg\clearxxx} \def\clearxxx#1{\global\expandafter\let\csname SET#1\endcsname=\relax} % @@value{foo} gets the text saved in variable foo. { \catcode`\_ = \active % % We might end up with active _ or - characters in the argument if % we're called from @@code, as @@code{@@value{foo-bar_}}. So \let any % such active characters to their normal equivalents. \gdef\value{\begingroup \catcode`\-=12 \catcode`\_=12 \indexbreaks \let_\normalunderscore \valuexxx} } \def\valuexxx#1{\expandablevalue{#1}\endgroup} % We have this subroutine so that we can handle at least some @@value's % properly in indexes (we \let\value to this in \indexdummies). Ones % whose names contain - or _ still won't work, but we can't do anything % about that. The command has to be fully expandable, since the result % winds up in the index file. This means that if the variable's value % contains other Texinfo commands, it's almost certain it will fail % (although perhaps we could fix that with sufficient work to do a % one-level expansion on the result, instead of complete). % \def\expandablevalue#1{% \expandafter\ifx\csname SET#1\endcsname\relax {[No value for ``#1'']}% \else \csname SET#1\endcsname \fi } % @@ifset VAR ... @@end ifset reads the `...' iff VAR has been defined % with @@set. % \def\ifset{\parsearg\ifsetxxx} \def\ifsetxxx #1{% \expandafter\ifx\csname SET#1\endcsname\relax \expandafter\ifsetfail \else \expandafter\ifsetsucceed \fi } \def\ifsetsucceed{\conditionalsucceed{ifset}} \def\ifsetfail{\nestedignore{ifset}} \defineunmatchedend{ifset} % @@ifclear VAR ... @@end ifclear reads the `...' iff VAR has never been % defined with @@set, or has been undefined with @@clear. % \def\ifclear{\parsearg\ifclearxxx} \def\ifclearxxx #1{% \expandafter\ifx\csname SET#1\endcsname\relax \expandafter\ifclearsucceed \else \expandafter\ifclearfail \fi } \def\ifclearsucceed{\conditionalsucceed{ifclear}} \def\ifclearfail{\nestedignore{ifclear}} \defineunmatchedend{ifclear} % @@iftex, @@ifnothtml, @@ifnotinfo always succeed; we read the text % following, through the first @@end iftex (etc.). Make `@@end iftex' % (etc.) valid only after an @@iftex. % \def\iftex{\conditionalsucceed{iftex}} \def\ifnothtml{\conditionalsucceed{ifnothtml}} \def\ifnotinfo{\conditionalsucceed{ifnotinfo}} \defineunmatchedend{iftex} \defineunmatchedend{ifnothtml} \defineunmatchedend{ifnotinfo} % We can't just want to start a group at @@iftex (for example) and end it % at @@end iftex, since then @@set commands inside the conditional have no % effect (they'd get reverted at the end of the group). So we must % define \Eiftex to redefine itself to be its previous value. (We can't % just define it to fail again with an ``unmatched end'' error, since % the @@ifset might be nested.) % \def\conditionalsucceed#1{% \edef\temp{% % Remember the current value of \E#1. \let\nece{prevE#1} = \nece{E#1}% % % At the `@@end #1', redefine \E#1 to be its previous value. \def\nece{E#1}{\let\nece{E#1} = \nece{prevE#1}}% }% \temp } % We need to expand lots of \csname's, but we don't want to expand the % control sequences after we've constructed them. % \def\nece#1{\expandafter\noexpand\csname#1\endcsname} % @@defininfoenclose. \let\definfoenclose=\comment \message{indexing,} % Index generation facilities % Define \newwrite to be identical to plain tex's \newwrite % except not \outer, so it can be used within \newindex. {\catcode`\@@=11 \gdef\newwrite{\alloc@@7\write\chardef\sixt@@@@n}} % \newindex {foo} defines an index named foo. % It automatically defines \fooindex such that % \fooindex ...rest of line... puts an entry in the index foo. % It also defines \fooindfile to be the number of the output channel for % the file that accumulates this index. The file's extension is foo. % The name of an index should be no more than 2 characters long % for the sake of vms. % \def\newindex#1{% \iflinks \expandafter\newwrite \csname#1indfile\endcsname \openout \csname#1indfile\endcsname \jobname.#1 % Open the file \fi \expandafter\xdef\csname#1index\endcsname{% % Define @@#1index \noexpand\doindex{#1}} } % @@defindex foo == \newindex{foo} \def\defindex{\parsearg\newindex} % Define @@defcodeindex, like @@defindex except put all entries in @@code. \def\newcodeindex#1{% \iflinks \expandafter\newwrite \csname#1indfile\endcsname \openout \csname#1indfile\endcsname \jobname.#1 \fi \expandafter\xdef\csname#1index\endcsname{% \noexpand\docodeindex{#1}} } \def\defcodeindex{\parsearg\newcodeindex} % @@synindex foo bar makes index foo feed into index bar. % Do this instead of @@defindex foo if you don't want it as a separate index. % The \closeout helps reduce unnecessary open files; the limit on the % Acorn RISC OS is a mere 16 files. \def\synindex#1 #2 {% \expandafter\let\expandafter\synindexfoo\expandafter=\csname#2indfile\endcsname \expandafter\closeout\csname#1indfile\endcsname \expandafter\let\csname#1indfile\endcsname=\synindexfoo \expandafter\xdef\csname#1index\endcsname{% define \xxxindex \noexpand\doindex{#2}}% } % @@syncodeindex foo bar similar, but put all entries made for index foo % inside @@code. \def\syncodeindex#1 #2 {% \expandafter\let\expandafter\synindexfoo\expandafter=\csname#2indfile\endcsname \expandafter\closeout\csname#1indfile\endcsname \expandafter\let\csname#1indfile\endcsname=\synindexfoo \expandafter\xdef\csname#1index\endcsname{% define \xxxindex \noexpand\docodeindex{#2}}% } % Define \doindex, the driver for all \fooindex macros. % Argument #1 is generated by the calling \fooindex macro, % and it is "foo", the name of the index. % \doindex just uses \parsearg; it calls \doind for the actual work. % This is because \doind is more useful to call from other macros. % There is also \dosubind {index}{topic}{subtopic} % which makes an entry in a two-level index such as the operation index. \def\doindex#1{\edef\indexname{#1}\parsearg\singleindexer} \def\singleindexer #1{\doind{\indexname}{#1}} % like the previous two, but they put @@code around the argument. \def\docodeindex#1{\edef\indexname{#1}\parsearg\singlecodeindexer} \def\singlecodeindexer #1{\doind{\indexname}{\code{#1}}} \def\indexdummies{% \def\ { }% % Take care of the plain tex accent commands. \def\"{\realbackslash "}% \def\`{\realbackslash `}% \def\'{\realbackslash '}% \def\^{\realbackslash ^}% \def\~{\realbackslash ~}% \def\={\realbackslash =}% \def\b{\realbackslash b}% \def\c{\realbackslash c}% \def\d{\realbackslash d}% \def\u{\realbackslash u}% \def\v{\realbackslash v}% \def\H{\realbackslash H}% % Take care of the plain tex special European modified letters. \def\oe{\realbackslash oe}% \def\ae{\realbackslash ae}% \def\aa{\realbackslash aa}% \def\OE{\realbackslash OE}% \def\AE{\realbackslash AE}% \def\AA{\realbackslash AA}% \def\o{\realbackslash o}% \def\O{\realbackslash O}% \def\l{\realbackslash l}% \def\L{\realbackslash L}% \def\ss{\realbackslash ss}% % Take care of texinfo commands likely to appear in an index entry. % (Must be a way to avoid doing expansion at all, and thus not have to % laboriously list every single command here.) \def\@@{@@}% will be @@@@ when we switch to @@ as escape char. % Need these in case \tex is in effect and \{ is a \delimiter again. % But can't use \lbracecmd and \rbracecmd because texindex assumes % braces and backslashes are used only as delimiters. \let\{ = \mylbrace \let\} = \myrbrace \def\_{{\realbackslash _}}% \def\w{\realbackslash w }% \def\bf{\realbackslash bf }% %\def\rm{\realbackslash rm }% \def\sl{\realbackslash sl }% \def\sf{\realbackslash sf}% \def\tt{\realbackslash tt}% \def\gtr{\realbackslash gtr}% \def\less{\realbackslash less}% \def\hat{\realbackslash hat}% \def\TeX{\realbackslash TeX}% \def\dots{\realbackslash dots }% \def\result{\realbackslash result}% \def\equiv{\realbackslash equiv}% \def\expansion{\realbackslash expansion}% \def\print{\realbackslash print}% \def\error{\realbackslash error}% \def\point{\realbackslash point}% \def\copyright{\realbackslash copyright}% \def\tclose##1{\realbackslash tclose {##1}}% \def\code##1{\realbackslash code {##1}}% \def\uref##1{\realbackslash uref {##1}}% \def\url##1{\realbackslash url {##1}}% \def\env##1{\realbackslash env {##1}}% \def\command##1{\realbackslash command {##1}}% \def\option##1{\realbackslash option {##1}}% \def\dotless##1{\realbackslash dotless {##1}}% \def\samp##1{\realbackslash samp {##1}}% \def\,##1{\realbackslash ,{##1}}% \def\t##1{\realbackslash t {##1}}% \def\r##1{\realbackslash r {##1}}% \def\i##1{\realbackslash i {##1}}% \def\b##1{\realbackslash b {##1}}% \def\sc##1{\realbackslash sc {##1}}% \def\cite##1{\realbackslash cite {##1}}% \def\key##1{\realbackslash key {##1}}% \def\file##1{\realbackslash file {##1}}% \def\var##1{\realbackslash var {##1}}% \def\kbd##1{\realbackslash kbd {##1}}% \def\dfn##1{\realbackslash dfn {##1}}% \def\emph##1{\realbackslash emph {##1}}% \def\acronym##1{\realbackslash acronym {##1}}% % % Handle some cases of @@value -- where the variable name does not % contain - or _, and the value does not contain any % (non-fully-expandable) commands. \let\value = \expandablevalue % \unsepspaces % Turn off macro expansion \turnoffmacros } % If an index command is used in an @@example environment, any spaces % therein should become regular spaces in the raw index file, not the % expansion of \tie (\\leavevmode \penalty \@@M \ ). {\obeyspaces \gdef\unsepspaces{\obeyspaces\let =\space}} % \indexnofonts no-ops all font-change commands. % This is used when outputting the strings to sort the index by. \def\indexdummyfont#1{#1} \def\indexdummytex{TeX} \def\indexdummydots{...} \def\indexnofonts{% % Just ignore accents. \let\,=\indexdummyfont \let\"=\indexdummyfont \let\`=\indexdummyfont \let\'=\indexdummyfont \let\^=\indexdummyfont \let\~=\indexdummyfont \let\==\indexdummyfont \let\b=\indexdummyfont \let\c=\indexdummyfont \let\d=\indexdummyfont \let\u=\indexdummyfont \let\v=\indexdummyfont \let\H=\indexdummyfont \let\dotless=\indexdummyfont % Take care of the plain tex special European modified letters. \def\oe{oe}% \def\ae{ae}% \def\aa{aa}% \def\OE{OE}% \def\AE{AE}% \def\AA{AA}% \def\o{o}% \def\O{O}% \def\l{l}% \def\L{L}% \def\ss{ss}% \let\w=\indexdummyfont \let\t=\indexdummyfont \let\r=\indexdummyfont \let\i=\indexdummyfont \let\b=\indexdummyfont \let\emph=\indexdummyfont \let\strong=\indexdummyfont \let\cite=\indexdummyfont \let\sc=\indexdummyfont %Don't no-op \tt, since it isn't a user-level command % and is used in the definitions of the active chars like <, >, |... %\let\tt=\indexdummyfont \let\tclose=\indexdummyfont \let\code=\indexdummyfont \let\url=\indexdummyfont \let\uref=\indexdummyfont \let\env=\indexdummyfont \let\acronym=\indexdummyfont \let\command=\indexdummyfont \let\option=\indexdummyfont \let\file=\indexdummyfont \let\samp=\indexdummyfont \let\kbd=\indexdummyfont \let\key=\indexdummyfont \let\var=\indexdummyfont \let\TeX=\indexdummytex \let\dots=\indexdummydots \def\@@{@@}% } % To define \realbackslash, we must make \ not be an escape. % We must first make another character (@@) an escape % so we do not become unable to do a definition. {\catcode`\@@=0 \catcode`\\=\other @@gdef@@realbackslash{\}} \let\indexbackslash=0 %overridden during \printindex. \let\SETmarginindex=\relax % put index entries in margin (undocumented)? % For \ifx comparisons. \def\emptymacro{\empty} % Most index entries go through here, but \dosubind is the general case. % \def\doind#1#2{\dosubind{#1}{#2}\empty} % Workhorse for all \fooindexes. % #1 is name of index, #2 is stuff to put there, #3 is subentry -- % \empty if called from \doind, as we usually are. The main exception % is with defuns, which call us directly. % \def\dosubind#1#2#3{% % Put the index entry in the margin if desired. \ifx\SETmarginindex\relax\else \insert\margin{\hbox{\vrule height8pt depth3pt width0pt #2}}% \fi {% \count255=\lastpenalty {% \indexdummies % Must do this here, since \bf, etc expand at this stage \escapechar=`\\ {% \let\folio = 0% We will expand all macros now EXCEPT \folio. \def\rawbackslashxx{\indexbackslash}% \indexbackslash isn't defined now % so it will be output as is; and it will print as backslash. % \def\thirdarg{#3}% % % If third arg is present, precede it with space in sort key. \ifx\thirdarg\emptymacro \let\subentry = \empty \else \def\subentry{ #3}% \fi % % First process the index entry with all font commands turned % off to get the string to sort by. {\indexnofonts \xdef\indexsorttmp{#2\subentry}}% % % Now the real index entry with the fonts. \toks0 = {#2}% % % If third (subentry) arg is present, add it to the index % string. And include a space. \ifx\thirdarg\emptymacro \else \toks0 = \expandafter{\the\toks0 \space #3}% \fi % % Set up the complete index entry, with both the sort key % and the original text, including any font commands. We write % three arguments to \entry to the .?? file, texindex reduces to % two when writing the .??s sorted result. \edef\temp{% \write\csname#1indfile\endcsname{% \realbackslash entry{\indexsorttmp}{\folio}{\the\toks0}}% }% % % If a skip is the last thing on the list now, preserve it % by backing up by \lastskip, doing the \write, then inserting % the skip again. Otherwise, the whatsit generated by the % \write will make \lastskip zero. The result is that sequences % like this: % @@end defun % @@tindex whatever % @@defun ... % will have extra space inserted, because the \medbreak in the % start of the @@defun won't see the skip inserted by the @@end of % the previous defun. % % But don't do any of this if we're not in vertical mode. We % don't want to do a \vskip and prematurely end a paragraph. % % Avoid page breaks due to these extra skips, too. % \iflinks \ifvmode \skip0 = \lastskip \ifdim\lastskip = 0pt \else \nobreak\vskip-\lastskip \fi \fi % \temp % do the write % % \ifvmode \ifdim\skip0 = 0pt \else \nobreak\vskip\skip0 \fi \fi \fi }% }% \penalty\count255 }% } % The index entry written in the file actually looks like % \entry {sortstring}{page}{topic} % or % \entry {sortstring}{page}{topic}{subtopic} % The texindex program reads in these files and writes files % containing these kinds of lines: % \initial {c} % before the first topic whose initial is c % \entry {topic}{pagelist} % for a topic that is used without subtopics % \primary {topic} % for the beginning of a topic that is used with subtopics % \secondary {subtopic}{pagelist} % for each subtopic. % Define the user-accessible indexing commands % @@findex, @@vindex, @@kindex, @@cindex. \def\findex {\fnindex} \def\kindex {\kyindex} \def\cindex {\cpindex} \def\vindex {\vrindex} \def\tindex {\tpindex} \def\pindex {\pgindex} \def\cindexsub {\begingroup\obeylines\cindexsub} {\obeylines % \gdef\cindexsub "#1" #2^^M{\endgroup % \dosubind{cp}{#2}{#1}}} % Define the macros used in formatting output of the sorted index material. % @@printindex causes a particular index (the ??s file) to get printed. % It does not print any chapter heading (usually an @@unnumbered). % \def\printindex{\parsearg\doprintindex} \def\doprintindex#1{\begingroup \dobreak \chapheadingskip{10000}% % \smallfonts \rm \tolerance = 9500 \indexbreaks % % See if the index file exists and is nonempty. % Change catcode of @@ here so that if the index file contains % \initial {@@} % as its first line, TeX doesn't complain about mismatched braces % (because it thinks @@} is a control sequence). \catcode`\@@ = 11 \openin 1 \jobname.#1s \ifeof 1 % \enddoublecolumns gets confused if there is no text in the index, % and it loses the chapter title and the aux file entries for the % index. The easiest way to prevent this problem is to make sure % there is some text. \putwordIndexNonexistent \else % % If the index file exists but is empty, then \openin leaves \ifeof % false. We have to make TeX try to read something from the file, so % it can discover if there is anything in it. \read 1 to \temp \ifeof 1 \putwordIndexIsEmpty \else % Index files are almost Texinfo source, but we use \ as the escape % character. It would be better to use @@, but that's too big a change % to make right now. \def\indexbackslash{\rawbackslashxx}% \catcode`\\ = 0 \escapechar = `\\ \begindoublecolumns \input \jobname.#1s \enddoublecolumns \fi \fi \closein 1 \endgroup} % These macros are used by the sorted index file itself. % Change them to control the appearance of the index. \def\initial#1{{% % Some minor font changes for the special characters. \let\tentt=\sectt \let\tt=\sectt \let\sf=\sectt % % Remove any glue we may have, we'll be inserting our own. \removelastskip % % We like breaks before the index initials, so insert a bonus. \penalty -300 % % Typeset the initial. Making this add up to a whole number of % baselineskips increases the chance of the dots lining up from column % to column. It still won't often be perfect, because of the stretch % we need before each entry, but it's better. % % No shrink because it confuses \balancecolumns. \vskip 1.67\baselineskip plus .5\baselineskip \leftline{\secbf #1}% \vskip .33\baselineskip plus .1\baselineskip % % Do our best not to break after the initial. \nobreak }} % This typesets a paragraph consisting of #1, dot leaders, and then #2 % flush to the right margin. It is used for index and table of contents % entries. The paragraph is indented by \leftskip. % \def\entry#1#2{\begingroup % % Start a new paragraph if necessary, so our assignments below can't % affect previous text. \par % % Do not fill out the last line with white space. \parfillskip = 0in % % No extra space above this paragraph. \parskip = 0in % % Do not prefer a separate line ending with a hyphen to fewer lines. \finalhyphendemerits = 0 % % \hangindent is only relevant when the entry text and page number % don't both fit on one line. In that case, bob suggests starting the % dots pretty far over on the line. Unfortunately, a large % indentation looks wrong when the entry text itself is broken across % lines. So we use a small indentation and put up with long leaders. % % \hangafter is reset to 1 (which is the value we want) at the start % of each paragraph, so we need not do anything with that. \hangindent = 2em % % When the entry text needs to be broken, just fill out the first line % with blank space. \rightskip = 0pt plus1fil % % A bit of stretch before each entry for the benefit of balancing columns. \vskip 0pt plus1pt % % Start a ``paragraph'' for the index entry so the line breaking % parameters we've set above will have an effect. \noindent % % Insert the text of the index entry. TeX will do line-breaking on it. #1% % The following is kludged to not output a line of dots in the index if % there are no page numbers. The next person who breaks this will be % cursed by a Unix daemon. \def\tempa{{\rm }}% \def\tempb{#2}% \edef\tempc{\tempa}% \edef\tempd{\tempb}% \ifx\tempc\tempd\ \else% % % If we must, put the page number on a line of its own, and fill out % this line with blank space. (The \hfil is overwhelmed with the % fill leaders glue in \indexdotfill if the page number does fit.) \hfil\penalty50 \null\nobreak\indexdotfill % Have leaders before the page number. % % The `\ ' here is removed by the implicit \unskip that TeX does as % part of (the primitive) \par. Without it, a spurious underfull % \hbox ensues. \ifpdf \pdfgettoks#2.\ \the\toksA % The page number ends the paragraph. \else \ #2% The page number ends the paragraph. \fi \fi% \par \endgroup} % Like \dotfill except takes at least 1 em. \def\indexdotfill{\cleaders \hbox{$\mathsurround=0pt \mkern1.5mu ${\it .}$ \mkern1.5mu$}\hskip 1em plus 1fill} \def\primary #1{\line{#1\hfil}} \newskip\secondaryindent \secondaryindent=0.5cm \def\secondary #1#2{ {\parfillskip=0in \parskip=0in \hangindent =1in \hangafter=1 \noindent\hskip\secondaryindent\hbox{#1}\indexdotfill #2\par }} % Define two-column mode, which we use to typeset indexes. % Adapted from the TeXbook, page 416, which is to say, % the manmac.tex format used to print the TeXbook itself. \catcode`\@@=11 \newbox\partialpage \newdimen\doublecolumnhsize \def\begindoublecolumns{\begingroup % ended by \enddoublecolumns % Grab any single-column material above us. \output = {% % % Here is a possibility not foreseen in manmac: if we accumulate a % whole lot of material, we might end up calling this \output % routine twice in a row (see the doublecol-lose test, which is % essentially a couple of indexes with @@setchapternewpage off). In % that case we just ship out what is in \partialpage with the normal % output routine. Generally, \partialpage will be empty when this % runs and this will be a no-op. See the indexspread.tex test case. \ifvoid\partialpage \else \onepageout{\pagecontents\partialpage}% \fi % \global\setbox\partialpage = \vbox{% % Unvbox the main output page. \unvbox\PAGE \kern-\topskip \kern\baselineskip }% }% \eject % run that output routine to set \partialpage % % Use the double-column output routine for subsequent pages. \output = {\doublecolumnout}% % % Change the page size parameters. We could do this once outside this % routine, in each of @@smallbook, @@afourpaper, and the default 8.5x11 % format, but then we repeat the same computation. Repeating a couple % of assignments once per index is clearly meaningless for the % execution time, so we may as well do it in one place. % % First we halve the line length, less a little for the gutter between % the columns. We compute the gutter based on the line length, so it % changes automatically with the paper format. The magic constant % below is chosen so that the gutter has the same value (well, +-<1pt) % as it did when we hard-coded it. % % We put the result in a separate register, \doublecolumhsize, so we % can restore it in \pagesofar, after \hsize itself has (potentially) % been clobbered. % \doublecolumnhsize = \hsize \advance\doublecolumnhsize by -.04154\hsize \divide\doublecolumnhsize by 2 \hsize = \doublecolumnhsize % % Double the \vsize as well. (We don't need a separate register here, % since nobody clobbers \vsize.) \advance\vsize by -\ht\partialpage \vsize = 2\vsize } % The double-column output routine for all double-column pages except % the last. % \def\doublecolumnout{% \splittopskip=\topskip \splitmaxdepth=\maxdepth % Get the available space for the double columns -- the normal % (undoubled) page height minus any material left over from the % previous page. \dimen@@ = \vsize \divide\dimen@@ by 2 % % box0 will be the left-hand column, box2 the right. \setbox0=\vsplit255 to\dimen@@ \setbox2=\vsplit255 to\dimen@@ \onepageout\pagesofar \unvbox255 \penalty\outputpenalty } \def\pagesofar{% % Re-output the contents of the output page -- any previous material, % followed by the two boxes we just split, in box0 and box2. \unvbox\partialpage % \hsize = \doublecolumnhsize \wd0=\hsize \wd2=\hsize \hbox to\pagewidth{\box0\hfil\box2}% } \def\enddoublecolumns{% \output = {% % Split the last of the double-column material. Leave it on the % current page, no automatic page break. \balancecolumns % % If we end up splitting too much material for the current page, % though, there will be another page break right after this \output % invocation ends. Having called \balancecolumns once, we do not % want to call it again. Therefore, reset \output to its normal % definition right away. (We hope \balancecolumns will never be % called on to balance too much material, but if it is, this makes % the output somewhat more palatable.) \global\output = {\onepageout{\pagecontents\PAGE}}% }% \eject \endgroup % started in \begindoublecolumns % % \pagegoal was set to the doubled \vsize above, since we restarted % the current page. We're now back to normal single-column % typesetting, so reset \pagegoal to the normal \vsize (after the % \endgroup where \vsize got restored). \pagegoal = \vsize } \def\balancecolumns{% % Called at the end of the double column material. \setbox0 = \vbox{\unvbox255}% like \box255 but more efficient, see p.120. \dimen@@ = \ht0 \advance\dimen@@ by \topskip \advance\dimen@@ by-\baselineskip \divide\dimen@@ by 2 % target to split to %debug\message{final 2-column material height=\the\ht0, target=\the\dimen@@.}% \splittopskip = \topskip % Loop until we get a decent breakpoint. {% \vbadness = 10000 \loop \global\setbox3 = \copy0 \global\setbox1 = \vsplit3 to \dimen@@ \ifdim\ht3>\dimen@@ \global\advance\dimen@@ by 1pt \repeat }% %debug\message{split to \the\dimen@@, column heights: \the\ht1, \the\ht3.}% \setbox0=\vbox to\dimen@@{\unvbox1}% \setbox2=\vbox to\dimen@@{\unvbox3}% % \pagesofar } \catcode`\@@ = \other \message{sectioning,} % Chapters, sections, etc. \newcount\chapno \newcount\secno \secno=0 \newcount\subsecno \subsecno=0 \newcount\subsubsecno \subsubsecno=0 % This counter is funny since it counts through charcodes of letters A, B, ... \newcount\appendixno \appendixno = `\@@ % \def\appendixletter{\char\the\appendixno} % We do the following for the sake of pdftex, which needs the actual % letter in the expansion, not just typeset. \def\appendixletter{% \ifnum\appendixno=`A A% \else\ifnum\appendixno=`B B% \else\ifnum\appendixno=`C C% \else\ifnum\appendixno=`D D% \else\ifnum\appendixno=`E E% \else\ifnum\appendixno=`F F% \else\ifnum\appendixno=`G G% \else\ifnum\appendixno=`H H% \else\ifnum\appendixno=`I I% \else\ifnum\appendixno=`J J% \else\ifnum\appendixno=`K K% \else\ifnum\appendixno=`L L% \else\ifnum\appendixno=`M M% \else\ifnum\appendixno=`N N% \else\ifnum\appendixno=`O O% \else\ifnum\appendixno=`P P% \else\ifnum\appendixno=`Q Q% \else\ifnum\appendixno=`R R% \else\ifnum\appendixno=`S S% \else\ifnum\appendixno=`T T% \else\ifnum\appendixno=`U U% \else\ifnum\appendixno=`V V% \else\ifnum\appendixno=`W W% \else\ifnum\appendixno=`X X% \else\ifnum\appendixno=`Y Y% \else\ifnum\appendixno=`Z Z% % The \the is necessary, despite appearances, because \appendixletter is % expanded while writing the .toc file. \char\appendixno is not % expandable, thus it is written literally, thus all appendixes come out % with the same letter (or @@) in the toc without it. \else\char\the\appendixno \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi} % Each @@chapter defines this as the name of the chapter. % page headings and footings can use it. @@section does likewise. \def\thischapter{} \def\thissection{} \newcount\absseclevel % used to calculate proper heading level \newcount\secbase\secbase=0 % @@raise/lowersections modify this count % @@raisesections: treat @@section as chapter, @@subsection as section, etc. \def\raisesections{\global\advance\secbase by -1} \let\up=\raisesections % original BFox name % @@lowersections: treat @@chapter as section, @@section as subsection, etc. \def\lowersections{\global\advance\secbase by 1} \let\down=\lowersections % original BFox name % Choose a numbered-heading macro % #1 is heading level if unmodified by @@raisesections or @@lowersections % #2 is text for heading \def\numhead#1#2{\absseclevel=\secbase\advance\absseclevel by #1 \ifcase\absseclevel \chapterzzz{#2} \or \seczzz{#2} \or \numberedsubseczzz{#2} \or \numberedsubsubseczzz{#2} \else \ifnum \absseclevel<0 \chapterzzz{#2} \else \numberedsubsubseczzz{#2} \fi \fi } % like \numhead, but chooses appendix heading levels \def\apphead#1#2{\absseclevel=\secbase\advance\absseclevel by #1 \ifcase\absseclevel \appendixzzz{#2} \or \appendixsectionzzz{#2} \or \appendixsubseczzz{#2} \or \appendixsubsubseczzz{#2} \else \ifnum \absseclevel<0 \appendixzzz{#2} \else \appendixsubsubseczzz{#2} \fi \fi } % like \numhead, but chooses numberless heading levels \def\unnmhead#1#2{\absseclevel=\secbase\advance\absseclevel by #1 \ifcase\absseclevel \unnumberedzzz{#2} \or \unnumberedseczzz{#2} \or \unnumberedsubseczzz{#2} \or \unnumberedsubsubseczzz{#2} \else \ifnum \absseclevel<0 \unnumberedzzz{#2} \else \unnumberedsubsubseczzz{#2} \fi \fi } % @@chapter, @@appendix, @@unnumbered. \def\thischaptername{No Chapter Title} \outer\def\chapter{\parsearg\chapteryyy} \def\chapteryyy #1{\numhead0{#1}} % normally numhead0 calls chapterzzz \def\chapterzzz #1{% \secno=0 \subsecno=0 \subsubsecno=0 \global\advance \chapno by 1 \message{\putwordChapter\space \the\chapno}% \chapmacro {#1}{\the\chapno}% \gdef\thissection{#1}% \gdef\thischaptername{#1}% % We don't substitute the actual chapter name into \thischapter % because we don't want its macros evaluated now. \xdef\thischapter{\putwordChapter{} \the\chapno: \noexpand\thischaptername}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash chapentry{\the\toks0}% {\the\chapno}}}% \temp \donoderef \global\let\section = \numberedsec \global\let\subsection = \numberedsubsec \global\let\subsubsection = \numberedsubsubsec } \outer\def\appendix{\parsearg\appendixyyy} \def\appendixyyy #1{\apphead0{#1}} % normally apphead0 calls appendixzzz \def\appendixzzz #1{% \secno=0 \subsecno=0 \subsubsecno=0 \global\advance \appendixno by 1 \message{\putwordAppendix\space \appendixletter}% \chapmacro {#1}{\putwordAppendix{} \appendixletter}% \gdef\thissection{#1}% \gdef\thischaptername{#1}% \xdef\thischapter{\putwordAppendix{} \appendixletter: \noexpand\thischaptername}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash chapentry{\the\toks0}% {\putwordAppendix{} \appendixletter}}}% \temp \appendixnoderef \global\let\section = \appendixsec \global\let\subsection = \appendixsubsec \global\let\subsubsection = \appendixsubsubsec } % @@centerchap is like @@unnumbered, but the heading is centered. \outer\def\centerchap{\parsearg\centerchapyyy} \def\centerchapyyy #1{{\let\unnumbchapmacro=\centerchapmacro \unnumberedyyy{#1}}} % @@top is like @@unnumbered. \outer\def\top{\parsearg\unnumberedyyy} \outer\def\unnumbered{\parsearg\unnumberedyyy} \def\unnumberedyyy #1{\unnmhead0{#1}} % normally unnmhead0 calls unnumberedzzz \def\unnumberedzzz #1{% \secno=0 \subsecno=0 \subsubsecno=0 % % This used to be simply \message{#1}, but TeX fully expands the % argument to \message. Therefore, if #1 contained @@-commands, TeX % expanded them. For example, in `@@unnumbered The @@cite{Book}', TeX % expanded @@cite (which turns out to cause errors because \cite is meant % to be executed, not expanded). % % Anyway, we don't want the fully-expanded definition of @@cite to appear % as a result of the \message, we just want `@@cite' itself. We use % \the to achieve this: TeX expands \the only once, % simply yielding the contents of . (We also do this for % the toc entries.) \toks0 = {#1}\message{(\the\toks0)}% % \unnumbchapmacro {#1}% \gdef\thischapter{#1}\gdef\thissection{#1}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash unnumbchapentry{\the\toks0}}}% \temp \unnumbnoderef \global\let\section = \unnumberedsec \global\let\subsection = \unnumberedsubsec \global\let\subsubsection = \unnumberedsubsubsec } % Sections. \outer\def\numberedsec{\parsearg\secyyy} \def\secyyy #1{\numhead1{#1}} % normally calls seczzz \def\seczzz #1{% \subsecno=0 \subsubsecno=0 \global\advance \secno by 1 % \gdef\thissection{#1}\secheading {#1}{\the\chapno}{\the\secno}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash secentry{\the\toks0}% {\the\chapno}{\the\secno}}}% \temp \donoderef \nobreak } \outer\def\appendixsection{\parsearg\appendixsecyyy} \outer\def\appendixsec{\parsearg\appendixsecyyy} \def\appendixsecyyy #1{\apphead1{#1}} % normally calls appendixsectionzzz \def\appendixsectionzzz #1{% \subsecno=0 \subsubsecno=0 \global\advance \secno by 1 % \gdef\thissection{#1}\secheading {#1}{\appendixletter}{\the\secno}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash secentry{\the\toks0}% {\appendixletter}{\the\secno}}}% \temp \appendixnoderef \nobreak } \outer\def\unnumberedsec{\parsearg\unnumberedsecyyy} \def\unnumberedsecyyy #1{\unnmhead1{#1}} % normally calls unnumberedseczzz \def\unnumberedseczzz #1{% \plainsecheading {#1}\gdef\thissection{#1}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash unnumbsecentry{\the\toks0}}}% \temp \unnumbnoderef \nobreak } % Subsections. \outer\def\numberedsubsec{\parsearg\numberedsubsecyyy} \def\numberedsubsecyyy #1{\numhead2{#1}} % normally calls numberedsubseczzz \def\numberedsubseczzz #1{% \gdef\thissection{#1}\subsubsecno=0 \global\advance \subsecno by 1 % \subsecheading {#1}{\the\chapno}{\the\secno}{\the\subsecno}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash subsecentry{\the\toks0}% {\the\chapno}{\the\secno}{\the\subsecno}}}% \temp \donoderef \nobreak } \outer\def\appendixsubsec{\parsearg\appendixsubsecyyy} \def\appendixsubsecyyy #1{\apphead2{#1}} % normally calls appendixsubseczzz \def\appendixsubseczzz #1{% \gdef\thissection{#1}\subsubsecno=0 \global\advance \subsecno by 1 % \subsecheading {#1}{\appendixletter}{\the\secno}{\the\subsecno}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash subsecentry{\the\toks0}% {\appendixletter}{\the\secno}{\the\subsecno}}}% \temp \appendixnoderef \nobreak } \outer\def\unnumberedsubsec{\parsearg\unnumberedsubsecyyy} \def\unnumberedsubsecyyy #1{\unnmhead2{#1}} %normally calls unnumberedsubseczzz \def\unnumberedsubseczzz #1{% \plainsubsecheading {#1}\gdef\thissection{#1}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash unnumbsubsecentry% {\the\toks0}}}% \temp \unnumbnoderef \nobreak } % Subsubsections. \outer\def\numberedsubsubsec{\parsearg\numberedsubsubsecyyy} \def\numberedsubsubsecyyy #1{\numhead3{#1}} % normally numberedsubsubseczzz \def\numberedsubsubseczzz #1{% \gdef\thissection{#1}\global\advance \subsubsecno by 1 % \subsubsecheading {#1} {\the\chapno}{\the\secno}{\the\subsecno}{\the\subsubsecno}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash subsubsecentry{\the\toks0}% {\the\chapno}{\the\secno}{\the\subsecno}{\the\subsubsecno}}}% \temp \donoderef \nobreak } \outer\def\appendixsubsubsec{\parsearg\appendixsubsubsecyyy} \def\appendixsubsubsecyyy #1{\apphead3{#1}} % normally appendixsubsubseczzz \def\appendixsubsubseczzz #1{% \gdef\thissection{#1}\global\advance \subsubsecno by 1 % \subsubsecheading {#1} {\appendixletter}{\the\secno}{\the\subsecno}{\the\subsubsecno}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash subsubsecentry{\the\toks0}% {\appendixletter}{\the\secno}{\the\subsecno}{\the\subsubsecno}}}% \temp \appendixnoderef \nobreak } \outer\def\unnumberedsubsubsec{\parsearg\unnumberedsubsubsecyyy} \def\unnumberedsubsubsecyyy #1{\unnmhead3{#1}} %normally unnumberedsubsubseczzz \def\unnumberedsubsubseczzz #1{% \plainsubsubsecheading {#1}\gdef\thissection{#1}% \toks0 = {#1}% \edef\temp{\noexpand\writetocentry{\realbackslash unnumbsubsubsecentry% {\the\toks0}}}% \temp \unnumbnoderef \nobreak } % These are variants which are not "outer", so they can appear in @@ifinfo. % Actually, they should now be obsolete; ordinary section commands should work. \def\infotop{\parsearg\unnumberedzzz} \def\infounnumbered{\parsearg\unnumberedzzz} \def\infounnumberedsec{\parsearg\unnumberedseczzz} \def\infounnumberedsubsec{\parsearg\unnumberedsubseczzz} \def\infounnumberedsubsubsec{\parsearg\unnumberedsubsubseczzz} \def\infoappendix{\parsearg\appendixzzz} \def\infoappendixsec{\parsearg\appendixseczzz} \def\infoappendixsubsec{\parsearg\appendixsubseczzz} \def\infoappendixsubsubsec{\parsearg\appendixsubsubseczzz} \def\infochapter{\parsearg\chapterzzz} \def\infosection{\parsearg\sectionzzz} \def\infosubsection{\parsearg\subsectionzzz} \def\infosubsubsection{\parsearg\subsubsectionzzz} % These macros control what the section commands do, according % to what kind of chapter we are in (ordinary, appendix, or unnumbered). % Define them by default for a numbered chapter. \global\let\section = \numberedsec \global\let\subsection = \numberedsubsec \global\let\subsubsection = \numberedsubsubsec % Define @@majorheading, @@heading and @@subheading % NOTE on use of \vbox for chapter headings, section headings, and such: % 1) We use \vbox rather than the earlier \line to permit % overlong headings to fold. % 2) \hyphenpenalty is set to 10000 because hyphenation in a % heading is obnoxious; this forbids it. % 3) Likewise, headings look best if no \parindent is used, and % if justification is not attempted. Hence \raggedright. \def\majorheading{\parsearg\majorheadingzzz} \def\majorheadingzzz #1{% {\advance\chapheadingskip by 10pt \chapbreak }% {\chapfonts \vbox{\hyphenpenalty=10000\tolerance=5000 \parindent=0pt\raggedright \rm #1\hfill}}\bigskip \par\penalty 200} \def\chapheading{\parsearg\chapheadingzzz} \def\chapheadingzzz #1{\chapbreak % {\chapfonts \vbox{\hyphenpenalty=10000\tolerance=5000 \parindent=0pt\raggedright \rm #1\hfill}}\bigskip \par\penalty 200} % @@heading, @@subheading, @@subsubheading. \def\heading{\parsearg\plainsecheading} \def\subheading{\parsearg\plainsubsecheading} \def\subsubheading{\parsearg\plainsubsubsecheading} % These macros generate a chapter, section, etc. heading only % (including whitespace, linebreaking, etc. around it), % given all the information in convenient, parsed form. %%% Args are the skip and penalty (usually negative) \def\dobreak#1#2{\par\ifdim\lastskip<#1\removelastskip\penalty#2\vskip#1\fi} \def\setchapterstyle #1 {\csname CHAPF#1\endcsname} %%% Define plain chapter starts, and page on/off switching for it % Parameter controlling skip before chapter headings (if needed) \newskip\chapheadingskip \def\chapbreak{\dobreak \chapheadingskip {-4000}} \def\chappager{\par\vfill\supereject} \def\chapoddpage{\chappager \ifodd\pageno \else \hbox to 0pt{} \chappager\fi} \def\setchapternewpage #1 {\csname CHAPPAG#1\endcsname} \def\CHAPPAGoff{% \global\let\contentsalignmacro = \chappager \global\let\pchapsepmacro=\chapbreak \global\let\pagealignmacro=\chappager} \def\CHAPPAGon{% \global\let\contentsalignmacro = \chappager \global\let\pchapsepmacro=\chappager \global\let\pagealignmacro=\chappager \global\def\HEADINGSon{\HEADINGSsingle}} \def\CHAPPAGodd{ \global\let\contentsalignmacro = \chapoddpage \global\let\pchapsepmacro=\chapoddpage \global\let\pagealignmacro=\chapoddpage \global\def\HEADINGSon{\HEADINGSdouble}} \CHAPPAGon \def\CHAPFplain{ \global\let\chapmacro=\chfplain \global\let\unnumbchapmacro=\unnchfplain \global\let\centerchapmacro=\centerchfplain} % Plain chapter opening. % #1 is the text, #2 the chapter number or empty if unnumbered. \def\chfplain#1#2{% \pchapsepmacro {% \chapfonts \rm \def\chapnum{#2}% \setbox0 = \hbox{#2\ifx\chapnum\empty\else\enspace\fi}% \vbox{\hyphenpenalty=10000 \tolerance=5000 \parindent=0pt \raggedright \hangindent = \wd0 \centerparametersmaybe \unhbox0 #1\par}% }% \nobreak\bigskip % no page break after a chapter title \nobreak } % Plain opening for unnumbered. \def\unnchfplain#1{\chfplain{#1}{}} % @@centerchap -- centered and unnumbered. \let\centerparametersmaybe = \relax \def\centerchfplain#1{{% \def\centerparametersmaybe{% \advance\rightskip by 3\rightskip \leftskip = \rightskip \parfillskip = 0pt }% \chfplain{#1}{}% }} \CHAPFplain % The default \def\unnchfopen #1{% \chapoddpage {\chapfonts \vbox{\hyphenpenalty=10000\tolerance=5000 \parindent=0pt\raggedright \rm #1\hfill}}\bigskip \par\nobreak } \def\chfopen #1#2{\chapoddpage {\chapfonts \vbox to 3in{\vfil \hbox to\hsize{\hfil #2} \hbox to\hsize{\hfil #1} \vfil}}% \par\penalty 5000 % } \def\centerchfopen #1{% \chapoddpage {\chapfonts \vbox{\hyphenpenalty=10000\tolerance=5000 \parindent=0pt \hfill {\rm #1}\hfill}}\bigskip \par\nobreak } \def\CHAPFopen{ \global\let\chapmacro=\chfopen \global\let\unnumbchapmacro=\unnchfopen \global\let\centerchapmacro=\centerchfopen} % Section titles. \newskip\secheadingskip \def\secheadingbreak{\dobreak \secheadingskip {-1000}} \def\secheading#1#2#3{\sectionheading{sec}{#2.#3}{#1}} \def\plainsecheading#1{\sectionheading{sec}{}{#1}} % Subsection titles. \newskip \subsecheadingskip \def\subsecheadingbreak{\dobreak \subsecheadingskip {-500}} \def\subsecheading#1#2#3#4{\sectionheading{subsec}{#2.#3.#4}{#1}} \def\plainsubsecheading#1{\sectionheading{subsec}{}{#1}} % Subsubsection titles. \let\subsubsecheadingskip = \subsecheadingskip \let\subsubsecheadingbreak = \subsecheadingbreak \def\subsubsecheading#1#2#3#4#5{\sectionheading{subsubsec}{#2.#3.#4.#5}{#1}} \def\plainsubsubsecheading#1{\sectionheading{subsubsec}{}{#1}} % Print any size section title. % % #1 is the section type (sec/subsec/subsubsec), #2 is the section % number (maybe empty), #3 the text. \def\sectionheading#1#2#3{% {% \expandafter\advance\csname #1headingskip\endcsname by \parskip \csname #1headingbreak\endcsname }% {% % Switch to the right set of fonts. \csname #1fonts\endcsname \rm % % Only insert the separating space if we have a section number. \def\secnum{#2}% \setbox0 = \hbox{#2\ifx\secnum\empty\else\enspace\fi}% % \vbox{\hyphenpenalty=10000 \tolerance=5000 \parindent=0pt \raggedright \hangindent = \wd0 % zero if no section number \unhbox0 #3}% }% \ifdim\parskip<10pt \nobreak\kern10pt\nobreak\kern-\parskip\fi \nobreak } \message{toc,} % Table of contents. \newwrite\tocfile % Write an entry to the toc file, opening it if necessary. % Called from @@chapter, etc. We supply {\folio} at the end of the % argument, which will end up as the last argument to the \...entry macro. % % We open the .toc file here instead of at @@setfilename or any other % given time so that @@contents can be put in the document anywhere. % \newif\iftocfileopened \def\writetocentry#1{% \iftocfileopened\else \immediate\openout\tocfile = \jobname.toc \global\tocfileopenedtrue \fi \iflinks \write\tocfile{#1{\folio}}\fi } \newskip\contentsrightmargin \contentsrightmargin=1in \newcount\savepageno \newcount\lastnegativepageno \lastnegativepageno = -1 % Finish up the main text and prepare to read what we've written % to \tocfile. % \def\startcontents#1{% % If @@setchapternewpage on, and @@headings double, the contents should % start on an odd page, unlike chapters. Thus, we maintain % \contentsalignmacro in parallel with \pagealignmacro. % From: Torbjorn Granlund \contentsalignmacro \immediate\closeout\tocfile % % Don't need to put `Contents' or `Short Contents' in the headline. % It is abundantly clear what they are. \unnumbchapmacro{#1}\def\thischapter{}% \savepageno = \pageno \begingroup % Set up to handle contents files properly. \catcode`\\=0 \catcode`\{=1 \catcode`\}=2 \catcode`\@@=11 % We can't do this, because then an actual ^ in a section % title fails, e.g., @@chapter ^ -- exponentiation. --karl, 9jul97. %\catcode`\^=7 % to see ^^e4 as \"a etc. juha@@piuha.ydi.vtt.fi \raggedbottom % Worry more about breakpoints than the bottom. \advance\hsize by -\contentsrightmargin % Don't use the full line length. % % Roman numerals for page numbers. \ifnum \pageno>0 \pageno = \lastnegativepageno \fi } % Normal (long) toc. \def\contents{% \startcontents{\putwordTOC}% \openin 1 \jobname.toc \ifeof 1 \else \closein 1 \input \jobname.toc \fi \vfill \eject \contentsalignmacro % in case @@setchapternewpage odd is in effect \pdfmakeoutlines \endgroup \lastnegativepageno = \pageno \pageno = \savepageno } % And just the chapters. \def\summarycontents{% \startcontents{\putwordShortTOC}% % \let\chapentry = \shortchapentry \let\unnumbchapentry = \shortunnumberedentry % We want a true roman here for the page numbers. \secfonts \let\rm=\shortcontrm \let\bf=\shortcontbf \let\sl=\shortcontsl \rm \hyphenpenalty = 10000 \advance\baselineskip by 1pt % Open it up a little. \def\secentry ##1##2##3##4{} \def\unnumbsecentry ##1##2{} \def\subsecentry ##1##2##3##4##5{} \def\unnumbsubsecentry ##1##2{} \def\subsubsecentry ##1##2##3##4##5##6{} \def\unnumbsubsubsecentry ##1##2{} \openin 1 \jobname.toc \ifeof 1 \else \closein 1 \input \jobname.toc \fi \vfill \eject \contentsalignmacro % in case @@setchapternewpage odd is in effect \endgroup \lastnegativepageno = \pageno \pageno = \savepageno } \let\shortcontents = \summarycontents \ifpdf \pdfcatalog{/PageMode /UseOutlines}% \fi % These macros generate individual entries in the table of contents. % The first argument is the chapter or section name. % The last argument is the page number. % The arguments in between are the chapter number, section number, ... % Chapter-level things, for both the long and short contents. \def\chapentry#1#2#3{\dochapentry{#2\labelspace#1}{#3}} % See comments in \dochapentry re vbox and related settings \def\shortchapentry#1#2#3{% \tocentry{\shortchaplabel{#2}\labelspace #1}{\doshortpageno\bgroup#3\egroup}% } % Typeset the label for a chapter or appendix for the short contents. % The arg is, e.g. `Appendix A' for an appendix, or `3' for a chapter. % We could simplify the code here by writing out an \appendixentry % command in the toc file for appendices, instead of using \chapentry % for both, but it doesn't seem worth it. % \newdimen\shortappendixwidth % \def\shortchaplabel#1{% % Compute width of word "Appendix", may change with language. \setbox0 = \hbox{\shortcontrm \putwordAppendix}% \shortappendixwidth = \wd0 % % We typeset #1 in a box of constant width, regardless of the text of % #1, so the chapter titles will come out aligned. \setbox0 = \hbox{#1}% \dimen0 = \ifdim\wd0 > \shortappendixwidth \shortappendixwidth \else 0pt \fi % % This space should be plenty, since a single number is .5em, and the % widest letter (M) is 1em, at least in the Computer Modern fonts. % (This space doesn't include the extra space that gets added after % the label; that gets put in by \shortchapentry above.) \advance\dimen0 by 1.1em \hbox to \dimen0{#1\hfil}% } \def\unnumbchapentry#1#2{\dochapentry{#1}{#2}} \def\shortunnumberedentry#1#2{\tocentry{#1}{\doshortpageno\bgroup#2\egroup}} % Sections. \def\secentry#1#2#3#4{\dosecentry{#2.#3\labelspace#1}{#4}} \def\unnumbsecentry#1#2{\dosecentry{#1}{#2}} % Subsections. \def\subsecentry#1#2#3#4#5{\dosubsecentry{#2.#3.#4\labelspace#1}{#5}} \def\unnumbsubsecentry#1#2{\dosubsecentry{#1}{#2}} % And subsubsections. \def\subsubsecentry#1#2#3#4#5#6{% \dosubsubsecentry{#2.#3.#4.#5\labelspace#1}{#6}} \def\unnumbsubsubsecentry#1#2{\dosubsubsecentry{#1}{#2}} % This parameter controls the indentation of the various levels. \newdimen\tocindent \tocindent = 3pc % Now for the actual typesetting. In all these, #1 is the text and #2 is the % page number. % % If the toc has to be broken over pages, we want it to be at chapters % if at all possible; hence the \penalty. \def\dochapentry#1#2{% \penalty-300 \vskip1\baselineskip plus.33\baselineskip minus.25\baselineskip \begingroup \chapentryfonts \tocentry{#1}{\dopageno\bgroup#2\egroup}% \endgroup \nobreak\vskip .25\baselineskip plus.1\baselineskip } \def\dosecentry#1#2{\begingroup \secentryfonts \leftskip=\tocindent \tocentry{#1}{\dopageno\bgroup#2\egroup}% \endgroup} \def\dosubsecentry#1#2{\begingroup \subsecentryfonts \leftskip=2\tocindent \tocentry{#1}{\dopageno\bgroup#2\egroup}% \endgroup} \def\dosubsubsecentry#1#2{\begingroup \subsubsecentryfonts \leftskip=3\tocindent \tocentry{#1}{\dopageno\bgroup#2\egroup}% \endgroup} % Final typesetting of a toc entry; we use the same \entry macro as for % the index entries, but we want to suppress hyphenation here. (We % can't do that in the \entry macro, since index entries might consist % of hyphenated-identifiers-that-do-not-fit-on-a-line-and-nothing-else.) \def\tocentry#1#2{\begingroup \vskip 0pt plus1pt % allow a little stretch for the sake of nice page breaks % Do not use \turnoffactive in these arguments. Since the toc is % typeset in cmr, so characters such as _ would come out wrong; we % have to do the usual translation tricks. \entry{#1}{#2}% \endgroup} % Space between chapter (or whatever) number and the title. \def\labelspace{\hskip1em \relax} \def\dopageno#1{{\rm #1}} \def\doshortpageno#1{{\rm #1}} \def\chapentryfonts{\secfonts \rm} \def\secentryfonts{\textfonts} \let\subsecentryfonts = \textfonts \let\subsubsecentryfonts = \textfonts \message{environments,} % @@foo ... @@end foo. % Since these characters are used in examples, it should be an even number of % \tt widths. Each \tt character is 1en, so two makes it 1em. % Furthermore, these definitions must come after we define our fonts. \newbox\dblarrowbox \newbox\longdblarrowbox \newbox\pushcharbox \newbox\bullbox \newbox\equivbox \newbox\errorbox %{\tentt %\global\setbox\dblarrowbox = \hbox to 1em{\hfil$\Rightarrow$\hfil} %\global\setbox\longdblarrowbox = \hbox to 1em{\hfil$\mapsto$\hfil} %\global\setbox\pushcharbox = \hbox to 1em{\hfil$\dashv$\hfil} %\global\setbox\equivbox = \hbox to 1em{\hfil$\ptexequiv$\hfil} % Adapted from the manmac format (p.420 of TeXbook) %\global\setbox\bullbox = \hbox to 1em{\kern.15em\vrule height .75ex width .85ex % depth .1ex\hfil} %} % @@point{}, @@result{}, @@expansion{}, @@print{}, @@equiv{}. \def\point{$\star$} \def\result{\leavevmode\raise.15ex\hbox to 1em{\hfil$\Rightarrow$\hfil}} \def\expansion{\leavevmode\raise.1ex\hbox to 1em{\hfil$\mapsto$\hfil}} \def\print{\leavevmode\lower.1ex\hbox to 1em{\hfil$\dashv$\hfil}} \def\equiv{\leavevmode\lower.1ex\hbox to 1em{\hfil$\ptexequiv$\hfil}} % Adapted from the TeXbook's \boxit. {\tentt \global\dimen0 = 3em}% Width of the box. \dimen2 = .55pt % Thickness of rules % The text. (`r' is open on the right, `e' somewhat less so on the left.) \setbox0 = \hbox{\kern-.75pt \tensf error\kern-1.5pt} \global\setbox\errorbox=\hbox to \dimen0{\hfil \hsize = \dimen0 \advance\hsize by -5.8pt % Space to left+right. \advance\hsize by -2\dimen2 % Rules. \vbox{ \hrule height\dimen2 \hbox{\vrule width\dimen2 \kern3pt % Space to left of text. \vtop{\kern2.4pt \box0 \kern2.4pt}% Space above/below. \kern3pt\vrule width\dimen2}% Space to right. \hrule height\dimen2} \hfil} % The @@error{} command. \def\error{\leavevmode\lower.7ex\copy\errorbox} % @@tex ... @@end tex escapes into raw Tex temporarily. % One exception: @@ is still an escape character, so that @@end tex works. % But \@@ or @@@@ will get a plain tex @@ character. \def\tex{\begingroup \catcode `\\=0 \catcode `\{=1 \catcode `\}=2 \catcode `\$=3 \catcode `\&=4 \catcode `\#=6 \catcode `\^=7 \catcode `\_=8 \catcode `\~=13 \let~=\tie \catcode `\%=14 \catcode 43=12 % plus \catcode`\"=12 \catcode`\==12 \catcode`\|=12 \catcode`\<=12 \catcode`\>=12 \escapechar=`\\ % \let\b=\ptexb \let\bullet=\ptexbullet \let\c=\ptexc \let\,=\ptexcomma \let\.=\ptexdot \let\dots=\ptexdots \let\equiv=\ptexequiv \let\!=\ptexexclam \let\i=\ptexi \let\{=\ptexlbrace \let\+=\tabalign \let\}=\ptexrbrace \let\*=\ptexstar \let\t=\ptext % \def\endldots{\mathinner{\ldots\ldots\ldots\ldots}}% \def\enddots{\relax\ifmmode\endldots\else$\mathsurround=0pt \endldots\,$\fi}% \def\@@{@@}% \let\Etex=\endgroup} % Define @@lisp ... @@endlisp. % @@lisp does a \begingroup so it can rebind things, % including the definition of @@endlisp (which normally is erroneous). % Amount to narrow the margins by for @@lisp. \newskip\lispnarrowing \lispnarrowing=0.4in % This is the definition that ^^M gets inside @@lisp, @@example, and other % such environments. \null is better than a space, since it doesn't % have any width. \def\lisppar{\null\endgraf} % Make each space character in the input produce a normal interword % space in the output. Don't allow a line break at this space, as this % is used only in environments like @@example, where each line of input % should produce a line of output anyway. % {\obeyspaces % \gdef\sepspaces{\obeyspaces\let =\tie}} % Define \obeyedspace to be our active space, whatever it is. This is % for use in \parsearg. {\sepspaces% \global\let\obeyedspace= } % This space is always present above and below environments. \newskip\envskipamount \envskipamount = 0pt % Make spacing and below environment symmetrical. We use \parskip here % to help in doing that, since in @@example-like environments \parskip % is reset to zero; thus the \afterenvbreak inserts no space -- but the % start of the next paragraph will insert \parskip % \def\aboveenvbreak{{\advance\envskipamount by \parskip \endgraf \ifdim\lastskip<\envskipamount \removelastskip \penalty-50 \vskip\envskipamount \fi}} \let\afterenvbreak = \aboveenvbreak % \nonarrowing is a flag. If "set", @@lisp etc don't narrow margins. \let\nonarrowing=\relax % @@cartouche ... @@end cartouche: draw rectangle w/rounded corners around % environment contents. \font\circle=lcircle10 \newdimen\circthick \newdimen\cartouter\newdimen\cartinner \newskip\normbskip\newskip\normpskip\newskip\normlskip \circthick=\fontdimen8\circle % \def\ctl{{\circle\char'013\hskip -6pt}}% 6pt from pl file: 1/2charwidth \def\ctr{{\hskip 6pt\circle\char'010}} \def\cbl{{\circle\char'012\hskip -6pt}} \def\cbr{{\hskip 6pt\circle\char'011}} \def\carttop{\hbox to \cartouter{\hskip\lskip \ctl\leaders\hrule height\circthick\hfil\ctr \hskip\rskip}} \def\cartbot{\hbox to \cartouter{\hskip\lskip \cbl\leaders\hrule height\circthick\hfil\cbr \hskip\rskip}} % \newskip\lskip\newskip\rskip \long\def\cartouche{% \begingroup \lskip=\leftskip \rskip=\rightskip \leftskip=0pt\rightskip=0pt %we want these *outside*. \cartinner=\hsize \advance\cartinner by-\lskip \advance\cartinner by-\rskip \cartouter=\hsize \advance\cartouter by 18.4pt % allow for 3pt kerns on either % side, and for 6pt waste from % each corner char, and rule thickness \normbskip=\baselineskip \normpskip=\parskip \normlskip=\lineskip % Flag to tell @@lisp, etc., not to narrow margin. \let\nonarrowing=\comment \vbox\bgroup \baselineskip=0pt\parskip=0pt\lineskip=0pt \carttop \hbox\bgroup \hskip\lskip \vrule\kern3pt \vbox\bgroup \hsize=\cartinner \kern3pt \begingroup \baselineskip=\normbskip \lineskip=\normlskip \parskip=\normpskip \vskip -\parskip \def\Ecartouche{% \endgroup \kern3pt \egroup \kern3pt\vrule \hskip\rskip \egroup \cartbot \egroup \endgroup }} % This macro is called at the beginning of all the @@example variants, % inside a group. \def\nonfillstart{% \aboveenvbreak \inENV % This group ends at the end of the body \hfuzz = 12pt % Don't be fussy \sepspaces % Make spaces be word-separators rather than space tokens. \singlespace \let\par = \lisppar % don't ignore blank lines \obeylines % each line of input is a line of output \parskip = 0pt \parindent = 0pt \emergencystretch = 0pt % don't try to avoid overfull boxes % @@cartouche defines \nonarrowing to inhibit narrowing % at next level down. \ifx\nonarrowing\relax \advance \leftskip by \lispnarrowing \exdentamount=\lispnarrowing \let\exdent=\nofillexdent \let\nonarrowing=\relax \fi } % Define the \E... control sequence only if we are inside the particular % environment, so the error checking in \end will work. % % To end an @@example-like environment, we first end the paragraph (via % \afterenvbreak's vertical glue), and then the group. That way we keep % the zero \parskip that the environments set -- \parskip glue will be % inserted at the beginning of the next paragraph in the document, after % the environment. % \def\nonfillfinish{\afterenvbreak\endgroup} % @@lisp: indented, narrowed, typewriter font. \def\lisp{\begingroup \nonfillstart \let\Elisp = \nonfillfinish \tt \let\kbdfont = \kbdexamplefont % Allow @@kbd to do something special. \gobble % eat return } % @@example: Same as @@lisp. \def\example{\begingroup \def\Eexample{\nonfillfinish\endgroup}\lisp} % @@small... is usually equivalent to the non-small (@@smallbook % redefines). We must call \example (or whatever) last in the % definition, since it reads the return following the @@example (or % whatever) command. % % This actually allows (for example) @@end display inside an % @@smalldisplay. Too bad, but makeinfo will catch the error anyway. % \def\smalldisplay{\begingroup\def\Esmalldisplay{\nonfillfinish\endgroup}\display} \def\smallexample{\begingroup\def\Esmallexample{\nonfillfinish\endgroup}\lisp} \def\smallformat{\begingroup\def\Esmallformat{\nonfillfinish\endgroup}\format} \def\smalllisp{\begingroup\def\Esmalllisp{\nonfillfinish\endgroup}\lisp} % Real @@smallexample and @@smalllisp (when @@smallbook): use smaller fonts. % Originally contributed by Pavel@@xerox. \def\smalllispx{\begingroup \def\Esmalllisp{\nonfillfinish\endgroup}% \def\Esmallexample{\nonfillfinish\endgroup}% \smallfonts \lisp } % @@display: same as @@lisp except keep current font. % \def\display{\begingroup \nonfillstart \let\Edisplay = \nonfillfinish \gobble } % @@smalldisplay (when @@smallbook): @@display plus smaller fonts. % \def\smalldisplayx{\begingroup \def\Esmalldisplay{\nonfillfinish\endgroup}% \smallfonts \rm \display } % @@format: same as @@display except don't narrow margins. % \def\format{\begingroup \let\nonarrowing = t \nonfillstart \let\Eformat = \nonfillfinish \gobble } % @@smallformat (when @@smallbook): @@format plus smaller fonts. % \def\smallformatx{\begingroup \def\Esmallformat{\nonfillfinish\endgroup}% \smallfonts \rm \format } % @@flushleft (same as @@format). % \def\flushleft{\begingroup \def\Eflushleft{\nonfillfinish\endgroup}\format} % @@flushright. % \def\flushright{\begingroup \let\nonarrowing = t \nonfillstart \let\Eflushright = \nonfillfinish \advance\leftskip by 0pt plus 1fill \gobble } % @@quotation does normal linebreaking (hence we can't use \nonfillstart) % and narrows the margins. % \def\quotation{% \begingroup\inENV %This group ends at the end of the @@quotation body {\parskip=0pt \aboveenvbreak}% because \aboveenvbreak inserts \parskip \singlespace \parindent=0pt % We have retained a nonzero parskip for the environment, since we're % doing normal filling. So to avoid extra space below the environment... \def\Equotation{\parskip = 0pt \nonfillfinish}% % % @@cartouche defines \nonarrowing to inhibit narrowing at next level down. \ifx\nonarrowing\relax \advance\leftskip by \lispnarrowing \advance\rightskip by \lispnarrowing \exdentamount = \lispnarrowing \let\nonarrowing = \relax \fi } \message{defuns,} % @@defun etc. % Allow user to change definition object font (\df) internally \def\setdeffont #1 {\csname DEF#1\endcsname} \newskip\defbodyindent \defbodyindent=.4in \newskip\defargsindent \defargsindent=50pt \newskip\deftypemargin \deftypemargin=12pt \newskip\deflastargmargin \deflastargmargin=18pt \newcount\parencount % define \functionparens, which makes ( and ) and & do special things. % \functionparens affects the group it is contained in. \def\activeparens{% \catcode`\(=\active \catcode`\)=\active \catcode`\&=\active \catcode`\[=\active \catcode`\]=\active} % Make control sequences which act like normal parenthesis chars. \let\lparen = ( \let\rparen = ) {\activeparens % Now, smart parens don't turn on until &foo (see \amprm) % Be sure that we always have a definition for `(', etc. For example, % if the fn name has parens in it, \boldbrax will not be in effect yet, % so TeX would otherwise complain about undefined control sequence. \global\let(=\lparen \global\let)=\rparen \global\let[=\lbrack \global\let]=\rbrack \gdef\functionparens{\boldbrax\let&=\amprm\parencount=0 } \gdef\boldbrax{\let(=\opnr\let)=\clnr\let[=\lbrb\let]=\rbrb} % This is used to turn on special parens % but make & act ordinary (given that it's active). \gdef\boldbraxnoamp{\let(=\opnr\let)=\clnr\let[=\lbrb\let]=\rbrb\let&=\ampnr} % Definitions of (, ) and & used in args for functions. % This is the definition of ( outside of all parentheses. \gdef\oprm#1 {{\rm\char`\(}#1 \bf \let(=\opnested \global\advance\parencount by 1 } % % This is the definition of ( when already inside a level of parens. \gdef\opnested{\char`\(\global\advance\parencount by 1 } % \gdef\clrm{% Print a paren in roman if it is taking us back to depth of 0. % also in that case restore the outer-level definition of (. \ifnum \parencount=1 {\rm \char `\)}\sl \let(=\oprm \else \char `\) \fi \global\advance \parencount by -1 } % If we encounter &foo, then turn on ()-hacking afterwards \gdef\amprm#1 {{\rm\}\let(=\oprm \let)=\clrm\ } % \gdef\normalparens{\boldbrax\let&=\ampnr} } % End of definition inside \activeparens %% These parens (in \boldbrax) actually are a little bolder than the %% contained text. This is especially needed for [ and ] \def\opnr{{\sf\char`\(}\global\advance\parencount by 1 } \def\clnr{{\sf\char`\)}\global\advance\parencount by -1 } \let\ampnr = \& \def\lbrb{{\bf\char`\[}} \def\rbrb{{\bf\char`\]}} % Active &'s sneak into the index arguments, so make sure it's defined. { \catcode`& = 13 \global\let& = \ampnr } % First, defname, which formats the header line itself. % #1 should be the function name. % #2 should be the type of definition, such as "Function". \def\defname #1#2{% % Get the values of \leftskip and \rightskip as they were % outside the @@def... \dimen2=\leftskip \advance\dimen2 by -\defbodyindent \noindent \setbox0=\hbox{\hskip \deflastargmargin{\rm #2}\hskip \deftypemargin}% \dimen0=\hsize \advance \dimen0 by -\wd0 % compute size for first line \dimen1=\hsize \advance \dimen1 by -\defargsindent %size for continuations \parshape 2 0in \dimen0 \defargsindent \dimen1 % Now output arg 2 ("Function" or some such) % ending at \deftypemargin from the right margin, % but stuck inside a box of width 0 so it does not interfere with linebreaking {% Adjust \hsize to exclude the ambient margins, % so that \rightline will obey them. \advance \hsize by -\dimen2 \rlap{\rightline{{\rm #2}\hskip -1.25pc }}}% % Make all lines underfull and no complaints: \tolerance=10000 \hbadness=10000 \advance\leftskip by -\defbodyindent \exdentamount=\defbodyindent {\df #1}\enskip % Generate function name } % Actually process the body of a definition % #1 should be the terminating control sequence, such as \Edefun. % #2 should be the "another name" control sequence, such as \defunx. % #3 should be the control sequence that actually processes the header, % such as \defunheader. \def\defparsebody #1#2#3{\begingroup\inENV% Environment for definitionbody \medbreak % % Define the end token that this defining construct specifies % so that it will exit this group. \def#1{\endgraf\endgroup\medbreak}% \def#2{\begingroup\obeylines\activeparens\spacesplit#3}% \parindent=0in \advance\leftskip by \defbodyindent \exdentamount=\defbodyindent \begingroup % \catcode 61=\active % 61 is `=' \obeylines\activeparens\spacesplit#3} % #1 is the \E... control sequence to end the definition (which we define). % #2 is the \...x control sequence for consecutive fns (which we define). % #3 is the control sequence to call to resume processing. % #4, delimited by the space, is the class name. % \def\defmethparsebody#1#2#3#4 {\begingroup\inENV % \medbreak % % Define the end token that this defining construct specifies % so that it will exit this group. \def#1{\endgraf\endgroup\medbreak}% \def#2##1 {\begingroup\obeylines\activeparens\spacesplit{#3{##1}}}% \parindent=0in \advance\leftskip by \defbodyindent \exdentamount=\defbodyindent \begingroup\obeylines\activeparens\spacesplit{#3{#4}}} % Used for @@deftypemethod and @@deftypeivar. % #1 is the \E... control sequence to end the definition (which we define). % #2 is the \...x control sequence for consecutive fns (which we define). % #3 is the control sequence to call to resume processing. % #4, delimited by a space, is the class name. % #5 is the method's return type. % \def\deftypemethparsebody#1#2#3#4 #5 {\begingroup\inENV \medbreak \def#1{\endgraf\endgroup\medbreak}% \def#2##1 ##2 {\begingroup\obeylines\activeparens\spacesplit{#3{##1}{##2}}}% \parindent=0in \advance\leftskip by \defbodyindent \exdentamount=\defbodyindent \begingroup\obeylines\activeparens\spacesplit{#3{#4}{#5}}} % Used for @@deftypeop. The change from \deftypemethparsebody is an % extra argument at the beginning which is the `category', instead of it % being the hardwired string `Method' or `Instance Variable'. We have % to account for this both in the \...x definition and in parsing the % input at hand. Thus also need a control sequence (passed as #5) for % the \E... definition to assign the category name to. % \def\deftypeopparsebody#1#2#3#4#5 #6 {\begingroup\inENV \medbreak \def#1{\endgraf\endgroup\medbreak}% \def#2##1 ##2 ##3 {% \def#4{##1}% \begingroup\obeylines\activeparens\spacesplit{#3{##2}{##3}}}% \parindent=0in \advance\leftskip by \defbodyindent \exdentamount=\defbodyindent \begingroup\obeylines\activeparens\spacesplit{#3{#5}{#6}}} \def\defopparsebody #1#2#3#4#5 {\begingroup\inENV % \medbreak % % Define the end token that this defining construct specifies % so that it will exit this group. \def#1{\endgraf\endgroup\medbreak}% \def#2##1 ##2 {\def#4{##1}% \begingroup\obeylines\activeparens\spacesplit{#3{##2}}}% \parindent=0in \advance\leftskip by \defbodyindent \exdentamount=\defbodyindent \begingroup\obeylines\activeparens\spacesplit{#3{#5}}} % These parsing functions are similar to the preceding ones % except that they do not make parens into active characters. % These are used for "variables" since they have no arguments. \def\defvarparsebody #1#2#3{\begingroup\inENV% Environment for definitionbody \medbreak % % Define the end token that this defining construct specifies % so that it will exit this group. \def#1{\endgraf\endgroup\medbreak}% \def#2{\begingroup\obeylines\spacesplit#3}% \parindent=0in \advance\leftskip by \defbodyindent \exdentamount=\defbodyindent \begingroup % \catcode 61=\active % \obeylines\spacesplit#3} % This is used for \def{tp,vr}parsebody. It could probably be used for % some of the others, too, with some judicious conditionals. % \def\parsebodycommon#1#2#3{% \begingroup\inENV % \medbreak % % Define the end token that this defining construct specifies % so that it will exit this group. \def#1{\endgraf\endgroup\medbreak}% \def#2##1 {\begingroup\obeylines\spacesplit{#3{##1}}}% \parindent=0in \advance\leftskip by \defbodyindent \exdentamount=\defbodyindent \begingroup\obeylines } \def\defvrparsebody#1#2#3#4 {% \parsebodycommon{#1}{#2}{#3}% \spacesplit{#3{#4}}% } % This loses on `@@deftp {Data Type} {struct termios}' -- it thinks the % type is just `struct', because we lose the braces in `{struct % termios}' when \spacesplit reads its undelimited argument. Sigh. % \let\deftpparsebody=\defvrparsebody % % So, to get around this, we put \empty in with the type name. That % way, TeX won't find exactly `{...}' as an undelimited argument, and % won't strip off the braces. % \def\deftpparsebody #1#2#3#4 {% \parsebodycommon{#1}{#2}{#3}% \spacesplit{\parsetpheaderline{#3{#4}}}\empty } % Fine, but then we have to eventually remove the \empty *and* the % braces (if any). That's what this does. % \def\removeemptybraces\empty#1\relax{#1} % After \spacesplit has done its work, this is called -- #1 is the final % thing to call, #2 the type name (which starts with \empty), and #3 % (which might be empty) the arguments. % \def\parsetpheaderline#1#2#3{% #1{\removeemptybraces#2\relax}{#3}% }% \def\defopvarparsebody #1#2#3#4#5 {\begingroup\inENV % \medbreak % % Define the end token that this defining construct specifies % so that it will exit this group. \def#1{\endgraf\endgroup\medbreak}% \def#2##1 ##2 {\def#4{##1}% \begingroup\obeylines\spacesplit{#3{##2}}}% \parindent=0in \advance\leftskip by \defbodyindent \exdentamount=\defbodyindent \begingroup\obeylines\spacesplit{#3{#5}}} % Split up #2 at the first space token. % call #1 with two arguments: % the first is all of #2 before the space token, % the second is all of #2 after that space token. % If #2 contains no space token, all of it is passed as the first arg % and the second is passed as empty. {\obeylines \gdef\spacesplit#1#2^^M{\endgroup\spacesplitfoo{#1}#2 \relax\spacesplitfoo}% \long\gdef\spacesplitfoo#1#2 #3#4\spacesplitfoo{% \ifx\relax #3% #1{#2}{}\else #1{#2}{#3#4}\fi}} % So much for the things common to all kinds of definitions. % Define @@defun. % First, define the processing that is wanted for arguments of \defun % Use this to expand the args and terminate the paragraph they make up \def\defunargs#1{\functionparens \sl % Expand, preventing hyphenation at `-' chars. % Note that groups don't affect changes in \hyphenchar. % Set the font temporarily and use \font in case \setfont made \tensl a macro. {\tensl\hyphenchar\font=0}% #1% {\tensl\hyphenchar\font=45}% \ifnum\parencount=0 \else \errmessage{Unbalanced parentheses in @@def}\fi% \interlinepenalty=10000 \advance\rightskip by 0pt plus 1fil \endgraf\nobreak\vskip -\parskip\nobreak } \def\deftypefunargs #1{% % Expand, preventing hyphenation at `-' chars. % Note that groups don't affect changes in \hyphenchar. % Use \boldbraxnoamp, not \functionparens, so that & is not special. \boldbraxnoamp \tclose{#1}% avoid \code because of side effects on active chars \interlinepenalty=10000 \advance\rightskip by 0pt plus 1fil \endgraf\nobreak\vskip -\parskip\nobreak } % Do complete processing of one @@defun or @@defunx line already parsed. % @@deffn Command forward-char nchars \def\deffn{\defmethparsebody\Edeffn\deffnx\deffnheader} \def\deffnheader #1#2#3{\doind {fn}{\code{#2}}% \begingroup\defname {#2}{#1}\defunargs{#3}\endgroup % \catcode 61=\other % Turn off change made in \defparsebody } % @@defun == @@deffn Function \def\defun{\defparsebody\Edefun\defunx\defunheader} \def\defunheader #1#2{\doind {fn}{\code{#1}}% Make entry in function index \begingroup\defname {#1}{\putwordDeffunc}% \defunargs {#2}\endgroup % \catcode 61=\other % Turn off change made in \defparsebody } % @@deftypefun int foobar (int @@var{foo}, float @@var{bar}) \def\deftypefun{\defparsebody\Edeftypefun\deftypefunx\deftypefunheader} % #1 is the data type. #2 is the name and args. \def\deftypefunheader #1#2{\deftypefunheaderx{#1}#2 \relax} % #1 is the data type, #2 the name, #3 the args. \def\deftypefunheaderx #1#2 #3\relax{% \doind {fn}{\code{#2}}% Make entry in function index \begingroup\defname {\defheaderxcond#1\relax$$$#2}{\putwordDeftypefun}% \deftypefunargs {#3}\endgroup % \catcode 61=\other % Turn off change made in \defparsebody } % @@deftypefn {Library Function} int foobar (int @@var{foo}, float @@var{bar}) \def\deftypefn{\defmethparsebody\Edeftypefn\deftypefnx\deftypefnheader} % \defheaderxcond#1\relax$$$ % puts #1 in @@code, followed by a space, but does nothing if #1 is null. \def\defheaderxcond#1#2$$${\ifx#1\relax\else\code{#1#2} \fi} % #1 is the classification. #2 is the data type. #3 is the name and args. \def\deftypefnheader #1#2#3{\deftypefnheaderx{#1}{#2}#3 \relax} % #1 is the classification, #2 the data type, #3 the name, #4 the args. \def\deftypefnheaderx #1#2#3 #4\relax{% \doind {fn}{\code{#3}}% Make entry in function index \begingroup \normalparens % notably, turn off `&' magic, which prevents % at least some C++ text from working \defname {\defheaderxcond#2\relax$$$#3}{#1}% \deftypefunargs {#4}\endgroup % \catcode 61=\other % Turn off change made in \defparsebody } % @@defmac == @@deffn Macro \def\defmac{\defparsebody\Edefmac\defmacx\defmacheader} \def\defmacheader #1#2{\doind {fn}{\code{#1}}% Make entry in function index \begingroup\defname {#1}{\putwordDefmac}% \defunargs {#2}\endgroup % \catcode 61=\other % Turn off change made in \defparsebody } % @@defspec == @@deffn Special Form \def\defspec{\defparsebody\Edefspec\defspecx\defspecheader} \def\defspecheader #1#2{\doind {fn}{\code{#1}}% Make entry in function index \begingroup\defname {#1}{\putwordDefspec}% \defunargs {#2}\endgroup % \catcode 61=\other % Turn off change made in \defparsebody } % @@defop CATEGORY CLASS OPERATION ARG... % \def\defop #1 {\def\defoptype{#1}% \defopparsebody\Edefop\defopx\defopheader\defoptype} % \def\defopheader#1#2#3{% \dosubind {fn}{\code{#2}}{\putwordon\ #1}% Make entry in function index \begingroup\defname {#2}{\defoptype\ \putwordon\ #1}% \defunargs {#3}\endgroup % } % @@deftypeop CATEGORY CLASS TYPE OPERATION ARG... % \def\deftypeop #1 {\def\deftypeopcategory{#1}% \deftypeopparsebody\Edeftypeop\deftypeopx\deftypeopheader \deftypeopcategory} % % #1 is the class name, #2 the data type, #3 the operation name, #4 the args. \def\deftypeopheader#1#2#3#4{% \dosubind{fn}{\code{#3}}{\putwordon\ \code{#1}}% entry in function index \begingroup \defname{\defheaderxcond#2\relax$$$#3} {\deftypeopcategory\ \putwordon\ \code{#1}}% \deftypefunargs{#4}% \endgroup } % @@deftypemethod CLASS TYPE METHOD ARG... % \def\deftypemethod{% \deftypemethparsebody\Edeftypemethod\deftypemethodx\deftypemethodheader} % % #1 is the class name, #2 the data type, #3 the method name, #4 the args. \def\deftypemethodheader#1#2#3#4{% \dosubind{fn}{\code{#3}}{\putwordon\ \code{#1}}% entry in function index \begingroup \defname{\defheaderxcond#2\relax$$$#3}{\putwordMethodon\ \code{#1}}% \deftypefunargs{#4}% \endgroup } % @@deftypeivar CLASS TYPE VARNAME % \def\deftypeivar{% \deftypemethparsebody\Edeftypeivar\deftypeivarx\deftypeivarheader} % % #1 is the class name, #2 the data type, #3 the variable name. \def\deftypeivarheader#1#2#3{% \dosubind{vr}{\code{#3}}{\putwordof\ \code{#1}}% entry in variable index \begingroup \defname{#3}{\putwordInstanceVariableof\ \code{#1}}% \defvarargs{#3}% \endgroup } % @@defmethod == @@defop Method % \def\defmethod{\defmethparsebody\Edefmethod\defmethodx\defmethodheader} % % #1 is the class name, #2 the method name, #3 the args. \def\defmethodheader#1#2#3{% \dosubind{fn}{\code{#2}}{\putwordon\ \code{#1}}% entry in function index \begingroup \defname{#2}{\putwordMethodon\ \code{#1}}% \defunargs{#3}% \endgroup } % @@defcv {Class Option} foo-class foo-flag \def\defcv #1 {\def\defcvtype{#1}% \defopvarparsebody\Edefcv\defcvx\defcvarheader\defcvtype} \def\defcvarheader #1#2#3{% \dosubind {vr}{\code{#2}}{\putwordof\ #1}% Make entry in var index \begingroup\defname {#2}{\defcvtype\ \putwordof\ #1}% \defvarargs {#3}\endgroup % } % @@defivar CLASS VARNAME == @@defcv {Instance Variable} CLASS VARNAME % \def\defivar{\defvrparsebody\Edefivar\defivarx\defivarheader} % \def\defivarheader#1#2#3{% \dosubind {vr}{\code{#2}}{\putwordof\ #1}% entry in var index \begingroup \defname{#2}{\putwordInstanceVariableof\ #1}% \defvarargs{#3}% \endgroup } % @@defvar % First, define the processing that is wanted for arguments of @@defvar. % This is actually simple: just print them in roman. % This must expand the args and terminate the paragraph they make up \def\defvarargs #1{\normalparens #1% \interlinepenalty=10000 \endgraf\nobreak\vskip -\parskip\nobreak} % @@defvr Counter foo-count \def\defvr{\defvrparsebody\Edefvr\defvrx\defvrheader} \def\defvrheader #1#2#3{\doind {vr}{\code{#2}}% \begingroup\defname {#2}{#1}\defvarargs{#3}\endgroup} % @@defvar == @@defvr Variable \def\defvar{\defvarparsebody\Edefvar\defvarx\defvarheader} \def\defvarheader #1#2{\doind {vr}{\code{#1}}% Make entry in var index \begingroup\defname {#1}{\putwordDefvar}% \defvarargs {#2}\endgroup % } % @@defopt == @@defvr {User Option} \def\defopt{\defvarparsebody\Edefopt\defoptx\defoptheader} \def\defoptheader #1#2{\doind {vr}{\code{#1}}% Make entry in var index \begingroup\defname {#1}{\putwordDefopt}% \defvarargs {#2}\endgroup % } % @@deftypevar int foobar \def\deftypevar{\defvarparsebody\Edeftypevar\deftypevarx\deftypevarheader} % #1 is the data type. #2 is the name, perhaps followed by text that % is actually part of the data type, which should not be put into the index. \def\deftypevarheader #1#2{% \dovarind#2 \relax% Make entry in variables index \begingroup\defname {\defheaderxcond#1\relax$$$#2}{\putwordDeftypevar}% \interlinepenalty=10000 \endgraf\nobreak\vskip -\parskip\nobreak \endgroup} \def\dovarind#1 #2\relax{\doind{vr}{\code{#1}}} % @@deftypevr {Global Flag} int enable \def\deftypevr{\defvrparsebody\Edeftypevr\deftypevrx\deftypevrheader} \def\deftypevrheader #1#2#3{\dovarind#3 \relax% \begingroup\defname {\defheaderxcond#2\relax$$$#3}{#1} \interlinepenalty=10000 \endgraf\nobreak\vskip -\parskip\nobreak \endgroup} % Now define @@deftp % Args are printed in bold, a slight difference from @@defvar. \def\deftpargs #1{\bf \defvarargs{#1}} % @@deftp Class window height width ... \def\deftp{\deftpparsebody\Edeftp\deftpx\deftpheader} \def\deftpheader #1#2#3{\doind {tp}{\code{#2}}% \begingroup\defname {#2}{#1}\deftpargs{#3}\endgroup} % These definitions are used if you use @@defunx (etc.) % anywhere other than immediately after a @@defun or @@defunx. % \def\defcvx#1 {\errmessage{@@defcvx in invalid context}} \def\deffnx#1 {\errmessage{@@deffnx in invalid context}} \def\defivarx#1 {\errmessage{@@defivarx in invalid context}} \def\defmacx#1 {\errmessage{@@defmacx in invalid context}} \def\defmethodx#1 {\errmessage{@@defmethodx in invalid context}} \def\defoptx #1 {\errmessage{@@defoptx in invalid context}} \def\defopx#1 {\errmessage{@@defopx in invalid context}} \def\defspecx#1 {\errmessage{@@defspecx in invalid context}} \def\deftpx#1 {\errmessage{@@deftpx in invalid context}} \def\deftypefnx#1 {\errmessage{@@deftypefnx in invalid context}} \def\deftypefunx#1 {\errmessage{@@deftypefunx in invalid context}} \def\deftypeivarx#1 {\errmessage{@@deftypeivarx in invalid context}} \def\deftypemethodx#1 {\errmessage{@@deftypemethodx in invalid context}} \def\deftypeopx#1 {\errmessage{@@deftypeopx in invalid context}} \def\deftypevarx#1 {\errmessage{@@deftypevarx in invalid context}} \def\deftypevrx#1 {\errmessage{@@deftypevrx in invalid context}} \def\defunx#1 {\errmessage{@@defunx in invalid context}} \def\defvarx#1 {\errmessage{@@defvarx in invalid context}} \def\defvrx#1 {\errmessage{@@defvrx in invalid context}} \message{macros,} % @@macro. % To do this right we need a feature of e-TeX, \scantokens, % which we arrange to emulate with a temporary file in ordinary TeX. \ifx\eTeXversion\undefined \newwrite\macscribble \def\scanmacro#1{% \begingroup \newlinechar`\^^M % Undo catcode changes of \startcontents and \doprintindex \catcode`\@@=0 \catcode`\\=12 \escapechar=`\@@ % Append \endinput to make sure that TeX does not see the ending newline. \toks0={#1\endinput}% \immediate\openout\macscribble=\jobname.tmp \immediate\write\macscribble{\the\toks0}% \immediate\closeout\macscribble \let\xeatspaces\eatspaces \input \jobname.tmp \endgroup } \else \def\scanmacro#1{% \begingroup \newlinechar`\^^M % Undo catcode changes of \startcontents and \doprintindex \catcode`\@@=0 \catcode`\\=12 \escapechar=`\@@ \let\xeatspaces\eatspaces\scantokens{#1\endinput}\endgroup} \fi \newcount\paramno % Count of parameters \newtoks\macname % Macro name \newif\ifrecursive % Is it recursive? \def\macrolist{} % List of all defined macros in the form % \do\macro1\do\macro2... % Utility routines. % Thisdoes \let #1 = #2, except with \csnames. \def\cslet#1#2{% \expandafter\expandafter \expandafter\let \expandafter\expandafter \csname#1\endcsname \csname#2\endcsname} % Trim leading and trailing spaces off a string. % Concepts from aro-bend problem 15 (see CTAN). {\catcode`\@@=11 \gdef\eatspaces #1{\expandafter\trim@@\expandafter{#1 }} \gdef\trim@@ #1{\trim@@@@ @@#1 @@ #1 @@ @@@@} \gdef\trim@@@@ #1@@ #2@@ #3@@@@{\trim@@@@@@\empty #2 @@} \def\unbrace#1{#1} \unbrace{\gdef\trim@@@@@@ #1 } #2@@{#1} } % Trim a single trailing ^^M off a string. {\catcode`\^^M=12\catcode`\Q=3% \gdef\eatcr #1{\eatcra #1Q^^MQ}% \gdef\eatcra#1^^MQ{\eatcrb#1Q}% \gdef\eatcrb#1Q#2Q{#1}% } % Macro bodies are absorbed as an argument in a context where % all characters are catcode 10, 11 or 12, except \ which is active % (as in normal texinfo). It is necessary to change the definition of \. % It's necessary to have hard CRs when the macro is executed. This is % done by making ^^M (\endlinechar) catcode 12 when reading the macro % body, and then making it the \newlinechar in \scanmacro. \def\macrobodyctxt{% \catcode`\~=12 \catcode`\^=12 \catcode`\_=12 \catcode`\|=12 \catcode`\<=12 \catcode`\>=12 \catcode`\+=12 \catcode`\{=12 \catcode`\}=12 \catcode`\@@=12 \catcode`\^^M=12 \usembodybackslash} \def\macroargctxt{% \catcode`\~=12 \catcode`\^=12 \catcode`\_=12 \catcode`\|=12 \catcode`\<=12 \catcode`\>=12 \catcode`\+=12 \catcode`\@@=12 \catcode`\\=12} % \mbodybackslash is the definition of \ in @@macro bodies. % It maps \foo\ => \csname macarg.foo\endcsname => #N % where N is the macro parameter number. % We define \csname macarg.\endcsname to be \realbackslash, so % \\ in macro replacement text gets you a backslash. {\catcode`@@=0 @@catcode`@@\=@@active @@gdef@@usembodybackslash{@@let\=@@mbodybackslash} @@gdef@@mbodybackslash#1\{@@csname macarg.#1@@endcsname} } \expandafter\def\csname macarg.\endcsname{\realbackslash} \def\macro{\recursivefalse\parsearg\macroxxx} \def\rmacro{\recursivetrue\parsearg\macroxxx} \def\macroxxx#1{% \getargs{#1}% now \macname is the macname and \argl the arglist \ifx\argl\empty % no arguments \paramno=0% \else \expandafter\parsemargdef \argl;% \fi \if1\csname ismacro.\the\macname\endcsname \message{Warning: redefining \the\macname}% \else \expandafter\ifx\csname \the\macname\endcsname \relax \else \errmessage{The name \the\macname\space is reserved}\fi \global\cslet{macsave.\the\macname}{\the\macname}% \global\expandafter\let\csname ismacro.\the\macname\endcsname=1% % Add the macroname to \macrolist \toks0 = \expandafter{\macrolist\do}% \xdef\macrolist{\the\toks0 \expandafter\noexpand\csname\the\macname\endcsname}% \fi \begingroup \macrobodyctxt \ifrecursive \expandafter\parsermacbody \else \expandafter\parsemacbody \fi} \def\unmacro{\parsearg\unmacroxxx} \def\unmacroxxx#1{% \if1\csname ismacro.#1\endcsname \global\cslet{#1}{macsave.#1}% \global\expandafter\let \csname ismacro.#1\endcsname=0% % Remove the macro name from \macrolist \begingroup \edef\tempa{\expandafter\noexpand\csname#1\endcsname}% \def\do##1{% \def\tempb{##1}% \ifx\tempa\tempb % remove this \else \toks0 = \expandafter{\newmacrolist\do}% \edef\newmacrolist{\the\toks0\expandafter\noexpand\tempa}% \fi}% \def\newmacrolist{}% % Execute macro list to define \newmacrolist \macrolist \global\let\macrolist\newmacrolist \endgroup \else \errmessage{Macro #1 not defined}% \fi } % This makes use of the obscure feature that if the last token of a % is #, then the preceding argument is delimited by % an opening brace, and that opening brace is not consumed. \def\getargs#1{\getargsxxx#1{}} \def\getargsxxx#1#{\getmacname #1 \relax\getmacargs} \def\getmacname #1 #2\relax{\macname={#1}} \def\getmacargs#1{\def\argl{#1}} % Parse the optional {params} list. Set up \paramno and \paramlist % so \defmacro knows what to do. Define \macarg.blah for each blah % in the params list, to be ##N where N is the position in that list. % That gets used by \mbodybackslash (above). % We need to get `macro parameter char #' into several definitions. % The technique used is stolen from LaTeX: let \hash be something % unexpandable, insert that wherever you need a #, and then redefine % it to # just before using the token list produced. % % The same technique is used to protect \eatspaces till just before % the macro is used. \def\parsemargdef#1;{\paramno=0\def\paramlist{}% \let\hash\relax\let\xeatspaces\relax\parsemargdefxxx#1,;,} \def\parsemargdefxxx#1,{% \if#1;\let\next=\relax \else \let\next=\parsemargdefxxx \advance\paramno by 1% \expandafter\edef\csname macarg.\eatspaces{#1}\endcsname {\xeatspaces{\hash\the\paramno}}% \edef\paramlist{\paramlist\hash\the\paramno,}% \fi\next} % These two commands read recursive and nonrecursive macro bodies. % (They're different since rec and nonrec macros end differently.) \long\def\parsemacbody#1@@end macro% {\xdef\temp{\eatcr{#1}}\endgroup\defmacro}% \long\def\parsermacbody#1@@end rmacro% {\xdef\temp{\eatcr{#1}}\endgroup\defmacro}% % This defines the macro itself. There are six cases: recursive and % nonrecursive macros of zero, one, and many arguments. % Much magic with \expandafter here. % \xdef is used so that macro definitions will survive the file % they're defined in; @@include reads the file inside a group. \def\defmacro{% \let\hash=##% convert placeholders to macro parameter chars \ifrecursive \ifcase\paramno % 0 \expandafter\xdef\csname\the\macname\endcsname{% \noexpand\scanmacro{\temp}}% \or % 1 \expandafter\xdef\csname\the\macname\endcsname{% \bgroup\noexpand\macroargctxt \noexpand\braceorline \expandafter\noexpand\csname\the\macname xxx\endcsname}% \expandafter\xdef\csname\the\macname xxx\endcsname##1{% \egroup\noexpand\scanmacro{\temp}}% \else % many \expandafter\xdef\csname\the\macname\endcsname{% \bgroup\noexpand\macroargctxt \noexpand\csname\the\macname xx\endcsname}% \expandafter\xdef\csname\the\macname xx\endcsname##1{% \expandafter\noexpand\csname\the\macname xxx\endcsname ##1,}% \expandafter\expandafter \expandafter\xdef \expandafter\expandafter \csname\the\macname xxx\endcsname \paramlist{\egroup\noexpand\scanmacro{\temp}}% \fi \else \ifcase\paramno % 0 \expandafter\xdef\csname\the\macname\endcsname{% \noexpand\norecurse{\the\macname}% \noexpand\scanmacro{\temp}\egroup}% \or % 1 \expandafter\xdef\csname\the\macname\endcsname{% \bgroup\noexpand\macroargctxt \noexpand\braceorline \expandafter\noexpand\csname\the\macname xxx\endcsname}% \expandafter\xdef\csname\the\macname xxx\endcsname##1{% \egroup \noexpand\norecurse{\the\macname}% \noexpand\scanmacro{\temp}\egroup}% \else % many \expandafter\xdef\csname\the\macname\endcsname{% \bgroup\noexpand\macroargctxt \expandafter\noexpand\csname\the\macname xx\endcsname}% \expandafter\xdef\csname\the\macname xx\endcsname##1{% \expandafter\noexpand\csname\the\macname xxx\endcsname ##1,}% \expandafter\expandafter \expandafter\xdef \expandafter\expandafter \csname\the\macname xxx\endcsname \paramlist{% \egroup \noexpand\norecurse{\the\macname}% \noexpand\scanmacro{\temp}\egroup}% \fi \fi} \def\norecurse#1{\bgroup\cslet{#1}{macsave.#1}} % \braceorline decides whether the next nonwhitespace character is a % {. If so it reads up to the closing }, if not, it reads the whole % line. Whatever was read is then fed to the next control sequence % as an argument (by \parsebrace or \parsearg) \def\braceorline#1{\let\next=#1\futurelet\nchar\braceorlinexxx} \def\braceorlinexxx{% \ifx\nchar\bgroup\else \expandafter\parsearg \fi \next} % We mant to disable all macros during \shipout so that they are not % expanded by \write. \def\turnoffmacros{\begingroup \def\do##1{\let\noexpand##1=\relax}% \edef\next{\macrolist}\expandafter\endgroup\next} % @@alias. % We need some trickery to remove the optional spaces around the equal % sign. Just make them active and then expand them all to nothing. \def\alias{\begingroup\obeyspaces\parsearg\aliasxxx} \def\aliasxxx #1{\aliasyyy#1\relax} \def\aliasyyy #1=#2\relax{\ignoreactivespaces \edef\next{\global\let\expandafter\noexpand\csname#1\endcsname=% \expandafter\noexpand\csname#2\endcsname}% \expandafter\endgroup\next} \message{cross references,} % @@xref etc. \newwrite\auxfile \newif\ifhavexrefs % True if xref values are known. \newif\ifwarnedxrefs % True if we warned once that they aren't known. % @@inforef is relatively simple. \def\inforef #1{\inforefzzz #1,,,,**} \def\inforefzzz #1,#2,#3,#4**{\putwordSee{} \putwordInfo{} \putwordfile{} \file{\ignorespaces #3{}}, node \samp{\ignorespaces#1{}}} % @@node's job is to define \lastnode. \def\node{\ENVcheck\parsearg\nodezzz} \def\nodezzz#1{\nodexxx [#1,]} \def\nodexxx[#1,#2]{\gdef\lastnode{#1}} \let\nwnode=\node \let\lastnode=\relax % The sectioning commands (@@chapter, etc.) call these. \def\donoderef{% \ifx\lastnode\relax\else \expandafter\expandafter\expandafter\setref{\lastnode}% {Ysectionnumberandtype}% \global\let\lastnode=\relax \fi } \def\unnumbnoderef{% \ifx\lastnode\relax\else \expandafter\expandafter\expandafter\setref{\lastnode}{Ynothing}% \global\let\lastnode=\relax \fi } \def\appendixnoderef{% \ifx\lastnode\relax\else \expandafter\expandafter\expandafter\setref{\lastnode}% {Yappendixletterandtype}% \global\let\lastnode=\relax \fi } % @@anchor{NAME} -- define xref target at arbitrary point. % \newcount\savesfregister \gdef\savesf{\relax \ifhmode \savesfregister=\spacefactor \fi} \gdef\restoresf{\relax \ifhmode \spacefactor=\savesfregister \fi} \gdef\anchor#1{\savesf \setref{#1}{Ynothing}\restoresf \ignorespaces} % \setref{NAME}{SNT} defines a cross-reference point NAME, namely % NAME-title, NAME-pg, and NAME-SNT. Called from \foonoderef. We have % to set \indexdummies so commands such as @@code in a section title % aren't expanded. It would be nicer not to expand the titles in the % first place, but there's so many layers that that is hard to do. % \def\setref#1#2{{% \indexdummies \pdfmkdest{#1}% \dosetq{#1-title}{Ytitle}% \dosetq{#1-pg}{Ypagenumber}% \dosetq{#1-snt}{#2}% }} % @@xref, @@pxref, and @@ref generate cross-references. For \xrefX, #1 is % the node name, #2 the name of the Info cross-reference, #3 the printed % node name, #4 the name of the Info file, #5 the name of the printed % manual. All but the node name can be omitted. % \def\pxref#1{\putwordsee{} \xrefX[#1,,,,,,,]} \def\xref#1{\putwordSee{} \xrefX[#1,,,,,,,]} \def\ref#1{\xrefX[#1,,,,,,,]} \def\xrefX[#1,#2,#3,#4,#5,#6]{\begingroup \unsepspaces \def\printedmanual{\ignorespaces #5}% \def\printednodename{\ignorespaces #3}% \setbox1=\hbox{\printedmanual}% \setbox0=\hbox{\printednodename}% \ifdim \wd0 = 0pt % No printed node name was explicitly given. \expandafter\ifx\csname SETxref-automatic-section-title\endcsname\relax % Use the node name inside the square brackets. \def\printednodename{\ignorespaces #1}% \else % Use the actual chapter/section title appear inside % the square brackets. Use the real section title if we have it. \ifdim \wd1 > 0pt % It is in another manual, so we don't have it. \def\printednodename{\ignorespaces #1}% \else \ifhavexrefs % We know the real title if we have the xref values. \def\printednodename{\refx{#1-title}{}}% \else % Otherwise just copy the Info node name. \def\printednodename{\ignorespaces #1}% \fi% \fi \fi \fi % % If we use \unhbox0 and \unhbox1 to print the node names, TeX does not % insert empty discretionaries after hyphens, which means that it will % not find a line break at a hyphen in a node names. Since some manuals % are best written with fairly long node names, containing hyphens, this % is a loss. Therefore, we give the text of the node name again, so it % is as if TeX is seeing it for the first time. \ifpdf \leavevmode \getfilename{#4}% \ifnum\filenamelength>0 \startlink attr{/Border [0 0 0]}% goto file{\the\filename.pdf} name{#1@@}% \else \startlink attr{/Border [0 0 0]}% goto name{#1@@}% \fi \linkcolor \fi % \ifdim \wd1 > 0pt \putwordsection{} ``\printednodename'' \putwordin{} \cite{\printedmanual}% \else % _ (for example) has to be the character _ for the purposes of the % control sequence corresponding to the node, but it has to expand % into the usual \leavevmode...\vrule stuff for purposes of % printing. So we \turnoffactive for the \refx-snt, back on for the % printing, back off for the \refx-pg. {\normalturnoffactive % Only output a following space if the -snt ref is nonempty; for % @@unnumbered and @@anchor, it won't be. \setbox2 = \hbox{\ignorespaces \refx{#1-snt}{}}% \ifdim \wd2 > 0pt \refx{#1-snt}\space\fi }% % [mynode], [\printednodename],\space % page 3 \turnoffactive \putwordpage\tie\refx{#1-pg}{}% \fi \endlink \endgroup} % \dosetq is the interface for calls from other macros % Use \normalturnoffactive so that punctuation chars such as underscore % and backslash work in node names. (\turnoffactive doesn't do \.) \def\dosetq#1#2{% {\let\folio=0% \normalturnoffactive \edef\next{\write\auxfile{\internalsetq{#1}{#2}}}% \iflinks \next \fi }% } % \internalsetq {foo}{page} expands into % CHARACTERS 'xrdef {foo}{...expansion of \Ypage...} % When the aux file is read, ' is the escape character \def\internalsetq #1#2{'xrdef {#1}{\csname #2\endcsname}} % Things to be expanded by \internalsetq \def\Ypagenumber{\folio} \def\Ytitle{\thissection} \def\Ynothing{} \def\Ysectionnumberandtype{% \ifnum\secno=0 \putwordChapter\xreftie\the\chapno % \else \ifnum \subsecno=0 \putwordSection\xreftie\the\chapno.\the\secno % \else \ifnum \subsubsecno=0 % \putwordSection\xreftie\the\chapno.\the\secno.\the\subsecno % \else % \putwordSection\xreftie\the\chapno.\the\secno.\the\subsecno.\the\subsubsecno % \fi \fi \fi } \def\Yappendixletterandtype{% \ifnum\secno=0 \putwordAppendix\xreftie'char\the\appendixno{}% \else \ifnum \subsecno=0 \putwordSection\xreftie'char\the\appendixno.\the\secno % \else \ifnum \subsubsecno=0 % \putwordSection\xreftie'char\the\appendixno.\the\secno.\the\subsecno % \else % \putwordSection\xreftie'char\the\appendixno.\the\secno.\the\subsecno.\the\subsubsecno % \fi \fi \fi } \gdef\xreftie{'tie} % Use TeX 3.0's \inputlineno to get the line number, for better error % messages, but if we're using an old version of TeX, don't do anything. % \ifx\inputlineno\thisisundefined \let\linenumber = \empty % Non-3.0. \else \def\linenumber{\the\inputlineno:\space} \fi % Define \refx{NAME}{SUFFIX} to reference a cross-reference string named NAME. % If its value is nonempty, SUFFIX is output afterward. \def\refx#1#2{% \expandafter\ifx\csname X#1\endcsname\relax % If not defined, say something at least. \angleleft un\-de\-fined\angleright \iflinks \ifhavexrefs \message{\linenumber Undefined cross reference `#1'.}% \else \ifwarnedxrefs\else \global\warnedxrefstrue \message{Cross reference values unknown; you must run TeX again.}% \fi \fi \fi \else % It's defined, so just use it. \csname X#1\endcsname \fi #2% Output the suffix in any case. } % This is the macro invoked by entries in the aux file. % \def\xrdef#1{\begingroup % Reenable \ as an escape while reading the second argument. \catcode`\\ = 0 \afterassignment\endgroup \expandafter\gdef\csname X#1\endcsname } % Read the last existing aux file, if any. No error if none exists. \def\readauxfile{\begingroup \catcode`\^^@@=\other \catcode`\^^A=\other \catcode`\^^B=\other \catcode`\^^C=\other \catcode`\^^D=\other \catcode`\^^E=\other \catcode`\^^F=\other \catcode`\^^G=\other \catcode`\^^H=\other \catcode`\^^K=\other \catcode`\^^L=\other \catcode`\^^N=\other \catcode`\^^P=\other \catcode`\^^Q=\other \catcode`\^^R=\other \catcode`\^^S=\other \catcode`\^^T=\other \catcode`\^^U=\other \catcode`\^^V=\other \catcode`\^^W=\other \catcode`\^^X=\other \catcode`\^^Z=\other \catcode`\^^[=\other \catcode`\^^\=\other \catcode`\^^]=\other \catcode`\^^^=\other \catcode`\^^_=\other \catcode`\@@=\other \catcode`\^=\other % It was suggested to define this as 7, which would allow ^^e4 etc. % in xref tags, i.e., node names. But since ^^e4 notation isn't % supported in the main text, it doesn't seem desirable. Furthermore, % that is not enough: for node names that actually contain a ^ % character, we would end up writing a line like this: 'xrdef {'hat % b-title}{'hat b} and \xrdef does a \csname...\endcsname on the first % argument, and \hat is not an expandable control sequence. It could % all be worked out, but why? Either we support ^^ or we don't. % % The other change necessary for this was to define \auxhat: % \def\auxhat{\def^{'hat }}% extra space so ok if followed by letter % and then to call \auxhat in \setq. % \catcode`\~=\other \catcode`\[=\other \catcode`\]=\other \catcode`\"=\other \catcode`\_=\other \catcode`\|=\other \catcode`\<=\other \catcode`\>=\other \catcode`\$=\other \catcode`\#=\other \catcode`\&=\other \catcode`+=\other % avoid \+ for paranoia even though we've turned it off % Make the characters 128-255 be printing characters {% \count 1=128 \def\loop{% \catcode\count 1=\other \advance\count 1 by 1 \ifnum \count 1<256 \loop \fi }% }% % The aux file uses ' as the escape (for now). % Turn off \ as an escape so we do not lose on % entries which were dumped with control sequences in their names. % For example, 'xrdef {$\leq $-fun}{page ...} made by @@defun ^^ % Reference to such entries still does not work the way one would wish, % but at least they do not bomb out when the aux file is read in. \catcode`\{=1 \catcode`\}=2 \catcode`\%=\other \catcode`\'=0 \catcode`\\=\other % \openin 1 \jobname.aux \ifeof 1 \else \closein 1 \input \jobname.aux \global\havexrefstrue \global\warnedobstrue \fi % Open the new aux file. TeX will close it automatically at exit. \openout\auxfile=\jobname.aux \endgroup} % Footnotes. \newcount \footnoteno % The trailing space in the following definition for supereject is % vital for proper filling; pages come out unaligned when you do a % pagealignmacro call if that space before the closing brace is % removed. (Generally, numeric constants should always be followed by a % space to prevent strange expansion errors.) \def\supereject{\par\penalty -20000\footnoteno =0 } % @@footnotestyle is meaningful for info output only. \let\footnotestyle=\comment \let\ptexfootnote=\footnote {\catcode `\@@=11 % % Auto-number footnotes. Otherwise like plain. \gdef\footnote{% \global\advance\footnoteno by \@@ne \edef\thisfootno{$^{\the\footnoteno}$}% % % In case the footnote comes at the end of a sentence, preserve the % extra spacing after we do the footnote number. \let\@@sf\empty \ifhmode\edef\@@sf{\spacefactor\the\spacefactor}\/\fi % % Remove inadvertent blank space before typesetting the footnote number. \unskip \thisfootno\@@sf \footnotezzz }% % Don't bother with the trickery in plain.tex to not require the % footnote text as a parameter. Our footnotes don't need to be so general. % % Oh yes, they do; otherwise, @@ifset and anything else that uses % \parseargline fail inside footnotes because the tokens are fixed when % the footnote is read. --karl, 16nov96. % \long\gdef\footnotezzz{\insert\footins\bgroup % We want to typeset this text as a normal paragraph, even if the % footnote reference occurs in (for example) a display environment. % So reset some parameters. \interlinepenalty\interfootnotelinepenalty \splittopskip\ht\strutbox % top baseline for broken footnotes \splitmaxdepth\dp\strutbox \floatingpenalty\@@MM \leftskip\z@@skip \rightskip\z@@skip \spaceskip\z@@skip \xspaceskip\z@@skip \parindent\defaultparindent % \smallfonts \rm % % Hang the footnote text off the number. \hang \textindent{\thisfootno}% % % Don't crash into the line above the footnote text. Since this % expands into a box, it must come within the paragraph, lest it % provide a place where TeX can split the footnote. \footstrut \futurelet\next\fo@@t } \def\fo@@t{\ifcat\bgroup\noexpand\next \let\next\f@@@@t \else\let\next\f@@t\fi \next} \def\f@@@@t{\bgroup\aftergroup\@@foot\let\next} \def\f@@t#1{#1\@@foot} \def\@@foot{\strut\par\egroup} }%end \catcode `\@@=11 % Set the baselineskip to #1, and the lineskip and strut size % correspondingly. There is no deep meaning behind these magic numbers % used as factors; they just match (closely enough) what Knuth defined. % \def\lineskipfactor{.08333} \def\strutheightpercent{.70833} \def\strutdepthpercent {.29167} % \def\setleading#1{% \normalbaselineskip = #1\relax \normallineskip = \lineskipfactor\normalbaselineskip \normalbaselines \setbox\strutbox =\hbox{% \vrule width0pt height\strutheightpercent\baselineskip depth \strutdepthpercent \baselineskip }% } % @@| inserts a changebar to the left of the current line. It should % surround any changed text. This approach does *not* work if the % change spans more than two lines of output. To handle that, we would % have adopt a much more difficult approach (putting marks into the main % vertical list for the beginning and end of each change). % \def\|{% % \vadjust can only be used in horizontal mode. \leavevmode % % Append this vertical mode material after the current line in the output. \vadjust{% % We want to insert a rule with the height and depth of the current % leading; that is exactly what \strutbox is supposed to record. \vskip-\baselineskip % % \vadjust-items are inserted at the left edge of the type. So % the \llap here moves out into the left-hand margin. \llap{% % % For a thicker or thinner bar, change the `1pt'. \vrule height\baselineskip width1pt % % This is the space between the bar and the text. \hskip 12pt }% }% } % For a final copy, take out the rectangles % that mark overfull boxes (in case you have decided % that the text looks ok even though it passes the margin). % \def\finalout{\overfullrule=0pt} % @@image. We use the macros from epsf.tex to support this. % If epsf.tex is not installed and @@image is used, we complain. % % Check for and read epsf.tex up front. If we read it only at @@image % time, we might be inside a group, and then its definitions would get % undone and the next image would fail. \openin 1 = epsf.tex \ifeof 1 \else \closein 1 % Do not bother showing banner with post-v2.7 epsf.tex (available in % doc/epsf.tex until it shows up on ctan). \def\epsfannounce{\toks0 = }% \input epsf.tex \fi % % We will only complain once about lack of epsf.tex. \newif\ifwarnednoepsf \newhelp\noepsfhelp{epsf.tex must be installed for images to work. It is also included in the Texinfo distribution, or you can get it from ftp://tug.org/tex/epsf.tex.} % \def\image#1{% \ifx\epsfbox\undefined \ifwarnednoepsf \else \errhelp = \noepsfhelp \errmessage{epsf.tex not found, images will be ignored}% \global\warnednoepsftrue \fi \else \imagexxx #1,,,\finish \fi } % % Arguments to @@image: % #1 is (mandatory) image filename; we tack on .eps extension. % #2 is (optional) width, #3 is (optional) height. % #4 is just the usual extra ignored arg for parsing this stuff. \def\imagexxx#1,#2,#3,#4\finish{% \ifpdf \centerline{\dopdfimage{#1}{#2}{#3}}% \else % \epsfbox itself resets \epsf?size at each figure. \setbox0 = \hbox{\ignorespaces #2}\ifdim\wd0 > 0pt \epsfxsize=#2\relax \fi \setbox0 = \hbox{\ignorespaces #3}\ifdim\wd0 > 0pt \epsfysize=#3\relax \fi \begingroup \catcode`\^^M = 5 % in case we're inside an example % If the image is by itself, center it. \ifvmode \nobreak\bigskip % Usually we'll have text after the image which will insert % \parskip glue, so insert it here too to equalize the space % above and below. \nobreak\vskip\parskip \nobreak \centerline{\epsfbox{#1.eps}}% \bigbreak \else % In the middle of a paragraph, no extra space. \epsfbox{#1.eps}% \fi \endgroup \fi } \message{localization,} % and i18n. % @@documentlanguage is usually given very early, just after % @@setfilename. If done too late, it may not override everything % properly. Single argument is the language abbreviation. % It would be nice if we could set up a hyphenation file here. % \def\documentlanguage{\parsearg\dodocumentlanguage} \def\dodocumentlanguage#1{% \tex % read txi-??.tex file in plain TeX. % Read the file if it exists. \openin 1 txi-#1.tex \ifeof1 \errhelp = \nolanghelp \errmessage{Cannot read language file txi-#1.tex}% \let\temp = \relax \else \def\temp{\input txi-#1.tex }% \fi \temp \endgroup } \newhelp\nolanghelp{The given language definition file cannot be found or is empty. Maybe you need to install it? In the current directory should work if nowhere else does.} % @@documentencoding should change something in TeX eventually, most % likely, but for now just recognize it. \let\documentencoding = \comment % Page size parameters. % \newdimen\defaultparindent \defaultparindent = 15pt \chapheadingskip = 15pt plus 4pt minus 2pt \secheadingskip = 12pt plus 3pt minus 2pt \subsecheadingskip = 9pt plus 2pt minus 2pt % Prevent underfull vbox error messages. \vbadness = 10000 % Don't be so finicky about underfull hboxes, either. \hbadness = 2000 % Following George Bush, just get rid of widows and orphans. \widowpenalty=10000 \clubpenalty=10000 % Use TeX 3.0's \emergencystretch to help line breaking, but if we're % using an old version of TeX, don't do anything. We want the amount of % stretch added to depend on the line length, hence the dependence on % \hsize. We call this whenever the paper size is set. % \def\setemergencystretch{% \ifx\emergencystretch\thisisundefined % Allow us to assign to \emergencystretch anyway. \def\emergencystretch{\dimen0}% \else \emergencystretch = .15\hsize \fi } % Parameters in order: 1) textheight; 2) textwidth; 3) voffset; % 4) hoffset; 5) binding offset; 6) topskip. Then whoever calls us can % set \parskip and call \setleading for \baselineskip. % \def\internalpagesizes#1#2#3#4#5#6{% \voffset = #3\relax \topskip = #6\relax \splittopskip = \topskip % \vsize = #1\relax \advance\vsize by \topskip \outervsize = \vsize \advance\outervsize by 2\topandbottommargin \pageheight = \vsize % \hsize = #2\relax \outerhsize = \hsize \advance\outerhsize by 0.5in \pagewidth = \hsize % \normaloffset = #4\relax \bindingoffset = #5\relax % \parindent = \defaultparindent \setemergencystretch } % @@letterpaper (the default). \def\letterpaper{{\globaldefs = 1 \parskip = 3pt plus 2pt minus 1pt \setleading{13.2pt}% % % If page is nothing but text, make it come out even. \internalpagesizes{46\baselineskip}{6in}{\voffset}{.25in}{\bindingoffset}{36pt}% }} % Use @@smallbook to reset parameters for 7x9.5 (or so) format. \def\smallbook{{\globaldefs = 1 \parskip = 2pt plus 1pt \setleading{12pt}% % \internalpagesizes{7.5in}{5.in}{\voffset}{.25in}{\bindingoffset}{16pt}% % \lispnarrowing = 0.3in \tolerance = 700 \hfuzz = 1pt \contentsrightmargin = 0pt \deftypemargin = 0pt \defbodyindent = .5cm % \let\smalldisplay = \smalldisplayx \let\smallexample = \smalllispx \let\smallformat = \smallformatx \let\smalllisp = \smalllispx }} % Use @@afourpaper to print on European A4 paper. \def\afourpaper{{\globaldefs = 1 \setleading{12pt}% \parskip = 3pt plus 2pt minus 1pt % \internalpagesizes{53\baselineskip}{160mm}{\voffset}{4mm}{\bindingoffset}{44pt}% % \tolerance = 700 \hfuzz = 1pt }} % A specific text layout, 24x15cm overall, intended for A4 paper. Top margin % 29mm, hence bottom margin 28mm, nominal side margin 3cm. \def\afourlatex{{\globaldefs = 1 \setleading{13.6pt}% % \afourpaper \internalpagesizes{237mm}{150mm}{3.6mm}{3.6mm}{3mm}{7mm}% % \globaldefs = 0 }} % Use @@afourwide to print on European A4 paper in wide format. \def\afourwide{% \afourpaper \internalpagesizes{9.5in}{6.5in}{\hoffset}{\normaloffset}{\bindingoffset}{7mm}% % \globaldefs = 0 } % @@pagesizes TEXTHEIGHT[,TEXTWIDTH] % Perhaps we should allow setting the margins, \topskip, \parskip, % and/or leading, also. Or perhaps we should compute them somehow. % \def\pagesizes{\parsearg\pagesizesxxx} \def\pagesizesxxx#1{\pagesizesyyy #1,,\finish} \def\pagesizesyyy#1,#2,#3\finish{{% \setbox0 = \hbox{\ignorespaces #2}\ifdim\wd0 > 0pt \hsize=#2\relax \fi \globaldefs = 1 % \parskip = 3pt plus 2pt minus 1pt \setleading{13.2pt}% % \internalpagesizes{#1}{\hsize}{\voffset}{\normaloffset}{\bindingoffset}{44pt}% }} % Set default to letter. % \letterpaper \message{and turning on texinfo input format.} % Define macros to output various characters with catcode for normal text. \catcode`\"=\other \catcode`\~=\other \catcode`\^=\other \catcode`\_=\other \catcode`\|=\other \catcode`\<=\other \catcode`\>=\other \catcode`\+=\other \catcode`\$=\other \def\normaldoublequote{"} \def\normaltilde{~} \def\normalcaret{^} \def\normalunderscore{_} \def\normalverticalbar{|} \def\normalless{<} \def\normalgreater{>} \def\normalplus{+} \def\normaldollar{$} % This macro is used to make a character print one way in ttfont % where it can probably just be output, and another way in other fonts, % where something hairier probably needs to be done. % % #1 is what to print if we are indeed using \tt; #2 is what to print % otherwise. Since all the Computer Modern typewriter fonts have zero % interword stretch (and shrink), and it is reasonable to expect all % typewriter fonts to have this, we can check that font parameter. % \def\ifusingtt#1#2{\ifdim \fontdimen3\font=0pt #1\else #2\fi} % Same as above, but check for italic font. Actually this also catches % non-italic slanted fonts since it is impossible to distinguish them from % italic fonts. But since this is only used by $ and it uses \sl anyway % this is not a problem. \def\ifusingit#1#2{\ifdim \fontdimen1\font>0pt #1\else #2\fi} % Turn off all special characters except @@ % (and those which the user can use as if they were ordinary). % Most of these we simply print from the \tt font, but for some, we can % use math or other variants that look better in normal text. \catcode`\"=\active \def\activedoublequote{{\tt\char34}} \let"=\activedoublequote \catcode`\~=\active \def~{{\tt\char126}} \chardef\hat=`\^ \catcode`\^=\active \def^{{\tt \hat}} \catcode`\_=\active \def_{\ifusingtt\normalunderscore\_} % Subroutine for the previous macro. \def\_{\leavevmode \kern.06em \vbox{\hrule width.3em height.1ex}} \catcode`\|=\active \def|{{\tt\char124}} \chardef \less=`\< \catcode`\<=\active \def<{{\tt \less}} \chardef \gtr=`\> \catcode`\>=\active \def>{{\tt \gtr}} \catcode`\+=\active \def+{{\tt \char 43}} \catcode`\$=\active \def${\ifusingit{{\sl\$}}\normaldollar} %\catcode 27=\active %\def^^[{$\diamondsuit$} % Set up an active definition for =, but don't enable it most of the time. {\catcode`\==\active \global\def={{\tt \char 61}}} \catcode`+=\active \catcode`\_=\active % If a .fmt file is being used, characters that might appear in a file % name cannot be active until we have parsed the command line. % So turn them off again, and have \everyjob (or @@setfilename) turn them on. % \otherifyactive is called near the end of this file. \def\otherifyactive{\catcode`+=\other \catcode`\_=\other} \catcode`\@@=0 % \rawbackslashxx output one backslash character in current font \global\chardef\rawbackslashxx=`\\ %{\catcode`\\=\other %@@gdef@@rawbackslashxx{\}} % \rawbackslash redefines \ as input to do \rawbackslashxx. {\catcode`\\=\active @@gdef@@rawbackslash{@@let\=@@rawbackslashxx }} % \normalbackslash outputs one backslash in fixed width font. \def\normalbackslash{{\tt\rawbackslashxx}} % \catcode 17=0 % Define control-q \catcode`\\=\active % Used sometimes to turn off (effectively) the active characters % even after parsing them. @@def@@turnoffactive{@@let"=@@normaldoublequote @@let\=@@realbackslash @@let~=@@normaltilde @@let^=@@normalcaret @@let_=@@normalunderscore @@let|=@@normalverticalbar @@let<=@@normalless @@let>=@@normalgreater @@let+=@@normalplus @@let$=@@normaldollar} @@def@@normalturnoffactive{@@let"=@@normaldoublequote @@let\=@@normalbackslash @@let~=@@normaltilde @@let^=@@normalcaret @@let_=@@normalunderscore @@let|=@@normalverticalbar @@let<=@@normalless @@let>=@@normalgreater @@let+=@@normalplus @@let$=@@normaldollar} % Make _ and + \other characters, temporarily. % This is canceled by @@fixbackslash. @@otherifyactive % If a .fmt file is being used, we don't want the `\input texinfo' to show up. % That is what \eatinput is for; after that, the `\' should revert to printing % a backslash. % @@gdef@@eatinput input texinfo{@@fixbackslash} @@global@@let\ = @@eatinput % On the other hand, perhaps the file did not have a `\input texinfo'. Then % the first `\{ in the file would cause an error. This macro tries to fix % that, assuming it is called before the first `\' could plausibly occur. % Also back turn on active characters that might appear in the input % file name, in case not using a pre-dumped format. % @@gdef@@fixbackslash{% @@ifx\@@eatinput @@let\ = @@normalbackslash @@fi @@catcode`+=@@active @@catcode`@@_=@@active } % Say @@foo, not \foo, in error messages. @@escapechar = `@@@@ % These look ok in all fonts, so just make them not special. @@catcode`@@& = @@other @@catcode`@@# = @@other @@catcode`@@% = @@other @@c Set initial fonts. @@textfonts @@rm @@c Local variables: @@c eval: (add-hook 'write-file-hooks 'time-stamp) @@c page-delimiter: "^\\\\message" @@c time-stamp-start: "def\\\\texinfoversion{" @@c time-stamp-format: "%:y-%02m-%02d.%02H" @@c time-stamp-end: "}" @@c End: @ gsl-1.0.8/doc/RCS/mktexi_inc~,v0000644000175000017500000003124111201030376014016 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @# @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @#!/usr/bin/env perl # # David Bateman Feb 02 2003 # # Extracts the help in texinfo format for particular function for use # in documentation. Based on make_index script from octave_forge. use strict; use File::Find; use File::Basename; use Text::Wrap; use FileHandle; use IPC::Open3; use POSIX ":sys_wait_h"; my $file = shift @@ARGV; my $docfile = shift @@ARGV; my $indexfile = shift @@ARGV; my $line; print("\\input texinfo \n"); print("\@@ifnottex \n"); print("\@@node Top \n"); print("\@@top Octave gsl \n"); print("\@@end ifnottex \n"); print("\@@node Concept Index \n"); print("\@@unnumbered Concept Index \n "); print("\@@printindex cp \n"); if ( open(IN,$file) ) { $line = ; my $tex = 0; while ($line) { if ($line =~ /^\@@DOCSTRING/) { my $found = 0; my $func = $line; $func =~ s/\@@DOCSTRING\(//; $func =~ s/\)[\n\r]+//; my $func0 = $func; my $func1 = $func; $func0 =~ s/,.*$//; $func1 =~ s/^.*,//; if ( open(DOC,$docfile) ) { while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func0$/) { my $desc = ""; my $docline; my $doctex = 0; while (($docline = ) && ($docline !~ /^\037/)) { $docline =~ s/^\s*-[*]- texinfo -[*]-\s*//; if ($docline =~ /\@@tex/) { $doctex = 1; } if ($doctex) { $docline =~ s/\\\\/\\/g; } if ($docline =~ /\@@end tex/) { $doctex = 0; } $desc .= $docline; } $desc =~ s/$func0/$func1/g; $desc =~ s/\@@seealso\{(.*[^}])\}/See also: \1/g; print "$desc", "\n"; $found = 1; last; } } close (DOC); if (! $found) { print "\@@emph{Not implemented}\n"; } } else { print STDERR "Could not open file $docfile\n"; exit 1; } } elsif ($line =~ /^\@@REFERENCE_SECTION/) { my $secfound = 0; my $sec = $line; $sec =~ s/\@@REFERENCE_SECTION\(//; $sec =~ s/\)[\n\r]+//; my @@listfunc = (); my $nfunc = 0; my $seccat = 0; if ( open(IND,$indexfile) ) { while () { next unless /^[^ ]/; my $section = $_; $section =~ s/[\n\r]+//; if ($section =~ /^(.*?)\s*>>\s*(.*?)$/) { $section =~ s/.*>>(.*)/\1/; $seccat = 1; } $section =~ s/^ *//; $section =~ s/ *$//; if ($section =~ /^$sec$/) { if ($seccat) { print "\@@iftex\n"; print "\@@section Functions by Category\n"; # Get the list of categories to index my $firstcat = 1; my $category; while () { last if />>/; if (/^[^ ]/) { if (! $firstcat) { print "\@@end table\n"; } else { $firstcat = 0; } $category = $_; $category =~ s/[\n\r]+//; print "\@@subsection $category\n"; print "\@@table \@@asis\n"; } elsif (/^\s+(\S.*\S)\s*=\s*(\S.*\S)\s*$/) { my $func = $1; my $desc = $2; print "\@@item $func\n"; print "$desc\n"; print "\n"; } else { if ($firstcat) { print STDERR "Error parsing index file\n"; exit 1; } s/^\s+//; my @@funcs = split /\s+/; while ($#funcs >= 0) { my $func = shift @@funcs; $func =~ s/^ *//; $func =~ s/[\n\r]+//; push @@listfunc, $func; $nfunc = $nfunc + 1; print "\@@item $func\n"; print func_summary($func, $docfile); print "\n"; } } } if (! $firstcat) { print "\@@end table\n"; } print "\n\@@section Functions Alphabetically\n"; print "\@@end iftex\n\n"; } else { # Get the list of functions to index my $indline; while (($indline = ) && ($indline =~ /^ /)) { if ($indline =~ /^\s+(\S.*\S)\s*=\s*(\S.*\S)\s*$/) { next; } $indline =~ s/^\s+//; my @@funcs = split(/\s+/,$indline); while ($#funcs >= 0) { my $func = shift @@funcs; $func =~ s/^ *//; $func =~ s/[\n\r]+//; push @@listfunc, $func; $nfunc = $nfunc + 1; } } } $secfound = 1; last; } } close (IND); if (! $secfound) { print STDERR "Did not find section $sec\n"; } } else { print STDERR "Could not open file $indexfile\n"; exit 1; } @@listfunc = sort(@@listfunc); my @@listfunc2 = (); my $indent = 16 - 3; print "\@@menu\n"; foreach my $func (@@listfunc) { if ( open(DOC,$docfile) ) { my $found = 0; while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func$/) { $found = 1; last; } } close (DOC); if ($found) { push @@listfunc2, $func; my $func0 = "${func}::"; my $entry = sprintf("* %-*s %s",$indent,$func0,func_summary($func,$docfile)); print wrap("","\t\t","$entry"), "\n"; } } else { print STDERR "Could not open file $indexfile\n"; exit 1; } } print "\@@end menu\n"; my $up = "Function Reference"; my $next; my $prev; my $mfunc = 1; foreach my $func (@@listfunc2) { if ($mfunc == $nfunc) { $next = ""; } else { $next = @@listfunc2[$mfunc]; $mfunc = $mfunc + 1; } print "\n\@@node $func, $next, $prev, $up\n"; if ($seccat) { print "\@@subsection $func\n\n"; } else { print "\@@section $func\n\n"; } $prev = $func; my $found = 0; my $desc = ""; if ( open(DOC,$docfile) ) { while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func$/) { my $docline; my $doctex = 0; while (($docline = ) && ($docline !~ /^\037/)) { $docline =~ s/^\s*-[*]- texinfo -[*]-\s*//; if ($docline =~ /\@@tex/) { $doctex = 1; } if ($doctex) { $docline =~ s/\\\\/\\/g; } if ($docline =~ /\@@end tex/) { $doctex = 0; } $desc .= $docline; } $desc =~ s/\@@seealso\{(.*[^}])\}/See also: \1/g; print "$desc", "\n"; $found = 1; last; } } close (DOC); if (! $found) { print "\@@emph{Not implemented}\n"; } } else { print STDERR "Could not open file $docfile\n"; exit 1; } } } else { if ($line =~ /\@@tex/) { $tex = 1; } if ($tex) { $line =~ s/\\\\/\\/g; } print "$line"; if ($line =~ /\@@end tex/) { $tex = 0; } } $line = ; } } else { print STDERR "Could not open file $file\n"; exit 1; }; print("\@@bye"); sub func_summary { # {{{1 my ($func, # in function name $docfile # in DOCSTRINGS ) = @@_; my $desc = ""; my $found = 0; if ( open(DOC,$docfile) ) { while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func$/) { my $docline; my $doctex = 0; while (($docline = ) && ($docline !~ /^\037/)) { if ($docline =~ /\@@tex/) { $doctex = 1; } if ($doctex) { $docline =~ s/\\\\/\\/g; } if ($docline =~ /\@@end tex/) { $doctex = 0; } $desc .= $docline; } $desc =~ s/\@@seealso\{(.*[^}])\}/See also: \1/g; $found = 1; last; } } close (DOC); if (! $found) { $desc = "\@@emph{Not implemented}"; } } else { print STDERR "Could not open file $docfile\n"; exit 1; } return first_sentence($desc); } # 1}}} sub first_sentence { # {{{1 # grab the first real sentence from the function documentation my ($desc) = @@_; my $retval = ''; my $line; my $next; my @@lines; my $trace = 0; # $trace = 1 if $desc =~ /Levenberg/; return "" unless defined $desc; if ($desc =~ /^\s*-[*]- texinfo -[*]-/) { # help text contains texinfo. Strip the indicator and run it # through makeinfo. (XXX FIXME XXX this needs to be a function) $desc =~ s/^\s*-[*]- texinfo -[*]-\s*//; my $cmd = "makeinfo --fill-column 1600 --no-warn --no-validate --no-headers --force --ifinfo"; open3(*Writer, *Reader, *Errer, $cmd) or die "Could not run info"; print Writer "\@@macro seealso {args}\n\n\@@noindent\nSee also: \\args\\.\n\@@end macro\n"; print Writer "$desc"; close(Writer); @@lines = ; close(Reader); my @@err = ; close(Errer); waitpid(-1,&WNOHANG); # Display source and errors, if any if (@@err) { my $n = 1; foreach $line ( split(/\n/,$desc) ) { printf "%2d: %s\n",$n++,$line; } print ">>> @@err"; } # Print trace showing formatted output # print "\n"; # Skip prototype and blank lines while (1) { return "" unless @@lines; $line = shift @@lines; next if $line =~ /^\s*-/; next if $line =~ /^\s*$/; last; } } else { # print "\n"; # Skip prototype and blank lines @@lines = split(/\n/,$desc); while (1) { return "" if ($#lines < 0); $line = shift @@lines; next if $line =~ /^\s*[Uu][Ss][Aa][Gg][Ee]/; # skip " usage " $line =~ s/^\s*\w+\s*://; # chop " blah : " print "strip blah: $line\n" if $trace; $line =~ s/^\s*[Ff]unction\s+//; # chop " function " print "strip function $line\n" if $trace; $line =~ s/^\s*\[.*\]\s*=\s*//; # chop " [a,b] = " print "strip []= $line\n" if $trace; $line =~ s/^\s*\w+\s*=\s*//; # chop " a = " print "strip a= $line\n" if $trace; $line =~ s/^\s*\w+\s*\([^\)]*\)\s*//; # chop " f(x) " print "strip f(x) $line\n" if $trace; $line =~ s/^\s*[;:]\s*//; # chop " ; " print "strip ; $line\n" if $trace; $line =~ s/^\s*[[:upper:]][[:upper:]0-9_]+//; # chop " BLAH" print "strip BLAH $line\n" if $trace; $line =~ s/^\s*\w*\s*[-]+\s+//; # chop " blah --- " print "strip blah --- $line\n" if $trace; $line =~ s/^\s*\w+ *\t\s*//; # chop " blah " print "strip blah $line\n" if $trace; $line =~ s/^\s*\w+\s\s+//; # chop " blah " print "strip blah $line\n" if $trace; # next if $line =~ /^\s*\[/; # skip [a,b] = f(x) # next if $line =~ /^\s*\w+\s*(=|\()/; # skip a = f(x) OR f(x) next if $line =~ /^\s*or\s*$/; # skip blah \n or \n blah next if $line =~ /^\s*$/; # skip blank line next if $line =~ /^\s?!\//; # skip # !/usr/bin/octave # XXX FIXME XXX should be testing for unmatched () in proto # before going to the next line! last; } } # Try to make a complete sentence, including the '.' if ( "$line " !~ /[^.][.]\s/ && $#lines >= 0) { my $next = $lines[0]; $line =~ s/\s*$//; # trim trailing blanks on last $next =~ s/^\s*//; # trim leading blanks on next $line .= " $next" if "$next " =~ /[^.][.]\s/; # ends the sentence } # Tidy up the sentence. chomp $line; # trim trailing newline, if there is one $line =~ s/^\s*//; # trim leading blanks on line $line =~ s/([^.][.])\s.*$/$1/; # trim everything after the sentence print "Skipping:\n$desc---\n" if $line eq ""; # And return it. return $line; } # 1}}} __END__ This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, see . This program is granted to the public domain. THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. @ gsl-1.0.8/doc/RCS/gsl.dvi,v0000644000175000017500000045563211201030376013052 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @# @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @÷ƒ’À;è TeX output 2008.05.15:1311‹ÿÿÿÿŸòŽ ƒ3* ý ÌÖ‘!Gó2Kñ`y ó3 cmr10Ýgsl_sf–¦f-*-“texinfo“-*-Ž©íD’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gó=ßêto“the˜GNU–W)Scien²!ti c˜Library‘ÿe.‘ÃzAll˜GSL“functions˜can–W=bMÞe˜called“withŽ¡‘.ùœbš²!y–¦fthe“GSL“names“within“oMÞcta˜v˜e.ŽŸíE‘!Gclausen–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gó>ßêÝ=‘¦f0.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸC‘!GSi–¦f-*-“texinfo“-*-ŽŸC’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉSi‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“Si‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“Sine“inš²!tegral“Si(x)“=“in˜t_0Þ^Ýx“dt“sin(t)/t.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ»$‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸC‘!GCi–¦f-*-“texinfo“-*-ŽŽŒ‹/BŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉCi‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“Ci‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Qroutines›Qcompute“the“Cosine“in²!tegral˜Ci(x)“=“-in•²!t_xÞ^Ýinft“y˜dt–Qcos(t)/t“for“x˜Þ>“Ý0.Ž¤ä’‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž© 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤•ñ‘!Gatanin²!t–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉatanint‘yšâ(éx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“atanint‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–@@routines“compute“the“Arctangenš²!t“in˜tegral‘@@A˜tanIn˜t(x)“=“in˜t_0Þ^Ýx“dt“arctan(t)/t.Ž¤ä’‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤•ñ‘!Gfermi_dirac_mhalf–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉfermi_dirac_mhalf‘yšâ(éx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“fermi_dirac_mhalf‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“complete“F‘ÿeermi-Dirac“in²!tegral“F_Þ{Ý-1/2Þ}Ý(x).Ž¤ä’‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤•ñ‘!Gfermi_dirac_half–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉfermi_dirac_half‘yšâ(éx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“fermi_dirac_half‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“complete“F‘ÿeermi-Dirac“in²!tegral“F_Þ{Ý1/2Þ}Ý(x).Ž¤ä’‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤•ñ‘!Gfermi_dirac_3half–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉfermi_dirac_3half‘yšâ(éx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“fermi_dirac_3half‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“complete“F‘ÿeermi-Dirac“in²!tegral“F_Þ{Ý3/2Þ}Ý(x).Ž¤ä’‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ•ñ‘!Ggamma_gsl–¦f-*-“texinfo“-*-ŽŽŒ‹9|ŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉgamma_gsl‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“gamma_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–garoutines›gbcompute“the“Gamma“function˜Gamma(x),‘— sub‘›»ject“to“x“not˜bMÞeing“aŽ¡‘.ùœnegativ•²!e›¿in“teger.‘ çThe˜function–¾is˜computed˜using˜the“real˜Lanczos˜methoMÞd.‘ çTheŽ¡‘.ùœmaxim²!um–]v‘ÿdDalue›\of“x˜suc²!h“that˜Gamma(x)“is“not˜considered“an˜o•²!v“er o“w‘]is˜giv“en‘]b“yŽ¡‘.ùœthe–¦fmacro“GSL_SF_GAMMA_XMAX“and“is“171.0.Ž©¹™‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ¹š‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ?ÿ‘!Glngamma_gsl–¦f-*-“texinfo“-*-ŽŸ@@’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlngamma_gsl‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“lngamma_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–gžroutines“compute›gthe“logarithm“of“the“Gamma˜function,‘t-log(Gamma(x)),‘t,sub-Ž¡‘.ùœject–£¾to“x›£½not“a“bMÞeing“negativ•²!e˜in“teger.‘ÕåF‘ÿeor˜xÞ<Ý0–£¾the“real“part˜of“log(Gamma(x))“isŽ¡‘.ùœreturned,‘rwhic•²!h›ðÖis‘ðÕequiv‘ÿdDalen“t˜to˜log(Þ|ÝGamma(x)Þ|Ý).‘½-The‘ðÕfunction˜is˜computed˜usingŽ¡‘.ùœthe–¦freal“Lanczos“methoMÞd.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ¹š‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ?ÿ‘!Ggammastar–¦f-*-“texinfo“-*-ŽŸ@@’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉgammastar‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“gammastar‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–oÙroutines›oÚcompute“the“regulated“Gamma˜F‘ÿeunction“GammaÞ^Ý*(x)“for“x˜Þ>“Ý0.‘Ë®TheŽ¡‘.ùœregulated–¦fgamma“function“is“givš²!en“b˜y‘ÿe,Ž¦‘.ùœGammaÞ^Ý*(x)–ƒ<=›ƒ;Gamma(x)/(sqrtÞ{Ý2piÞ}“ÝxÞ^{Ý(x-1/2)Þ}“Ýexp(-x))“=˜(1“+“(1/12x)˜+“...)Ž¡‘.ùœfor–¦fx“to“inft²!yŽŸ¹š‘.ùœand–¦fis“a“useful“suggestion“of“T‘ÿeemme.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤@@‘!Ggammain²!v_gsl–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉgammainv_gsl‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“gammainv_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¤5routines›¤4compute“the˜reciproMÞcal“of˜the“gamma“function,‘ã§1/Gamma(x)“usingŽ¡‘.ùœthe–¦freal“Lanczos“methoMÞd.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ@@‘!Glam²!bMÞert_W0–¦f-*-“texinfo“-*-ŽŽŒ‹DñŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlambert_W0‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“lambert_W0‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦fcompute“the“principal“brancš²!h“of“the“Lam˜bMÞert“W“function,“W_0(x).Ž©¹™‘.ùœLam²!bMÞert's›Œ³W‘Œ6functions,–FW(x),“are˜de ned˜to˜bMÞe˜solutions‘Œ´of˜the˜equation˜W(x)Ž¡‘.ùœexp(W(x))–b£=“x.‘ “This“function“has‘b¢mš²!ultiple“branc˜hes“for“x‘b¢Þ<“Ý0;‘@@Áho˜w˜ev˜er,‘ѱit“hasŽ¡‘.ùœonly›ct•²!w“o˜real-v‘ÿdDalued˜branc“hes.‘3ÓW‘ÿee˜de ne˜W_0(x)˜to˜bMÞe‘bthe˜principal˜branc“h,‘4âwhereŽ¡‘.ùœW‘}!Þ>–}+Ý-1“for“x“Þ<“Ý0,›…jand“W_Þ{Ý-1Þ}Ý(x)“to“bMÞe“the“other“real“branc²!h,˜where“W‘}!Þ<“Ý-1“for“x“Þ<“Ý0.ŽŸ¹š‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ@@‘!Glam²!bMÞert_Wm1–¦f-*-“texinfo“-*-ŽŸ?ÿ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlambert_Wm1‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“lambert_Wm1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–:Bcompute“the“secondary‘:Areal-v‘ÿdDalued“brancš²!h“of“the“Lam˜bMÞert“W‘:function,‘_9W_Þ{Ý-Ž¡‘.ùœ1Þ}Ý(x).ŽŸ¹š‘.ùœLam²!bMÞert's›Œ³W‘Œ6functions,–FW(x),“are˜de ned˜to˜bMÞe˜solutions‘Œ´of˜the˜equation˜W(x)Ž¡‘.ùœexp(W(x))–b£=“x.‘ “This“function“has‘b¢mš²!ultiple“branc˜hes“for“x‘b¢Þ<“Ý0;‘@@Áho˜w˜ev˜er,‘ѱit“hasŽ¡‘.ùœonly›ct•²!w“o˜real-v‘ÿdDalued˜branc“hes.‘3ÓW‘ÿee˜de ne˜W_0(x)˜to˜bMÞe‘bthe˜principal˜branc“h,‘4âwhereŽ¡‘.ùœW‘}!Þ>–}+Ý-1“for“x“Þ<“Ý0,›…jand“W_Þ{Ý-1Þ}Ý(x)“to“bMÞe“the“other“real“branc²!h,˜where“W‘}!Þ<“Ý-1“for“x“Þ<“Ý0.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤@@‘!Glog_1plusx–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlog_1plusx‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“log_1plusx‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–žkroutines“compute“log(1“+›žlx)“for“x“Þ>“Ý-1“using“an“algorithm˜that“is“accurate“forŽ¡‘.ùœsmall‘¦fx.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤@@‘!Glog_1plusx_mx–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlog_1plusx_mx‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“log_1plusx_mx‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ŸYroutines›ŸXcompute“log(1˜+“x)“-˜x“for˜x“Þ>˜Ý-1“using“an˜algorithm“that˜is“accurateŽ¡‘.ùœfor–¦fsmall“x.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ@@‘!Gpsi–¦f-*-“texinfo“-*-ŽŽŒ‹ QCŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉpsi‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“psi‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“digamma“function“psi(x)“for“general“x,“x“e“0.Ž¤úœ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž© 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤‰n‘!Gpsi_1piy–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉpsi_1piy‘yšâ(éx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“psi_1piy‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–è6routines“compute“the“real“part“of“the“digamma“function“on“the“line“1+i“y‘ÿe,Ž¦‘.ùœRe[psi(1–¦f+“i“y)].ŽŸúœ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸú‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¡‘!Gsync²!hrotron_1–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉsynchrotron_1‘yšâ(éx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“synchrotron_1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–GCroutines“compute‘GDthe“ rst“syncš²!hrotron“function“x“in˜t_xÞ^Ýinft˜y‘GDdt“K_Þ{Ý5/3Þ}Ý(t)“forŽ¦‘.ùœx–¦fÞ>Ý=“0.Ž¤úœ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤‰n‘!Gsync²!hrotron_2–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉsynchrotron_2‘yšâ(éx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“synchrotron_2‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“second“sync²!hrotron“function“x“K_Þ{Ý2/3Þ}Ý(x)“for“x“Þ>Ý=“0.Ž¤úœ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ‰o‘!GtranspMÞort_2–¦f-*-“texinfo“-*-ŽŸ‰n’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉtransport_2‘yšâ(éx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“transport_2‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“transpMÞort“function“J(2,x).Ž¡‘.ùœThe–üztranspMÞort›üyfunctions“J(n,x)“are“de ned˜bš²!y“the“in˜tegral“represen˜tations‘üyJ(n,x)“:=Ž¦‘.ùœin²!t_0Þ^Ýx–¦fdt“tÞ^Ýn“eÞ^Ýt“/(eÞ^Ýt“-“1)Þ^Ý2.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ‰n‘!GtranspMÞort_3–¦f-*-“texinfo“-*-ŽŽŒ‹ ^0ŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉtransport_3‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“transport_3‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“transpMÞort“function“J(3,x).Ž©²‚‘.ùœThe–üztranspMÞort›üyfunctions“J(n,x)“are“de ned˜bš²!y“the“in˜tegral“represen˜tations‘üyJ(n,x)“:=Ž¡‘.ùœin²!t_0Þ^Ýx–¦fdt“tÞ^Ýn“eÞ^Ýt“/(eÞ^Ýt“-“1)Þ^Ý2.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ±‘!GtranspMÞort_4–¦f-*-“texinfo“-*-ŽŸ± ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉtransport_4‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“transport_4‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“transpMÞort“function“J(4,x).ŽŸ²‘.ùœThe–üztranspMÞort›üyfunctions“J(n,x)“are“de ned˜bš²!y“the“in˜tegral“represen˜tations‘üyJ(n,x)“:=Ž¡‘.ùœin²!t_0Þ^Ýx–¦fdt“tÞ^Ýn“eÞ^Ýt“/(eÞ^Ýt“-“1)Þ^Ý2.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ± ‘!GtranspMÞort_5–¦f-*-“texinfo“-*-ŽŸ±’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉtransport_5‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“transport_5‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“transpMÞort“function“J(5,x).Ž¦‘.ùœThe–üztranspMÞort›üyfunctions“J(n,x)“are“de ned˜bš²!y“the“in˜tegral“represen˜tations‘üyJ(n,x)“:=Ž¡‘.ùœin²!t_0Þ^Ýx–¦fdt“tÞ^Ýn“eÞ^Ýt“/(eÞ^Ýt“-“1)Þ^Ý2.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ±‘!Gsinc_gsl–¦f-*-“texinfo“-*-ŽŸ± ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉsinc_gsl‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“sinc_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“sinc(x)“=“sin(pi“x)“/“(pi“x)“for“an²!y“v‘ÿdDalue“of“x.ŽŸ²‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ± ‘!Glnsinh–¦f-*-“texinfo“-*-ŽŸ±’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlnsinh‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“lnsinh‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“log(sinh(x))“for“x“Þ>“Ý0.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹ j:ŸòŽ ƒ3* ý ÌÖ‘!GÝlncosh–¦f-*-“texinfo“-*-Ž©Rµ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlncosh‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“lncosh‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“log(cosh(x))“for“an²!y“x.Ž¤è^‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gzeta–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉzeta‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“zeta‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“Riemann“zeta“function“zeta(s)“for“arbitrary“s,“s“e“1.Ž©è^‘.ùœThe–b¨Riemann›b©zeta“function˜is“de ned“b²!y˜the“in nite˜sum“zeta(s)˜=“sum_Þ{Ýk=1Þ}^Ýinft²!yŽ¡‘.ùœkÞ^{Ý-sÞ}Ý.ŽŸè_‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Rµ‘!Geta–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉeta‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“eta‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“eta“function“eta(s)“for“arbitrary“s.Ž¦‘.ùœThe–¦feta“function“is“de ned“b²!y“eta(s)“=“(1-2Þ^{Ý1-sÞ}Ý)“zeta(s).Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Rµ‘!GbMÞessel_Jn–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_Jn‘yšâ(éná,‘¦féx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_Jn‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“regular“cylindrical“Bessel“function“of“order“n,“J_n(x).Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž©è_‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸRµ‘!GbMÞessel_Yn–¦f-*-“texinfo“-*-ŽŸR´’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_Yn‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_Yn‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–&Üroutines›&Ýcompute“the“irregular˜cylindrical“Bessel“function˜of“order“n,‘FúY_n(x),Ž¡‘.ùœfor‘¦fxÞ>Ý0.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸè^‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹ v¹ŸòŽ ƒ3* ý ÌÖ‘!GÝbMÞessel_In–¦f-*-“texinfo“-*-Ž©’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_In‘yšâ(éná,‘¦féx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_In‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–?ºroutines›?¹compute“the“regular˜moMÞdi ed“cylindrical˜Bessel“function“of˜order“n,Ž¡‘.ùœI_n(x).Ž¤™™‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_In_scaled–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_In_scaled‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_In_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–8©routines›8¨compute“the˜scaled“regular˜moMÞdi ed“cylindrical˜Bessel“function˜ofŽ¡‘.ùœorder–¦fn,“exp(-Þ|ÝxÞ|Ý)“I_n(x)Ž¤™™‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_Kn–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_Kn‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_Kn‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–• routines›•!compute“the“irregular“moMÞdi ed˜cylindrical“Bessel“function“of˜order“n,Ž¡‘.ùœK_n(x),–¦ffor“x“Þ>“Ý0.Ž¤™™‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_Kn_scaled–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_Kn_scaled‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_Kn_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ™™‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_jl–¦f-*-“texinfo“-*-ŽŸÿÿ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_jl‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_jl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–>qroutines“compute“the‘>pregular“spherical“Bessel“function“of“order“l,–dsj_l(x),“for‘>qlŽ¡‘.ùœÞ>Ý=–¦f0“and“x“Þ>Ý=“0.ŽŸ™š‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ™™‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹ ‚}ŸòŽ ƒ3* ý ÌÖ‘!GÝbMÞessel_yl–¦f-*-“texinfo“-*-Ž©å`’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_yl‘yšâ(éná,‘¦féx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_yl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–‚íroutines“compute“the“irregular“spherical“Bessel“function“of“order“l,–Šy_l(x),“for‘‚ílŽ¡‘.ùœÞ>Ý=‘¦f0.ŽŸ I‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ J‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_il_scaled–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_il_scaled‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_il_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–(Òroutines›(Ócompute“the“scaled“regular˜moMÞdi ed“spherical“Bessel“function˜of“orderŽ¡‘.ùœl,–¦fexp(-Þ|ÝxÞ|Ý)“i_l(x)Ž¤ I‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_kl_scaled–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_kl_scaled‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_kl_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–>routines“compute“the“scaled“irregular“moMÞdi ed“spherical“Bessel“function“ofŽ¡‘.ùœorder–¦fl,“exp(x)“k_l(x),“for“xÞ>Ý0.ŽŸ J‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ I‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gexprel_n–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉexprel_n‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“exprel_n‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–“routines“compute“the“N-relativš²!e“expMÞonen˜tial,‘Ÿwhic˜h“is“the“n-th“generalizationŽ¡‘.ùœof–b÷the›bøfunctions“gsl_sf_exprel“and˜gsl_sf_exprel2.‘‘The“N-relativš²!e“expMÞonen˜tial‘bøis“giv˜enŽ¡‘.ùœb²!y‘ÿe,Ž© I‘.ùœexprel_N(x)–ÇF=“N!/xÞ^ÝN‘ƺ(exp(x)“-“sum_Þ{Ýk=0Þ}^{ÝN-1Þ}“ÝxÞ^Ýk/k!)‘ @@}=“1“+“x/(N+1)“+Ž¡‘.ùœxÞ^Ý2/((N+1)(N+2))–¦f+“...‘ÝÝ=“1F1“(1,1+N,x)ŽŸ J‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸå`‘!Gfermi_dirac_in²!t–¦f-*-“texinfo“-*-ŽŽŒ‹Ž8ŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉfermi_dirac_int‘yšâ(éná,‘¦féx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“fermi_dirac_int‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–OÖroutines›O×compute“the˜complete“F‘ÿeermi-Dirac˜in²!tegral“with˜an“in²!teger˜index“of˜j,Ž¡‘.ùœF_j(x)–¦f=“(1/Gamma(j+1))“in•²!t_0Þ^Ýinft“y–¦fdt“(tÞ^Ýj“/(exp(t-x)+1)).Ž¤ó3‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž© 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤³3‘!Gta²!ylorcoMÞe –¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉtaylorcoeff‘yšâ(éná,‘¦féx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“taylorcoeff‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“T‘ÿeaš²!ylor“coMÞecien˜t“xÞ^Ýn“/“n!‘ÝÝfor“x“Þ>Ý=“0,“n“Þ>Ý=“0.ŽŸó3‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸó2‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¡‘!Glegendre_Pl–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlegendre_Pl‘yšâ(éná,‘¦féx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“legendre_Pl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–Ojfunctions›Oiev‘ÿdDaluate“the“Legendre“pMÞolynomial˜P_l(x)“for“a˜spMÞeci c“v‘ÿdDalue“of“l,‘yªxŽ¦‘.ùœsub‘›»ject–¦fto“l“Þ>Ý=“0,“Þ|ÝxÞ|“<Ý=“1Ž¤ó3‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤³3‘!Glegendre_Ql–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlegendre_Ql‘yšâ(éná,‘¦féx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“legendre_Ql‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“Legendre“function“Q_l(x)“for“x“Þ>“Ý-1,“x“!=“1“and“l“Þ>Ý=“0.Ž¤ó3‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ³2‘!Gpsi_n–¦f-*-“texinfo“-*-ŽŸ³3’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉpsi_n‘yšâ(éná,‘¦féx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“psi_n‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“pMÞolygamma“function“psiÞ^{Ý(m)Þ}Ý(x)“for“m“Þ>Ý=“0,“x“Þ>“Ý0.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ³3‘!GbMÞessel_Jn²!u–¦f-*-“texinfo“-*-ŽŽŒ‹™HŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Jnu‘yšâ(éxá,‘¦féy‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Jnu‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Ukroutines“compute›Ujthe“regular“cylindrical“Bessel“function“of˜fractional“order“n²!u,Ž¡‘.ùœJ_u(x).Ž¤V¥‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž©z‘!GbMÞessel_Yn²!u–¦f-*-“texinfo“-*-ŽŸz’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Ynu‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Ynu‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–l¦routines›l¥compute“the˜irregular“cylindrical“Bessel˜function“of˜fractional“orderŽ¡‘.ùœn²!u,‘¦fY_u(x).Ž¤V¥‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_In²!u–¦f-*-“texinfo“-*-Ž©z’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Inu‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Inu‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Uroutines“compute“the“regular“moMÞdi ed‘TBessel“function“of“fractional“order“n²!u,Ž¡‘.ùœI_u(x)–¦ffor“xÞ>Ý0,“uÞ>Ý0.Ž¤V¥‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_In²!u_scaled–¦f-*-“texinfo“-*-ŽŸz’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Inu_scaled‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Inu_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Ü_routines›Ü^compute“the“scaled“regular˜moMÞdi ed“Bessel“function“of˜fractional“orderŽ¡‘.ùœn²!u,–¦fexp(-Þ|ÝxÞ|Ý)I_u(x)“for“xÞ>Ý0,“uÞ>Ý0.Ž¤V¥‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_Kn²!u–¦f-*-“texinfo“-*-ŽŸz’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Knu‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Knu‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–q¼routines›q»compute“the˜irregular“moMÞdi ed˜Bessel“function˜of“fractional˜order“n²!u,Ž¡‘.ùœK_u(x)–¦ffor“xÞ>Ý0,“uÞ>Ý0.Ž¤V¥‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™ŽŸ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹¥lŸòŽ ƒ3* ý ÌÖ‘!GÝbMÞessel_lnKn²!u–¦f-*-“texinfo“-*-Ž©Ã’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_lnKnu‘yšâ(éxá,‘¦féy‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_lnKnu‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Îroutines›Îcompute“the“logarithm“of˜the“irregular“moMÞdi ed“Bessel˜function“ofŽ¡‘.ùœfractional–¦forder“n²!u,“ln(K_u(x))“for“xÞ>Ý0,“uÞ>Ý0.Ž¤ Ö‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_Kn²!u_scaled–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Knu_scaled‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Knu_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–êroutines›êcompute“the“scaled˜irregular“moMÞdi ed“Bessel“function˜of“fractionalŽ¡‘.ùœorder–¦fn²!u,“exp(+Þ|ÝxÞ|Ý)“K_u(x)“for“xÞ>Ý0,“uÞ>Ý0.Ž¤ Ö‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gexp_m²!ult–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉexp_mult‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“exp_mult‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ò`routines›ò_expMÞonen²!tiate“x˜and“m•²!ultiply˜b“y–ò`the“factor˜y“to˜return“the˜proMÞduct“yŽ¡‘.ùœexp(x).Ž¤ Ö‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gfermi_dirac_inc_0–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉfermi_dirac_inc_0‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“fermi_dirac_inc_0‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–FÎroutines“compute“the“incomplete“F‘ÿeermi-Dirac‘FÏin²!tegral“with“an“index“of“zero,Ž¡‘.ùœF_0(x,b)–¦f=“ln(1“+“eÞ^{Ýb-xÞ}Ý)“-“(b-x).Ž¤ Ö‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gp•MÞo“c²!h–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉpoch‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“poch‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“P•²!ošMÞc“hhammer‘¦fsym“b˜olŽ¤ Ö‘.ùœ(a)_x–¦f:=“Gamma(a“+“x)/Gamma(a),Ž¡‘.ùœsub‘›»ject–to›a“and“a+x˜not“bMÞeing“negativ•²!e˜in“tegers.‘AàThe›P“oMÞc“hhammer˜sym“bMÞol‘is˜alsoŽŸ 33‘.ùœknoš²!wn–¦fas“the“ApMÞell“sym˜bMÞol.ŽŽŒ‹±ªŸòŽ ƒ3* ý ÌÖ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ“é‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž© 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ôŸ‘!Glnp•MÞo“c²!h–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉlnpoch‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“lnpoch‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–Ò-routines›Ò.compute“the“logarithm˜of“the“P•²!ošMÞc“hhammer‘Ò-sym“b˜ol,‘]log((a)_x)‘Ò-=Ž¦‘.ùœlog(Gamma(a–¦f+“x)/Gamma(a))“for“a“Þ>“Ý0,“a+x“Þ>“Ý0.Ž¤“é‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ôŸ‘!Gp•MÞo“c²!hrel–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉpochrel‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“pochrel‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–Kñroutines›Kòcompute“the˜relativš²!e“P˜oMÞc˜hhammer“sym˜bMÞol›Kò((a,x)“-˜1)/x“where˜(a,x)“=Ž¦‘.ùœ(a)_x–¦f:=“Gamma(a“+“x)/Gamma(a).Ž¤“é‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸôž‘!Ggamma_inc_Q–¦f-*-“texinfo“-*-ŽŸôŸ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉgamma_inc_Q‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“gamma_inc_Q‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–~øroutines›~ùcompute“the“normalized˜incomplete“Gamma“F‘ÿeunction˜Q(a,x)“=Ž¦‘.ùœ1/Gamma(a)›¦fin•²!t_xinft“y˜dt˜tÞ^{Ýa-1Þ}˜Ýexp(-t)˜for˜a˜Þ>˜Ý0,˜x˜Þ>Ý=˜0.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ôŸ‘!Ggamma_inc_P–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉgamma_inc_P‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“gamma_inc_P‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–(ïroutines›(ðcompute“the“complemen²!tary˜normalized“incomplete˜Gamma“F‘ÿeunctionŽ¦‘.ùœP(a,x)–¦f=“1/Gamma(a)“in²!t_0Þ^Ýx“dt“tÞ^{Ýa-1Þ}“Ýexp(-t)“for“a“Þ>“Ý0,“x“Þ>Ý=“0.Ž¤“é‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸôŸ‘!Ggamma_inc–¦f-*-“texinfo“-*-ŽŽŒ‹½ØŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉgamma_inc‘yšâ(éxá,‘¦féy‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“gamma_inc‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–°functions›±compute“the“incomplete˜Gamma“F‘ÿeunction“the˜normalization“factorŽ¡‘.ùœincluded–Þ¦in›Þ¥the“previously˜de ned“functions:‘N\Gamma(a,x)˜=“in•²!t_xinft“y˜dt‘Þ¦tÞ^{Ýa-1Þ}Ž¡‘.ùœÝexp(-t)–¦ffor“a“real“and“x“Þ>Ý=“0.Ž¤V¥‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž©z‘!GbMÞeta_gsl–¦f-*-“texinfo“-*-ŽŸz’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbeta_gsl‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“beta_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–nïroutines“compute“the“Beta“F‘ÿeunction,‘­:B(a,b)“=“Gamma(a)Gamma(b)/Gamma(a+b)Ÿ¼Ì„ ó2Ž¡‘.ùœfor–¦fa“Þ>“Ý0,“b“Þ>“Ý0.Ž¤V¥‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gln²!bMÞeta–¦f-*-“texinfo“-*-Ž©z’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉlnbeta‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“lnbeta‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¸ûroutines“compute“the“logarithm“of‘¸úthe“Beta“F‘ÿeunction,›½ log(B(a,b))“for“a“Þ>“Ý0,˜bŽ¡‘.ùœÞ>‘¦fÝ0.Ž¤V¥‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gh²!ypMÞerg_0F1–¦f-*-“texinfo“-*-ŽŸz’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉhyperg_0F1‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“hyperg_0F1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“h²!ypMÞergeometric“function“0F1(c,x).Ž¤V¥‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GconicalP_half–¦f-*-“texinfo“-*-ŽŸz’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉconicalP_half‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“conicalP_half‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ÍÏroutines›ÍÎcompute“the˜irregular“Spherical“Conical˜F‘ÿeunction“PÞ^{Ý1/2Þ}Ý_Þ{Ý-1/2˜+“iŽ¡‘.ùœlam²!bMÞdaÞ}Ý(x)–¦ffor“x“Þ>“Ý-1.Ž¤V¥‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™ŽŸ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹ÉEŸòŽ ƒ3* ý ÌÖ‘!GÝconicalP_mhalf–¦f-*-“texinfo“-*-Ž©)’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉconicalP_mhalf‘yšâ(éxá,‘¦féy‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“conicalP_mhalf‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–,routines›,compute“the“regular“Spherical˜Conical“F‘ÿeunction“PÞ^{Ý-1/2Þ}Ý_Þ{Ý-1/2˜+“iŽ¡‘.ùœlam²!bMÞdaÞ}Ý(x)–¦ffor“x“Þ>“Ý-1.ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GconicalP_0–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉconicalP_0‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“conicalP_0‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“conical“function“PÞ^Ý0_Þ{Ý-1/2“+“i“lam²!bMÞdaÞ}Ý(x)“for“x“Þ>“Ý-1.ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GconicalP_1–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉconicalP_1‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“conicalP_1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“conical“function“PÞ^Ý1_Þ{Ý-1/2“+“i“lam²!bMÞdaÞ}Ý(x)“for“x“Þ>“Ý-1.ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Ghzeta–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉhzeta‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“hzeta‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“Hurwitz“zeta“function“zeta(s,q)“for“s“Þ>“Ý1,“q“Þ>“Ý0.ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gairy_Ai–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Ai‘yšâ(éxá,‘¦fémode‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Ai‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–cMroutines›cNcompute“the˜Airy“function˜Ai(x)“with˜an“accuracy˜spMÞeci ed“b²!y˜moMÞde.ŽŸ+„‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽ©#ב.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.Ž¦‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.ŽŽŒ‹Õ—ŸòŽ ƒ3* ý ÌÖ‘.ùœÝ2–¦f=“GSL_PREC_APPR•²!O“XŽ¤ 33‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.Ž©¶”‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸà‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ ‘!Gairy_Bi–¦f-*-“texinfo“-*-ŽŸ ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Bi‘yšâ(éxá,‘¦fémode‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Bi‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–m routines“compute“the›m Airy“function“Bi(x)“with“an“accuracy˜spšMÞeci ed“b²!y“mo˜de.ŽŸà‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸ¶•‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.ŽŸà‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.ŽŸà‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž©à‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ ‘!Gairy_Ai_scaled–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Ai_scaled‘yšâ(éxá,‘¦fémode‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Ai_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ßKroutines›ßLcompute“a“scaled“v²!ersion˜of“the“Airy“function˜S_A(x)“Ai(x).‘ˆF‘ÿeor“xÞ>Ý0Ž¡‘.ùœthe–¦fscaling“factor“S_A(x)“is“exp(+(2/3)“xÞ^Ý(3/2)),“and“is“1“for“xÞ<Ý0.Ž¦‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸ¶”‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.Ž©à‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸ¶”‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸà‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ ‘!Gairy_Bi_scaled–¦f-*-“texinfo“-*-ŽŽŒ‹áŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Bi_scaled‘yšâ(éxá,‘¦fémode‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Bi_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–îÞroutines“compute“a“scaled“v²!ersion“of“the‘îÝAiry“function“S_B(x)“Bi(x).‘·EF‘ÿeor“xÞ>Ý0Ž¡‘.ùœthe–¦fscaling“factor“S_B(x)“is“exp(-(2/3)“xÞ^Ý(3/2)),“and“is“1“for“xÞ<Ý0.ŽŸ Ö‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽ©èz‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.ŽŸèy‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸèy‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž© Ö‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Ã‘!Gairy_Ai_deriv–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Ai_deriv‘yšâ(éxá,‘¦fémode‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Ai_deriv‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Ýroutines›Ýcompute“the˜Airy“function˜deriv‘ÿdDativ²!e“Ai'(x)˜with“an˜accuracy“spMÞeci edŽ¡‘.ùœb²!y‘¦fmoMÞde.Ž¦‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽ©èz‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.ŽŸèy‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸèy‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž© Ö‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Ã‘!Gairy_Bi_deriv–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Bi_deriv‘yšâ(éxá,‘¦fémode‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Bi_deriv‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ç²routines›ç±compute“the“Airy“function˜deriv‘ÿdDativ²!e“Bi'(x)“with“an˜accuracy“spMÞeci edŽ¡‘.ùœb²!y‘¦fmoMÞde.Ž¦‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸèz‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.ŽŸèy‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.ŽŽŒ‹뵟òŽ ƒ3* ý ÌÖ‘.ùœÝ2–¦f=“GSL_PREC_APPR•²!O“XŽ¤ 33‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸ%-‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž©0‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Ë+‘!Gairy_Ai_deriv_scaled–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Ai_deriv_scaled‘yšâ(éxá,‘¦fémode‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Ai_deriv_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“deriv‘ÿdDativ²!e“of“the“scaled“Airy“function“S_A(x)“Ai(x).Ž¦‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸ%-‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.Ž©/‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸ%.‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž©/‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸË+‘!Gairy_Bi_deriv_scaled–¦f-*-“texinfo“-*-ŽŸË,’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Bi_deriv_scaled‘yšâ(éxá,‘¦fémode‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Bi_deriv_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“deriv‘ÿdDativ²!e“of“the“scaled“Airy“function“S_B(x)“Bi(x).Ž¦‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽ©%-‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.ŽŸ0‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.ŽŸ/‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ/‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸË,‘!Gellin²!t_Kcomp–¦f-*-“texinfo“-*-ŽŸË+’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉellint_Kcomp‘yšâ(éxá,‘¦fémode‘câ)ŽŽŒ‹öüŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“ellint_Kcomp‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¤ 33‘.ùœÝThese–¦froutines“compute“the“complete“elliptic“in²!tegral“K(k)ŽŸ"ïŸý b’¡Ró:  b> ó3 cmmi10åK‘ÈÝ(åkX?Ý)ŽŽ’½ì=‘ §Ÿò&»óú±u cmex10½ZŽŸôŸ‘ ¨ó 0e—rcmmi7´@@L=óÙ“ Rcmr7®2ŽŸ@@‘˜á0ŽŽŸø—ž‘@@Ñ%ådtŽ‘“ÒŸÞȉfeP!ñŸ[rŸó¤‡½qŽ‘ Ÿó¤‡‰feF!ðŸ [yÝ(1–nìó;!",š ó3 cmsy10æ“åkX?ŸüÖ0®2Ž‘§ãÝsinŽ‘™Ÿû(¾®2Ž‘– Ý(åtÝ))ŽŽŽŽŽŽŽŽŽŽŽŸ%áE‘.ùœThe–Æ«notation“used“here“is“based“on“Carlson,‘νáNumerisc²!he“Mathematik‘p¯Ý33“(1979)“andŽ¡‘.ùœdi ers–Ìûslighš²!tly“from“that“used“b˜y“Abramo˜witz“&“Stegun,‘øvwhere“the“functions“are“giv˜enŽ¡‘.ùœin–¦fterms“of“the“parameter“åm– §Ý=“åkX?Ÿü¾®2Ž‘Ô²Ý.ŽŸ%c‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽ©“‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.ŽŸ”‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž©%d‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ Ñ!Gellin²!t_Ecomp–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉellint_Ecomp‘yšâ(éxá,‘¦fémode‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“ellint_Ecomp‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Ùroutines“compute›Ùthe“complete“elliptic“in²!tegral“E(k)“to˜the“accuracy“spMÞeci edŽ¡‘.ùœb²!y–¦fthe“mošMÞde“v‘ÿdDariable“mo˜de.Ž¦Ÿ–iŸ#’ž`ÞåE‘¡’Ý(åkX?Ý)ŽŽ’¸²F=‘ §Ÿò&»½ZŽŸôŸ‘ ¨´@@L=®2ŽŸ@@‘˜á0ŽŽ‘`ŸŸóv½qŽ‘&` Ÿóv‰feF!ðŸ åŠÝ(1–nìæ“åkX?ŸüÖ0®2Ž‘§ãÝsinŽ‘™Ÿû(¾®2Ž‘– Ý(åtÝ))ŽŽŽ‘l‚ådtŽŽŽŽŽŸ'‘.ùœÝThe–Æ«notation“used“here“is“based“on“Carlson,‘νáNumerisc²!he“Mathematik‘p¯Ý33“(1979)“andŽ¡‘.ùœdi ers–Ìûslighš²!tly“from“that“used“b˜y“Abramo˜witz“&“Stegun,‘øvwhere“the“functions“are“giv˜enŽ¡‘.ùœin–¦fterms“of“the“parameter“åm– §Ý=“åkX?Ÿü¾®2Ž‘Ô²Ý.Ž¦‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽ©“‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.Ž¦‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.ŽŸ”‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ%c‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹dŸòŽ ƒ3* ý ÌÖ‘!GÝairy_zero_Ai–¦f-*-“texinfo“-*-Ž©ÁÔ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_zero_Ai‘yšâ(én‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_zero_Ai‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“loMÞcation“of“the“s-th“zero“of“the“Airy“function“Ai(x).ŽŸzƒ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸz„‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÁÓ‘!Gairy_zero_Bi–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_zero_Bi‘yšâ(én‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_zero_Bi‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“loMÞcation“of“the“s-th“zero“of“the“Airy“function“Bi(x).ŽŸz„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸzƒ‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gairy_zero_Ai_deriv–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_zero_Ai_deriv‘yšâ(én‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_zero_Ai_deriv‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ñ¡routines“compute›ñ¢the“loMÞcation“of“the˜s-th“zero“of“the˜Airy“function“deriv‘ÿdDativ²!eŽ¡‘.ùœAi(x).Ž¤zƒ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gairy_zero_Bi_deriv–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_zero_Bi_deriv‘yšâ(én‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_zero_Bi_deriv‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ñ¡routines“compute›ñ¢the“loMÞcation“of“the˜s-th“zero“of“the˜Airy“function“deriv‘ÿdDativ²!eŽ¡‘.ùœBi(x).ŽŸzƒ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸz„‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÁÓ‘!GbMÞessel_zero_J0–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_zero_J0‘yšâ(én‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_zero_J0‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–+routines“compute“the“lošMÞcation“of“the“s-th“p˜ositiv²!e“zero“of“the“Bessel“functionŽ¡‘.ùœJ_0(x).ŽŸz„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸzƒ‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹ ZŸòŽ ƒ3* ý ÌÖ‘!GÝbMÞessel_zero_J1–¦f-*-“texinfo“-*-Ž©)’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_zero_J1‘yšâ(én‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_zero_J1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–+routines“compute“the“lošMÞcation“of“the“s-th“p˜ositiv²!e“zero“of“the“Bessel“functionŽ¡‘.ùœJ_1(x).ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gpsi_1_in²!t–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉpsi_1_int‘yšâ(én‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“psi_1_int‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“T‘ÿerigamma“function“psi(n)“for“pMÞositivš²!e“in˜teger“n.ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gzeta_in²!t–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉzeta_int‘yšâ(én‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“zeta_int‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“Riemann“zeta“function“zeta(n)“for“in²!teger“n,“n“e“1.ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Geta_in²!t–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉeta_int‘yšâ(én‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“eta_int‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“eta“function“eta(n)“for“in²!teger“n.ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Glegendre_Plm–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlegendre_Plm‘yšâ(éná,–¦fémá,“éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“legendre_Plm‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ãÎroutines“compute“the“assošMÞciated“Legendre“p˜olynomial‘ãÍP_lÞ^Ým(x)“for“m“Þ>Ý=“0,‘ó(lŽ¡‘.ùœÞ>Ý=–¦fm,“Þ|ÝxÞ|“<Ý=“1.ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Glegendre_sphPlm–¦f-*-“texinfo“-*-ŽŽŒ‹2ŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlegendre_sphPlm‘yšâ(éná,–¦fémá,“éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“legendre_sphPlm‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese– *9routines“compute“the‘ *8normalized“assošMÞciated“Legendre“p˜olynomialŽ¡‘.ùœ$sqrtÞ{Ý(2l+1)/(4pi)Þ}– ØÝsqrtÞ{Ý(l-m)!/(l+m)!Þ}› ÙÝP_lÞ^Ým(x)$“suitable˜for“use˜in“sphericalŽ¡‘.ùœharmonics.‘ÎUThe–wÎparameters›wÍm²!ust“satisfy˜m“Þ>Ý=“0,‘l˜Þ>Ý=“m,‘Þ|ÝxÞ|“<Ý=˜1.‘ÎUTheses“routinesŽ¡‘.ùœa•²!v“oid–¦fthe“o•²!v“er o“ws–¦fthat“oMÞccur“for“the“standard“normalization“of“P_lÞ^Ým(x).Ž¤ Ö‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž© 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Ã‘!Gh²!ypMÞerg_U–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géout‘°Yè=‘LÉhyperg_U‘yšâ(éx0á,–¦féx1á,“éx2‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éoutè,–LÉéerr‘cè]“=“hyperg_U‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝSecondary–iõCon uen²!t“Hyp•MÞergo“emetric›iôU‘iæfunction–iõA&E‘iå13.1.3“All“input˜are“double“asŽ¦‘.ùœis–¦fthe“output.Ž¤ Ö‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áoutÝ.a.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Ã‘!Gh²!ypMÞerg_1F1–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géout‘°Yè=‘LÉhyperg_1F1‘yšâ(éx0á,–¦féx1á,“éx2‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éoutè,–LÉéerr‘cè]“=“hyperg_1F1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝPrimary–ã¶Con uen²!t“Hyp•MÞergo“emetric›ã·U‘ã¦function–ã¶A&E‘ã§13.1.3“All“inputs˜are“double“asŽ¦‘.ùœis–¦fthe“output.Ž¤ Ö‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áoutÝ.a.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Ã‘!Ggsl_sf–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gègsl_sf‘yšâ()Ž¦‘.ùœÝOcta•²!v“e–W=bindings›W>to“the˜GNU–W)Scien²!ti c˜Library‘ÿe.‘ÃzAll˜GSL“functions˜can–W=bMÞe˜called“withŽ¦‘.ùœbš²!y–¦fthe“GSL“names“within“oMÞcta˜v˜e.Ž¡‘!Gclausen–¦f-*-“texinfo“-*-ŽŸÃ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉclausen‘yšâ(éx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“clausen‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThe–¦fClausen“function“is“de ned“bš²!y“the“follo˜wing“in˜tegral,ŽŸ ב.ùœCl_2(x)–¦f=“-“in²!t_0Þ^Ýx“dt“log(2“sin(t/2))Ž¤ Ö‘.ùœIt–¦fis“related“to“the“dilogarithm“b²!y“Cl_2(theta)“=“Im“Li_2(exp(i“theta)).Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÃ‘!Gda²!wson–¦f-*-“texinfo“-*-ŽŽŒ‹$ÞŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉdawson‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“dawson‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThe›šÊDa•²!wson‘šÉin“tegral˜is˜de ned‘šÉb“y˜exp(-xÞ^Ý2)˜in“t_0Þ^Ýx–šÉdt˜exp(tÞ^Ý2).‘ÙþA‘šÇtable“of˜Da²!wsonŽ¡‘.ùœinš²!tegral–¦fcan“bMÞe“found“in“Abramo˜witz“&“Stegun,“T‘ÿeable“7.5.Ž©m‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸn‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤¨‘!Gdeb•²!y“e_1–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉdebye_1‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“debye_1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThe›¦fDeb•²!y“e˜functions˜are˜de ned˜b“y˜the˜in“tegralŽ¦‘.ùœD_n(x)–¦f=“n/xÞ^Ýn“in²!t_0Þ^Ýx“dt“(tÞ^Ýn/(eÞ^Ýt“-“1)).Ž¦‘.ùœF‘ÿeor–¦ffurther“information“see“Abramo²!witz“&“Stegun,“Section“27.1.ŽŸn‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤¨‘!Gdeb•²!y“e_2–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉdebye_2‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“debye_2‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThe›¦fDeb•²!y“e˜functions˜are˜de ned˜b“y˜the˜in“tegralŽ¦‘.ùœD_n(x)–¦f=“n/xÞ^Ýn“in²!t_0Þ^Ýx“dt“(tÞ^Ýn/(eÞ^Ýt“-“1)).Ž¤n‘.ùœF‘ÿeor–¦ffurther“information“see“Abramo²!witz“&“Stegun,“Section“27.1.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ¨‘!Gdeb•²!y“e_3–¦f-*-“texinfo“-*-ŽŸ§’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉdebye_3‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“debye_3‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThe›¦fDeb•²!y“e˜functions˜are˜de ned˜b“y˜the˜in“tegralŽ¤n‘.ùœD_n(x)–¦f=“n/xÞ^Ýn“in²!t_0Þ^Ýx“dt“(tÞ^Ýn/(eÞ^Ýt“-“1)).Ž¦‘.ùœF‘ÿeor–¦ffurther“information“see“Abramo²!witz“&“Stegun,“Section“27.1.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™ŽŸ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ¨‘!Gdeb•²!y“e_4–¦f-*-“texinfo“-*-ŽŽŒ‹1*ŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉdebye_4‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“debye_4‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThe›¦fDeb•²!y“e˜functions˜are˜de ned˜b“y˜the˜in“tegralŽ¤""‘.ùœD_n(x)–¦f=“n/xÞ^Ýn“in²!t_0Þ^Ýx“dt“(tÞ^Ýn/(eÞ^Ýt“-“1)).Ž¡‘.ùœF‘ÿeor–¦ffurther“information“see“Abramo²!witz“&“Stegun,“Section“27.1.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž©ÿÿ‘!Gerf_gsl–¦f-*-“texinfo“-*-ŽŸ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉerf_gsl‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“erf_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–q¼routines›q»compute“the“error“function˜erf(x)“=“(2/sqrt(pi))“in²!t_0Þ^Ýx˜dt“exp(-tÞ^Ý2).Ž¤""‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gerfc_gsl–¦f-*-“texinfo“-*-ŽŸ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉerfc_gsl‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“erfc_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–.·routines›.¸compute“the“complemen²!tary˜error“function“erfc(x)˜=“1“-˜erf(x)“=Ž¡‘.ùœ(2/sqrt(pi))›¦fin•²!t_xÞ^Ýinft“y˜exp(-tÞ^Ý2).Ž¤""‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Glog_erfc–¦f-*-“texinfo“-*-Ž©’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlog_erfc‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“log_erfc‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–€vroutines›€ucompute“the˜logarithm“of˜the“complemen²!tary˜error“functionŽ¡‘.ùœlog(erfc(x)).Ž¤""‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gerf_Z–¦f-*-“texinfo“-*-ŽŸÿÿ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉerf_Z‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“erf_Z‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ÿroutines“compute›the“Gaussian“probabilit²!y“function“Z(x)˜=“(1/(2pi))“exp(-Ž¡‘.ùœxÞ^Ý2/2).Ž¤""‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™ŽŸ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹;ãŸòŽ ƒ3* ý ÌÖ‘!GÝerf_Q–¦f-*-“texinfo“-*-Ž©LÌ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉerf_Q‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“erf_Q‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese– routines“compute“the› uppMÞer“tail“of“the“Gaussian“probabilit²!y˜function“Q(x)“=Ž¡‘.ùœ(1/(2pi))›¦fin•²!t_xÞ^Ýinft“y˜dt˜exp(-tÞ^Ý2/2).Ž¤@@‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Ghazard–¦f-*-“texinfo“-*-Ž©LÍ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉhazard‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“hazard‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThe–7=hazard“function“for“the“normal“distrbution,‘›ralso“knoš²!wn“as“the“in˜v˜erse“Mill'sŽ¡‘.ùœratio,‘ª is–©ade ned“as“h(x)“=›©bZ(x)/Q(x)“=“sqrtÞ{Ý2/pi“exp(-xÞ^Ý2“/“2)“/“erfc(x/sqrt˜2)Þ}Ý.‘æÎItŽ¡‘.ùœdecreases–å¼rapidly“as“x“approacš²!hes“-inft˜y“and‘å»asymptotes“to“h(x)“sim“x“as“x“approac˜hesŽ¡‘.ùœ+inft²!y‘ÿe.ŽŸ?ÿ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ@@‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gexpm1–¦f-*-“texinfo“-*-ŽŸLÌ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉexpm1‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“expm1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–3ïroutines“compute“the›3ðquan•²!tit“y–3ïexp(x)-1“using“an“algorithm“that˜is“accurate“forŽ¡‘.ùœsmall‘¦fx.ŽŸ@@‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ?ÿ‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gexprel–¦f-*-“texinfo“-*-Ž©LÌ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉexprel‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“exprel‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ãsroutines›ãrcompute“the˜quan•²!tit“y–ãs(exp(x)-1)/x˜using“an˜algorithm“that˜is“accurateŽ¡‘.ùœfor››small–›x.‘ÚF‘ÿeor“small˜x˜the˜algorithm“is˜based˜on“the˜expansion˜(exp(x)-1)/x˜=“1˜+Ž¡‘.ùœx/2–¦f+“xÞ^Ý2/(2*3)“+“xÞ^Ý3/(2*3*4)“+“dots.Ž¤@@‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™ŽŸ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gexprel_2–¦f-*-“texinfo“-*-ŽŽŒ‹G­ŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉexprel_2‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“exprel_2‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–•#routines›•$compute“the˜quan•²!tit“y–•#2(exp(x)-1-x)/xÞ^Ý2“using˜an“algorithm˜that“isŽ¡‘.ùœaccurate–í¾for›í¿small“x.‘³æF‘ÿeor˜small“x“the˜algorithm“is˜based“on“the˜expansion“2(exp(x)-Ž¡‘.ùœ1-x)/xÞ^Ý2–¦f=“1“+“x/3“+“xÞ^Ý2/(3*4)“+“xÞ^Ý3/(3*4*5)“+“dots.Ž¤¡¯‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž©~§‘!Gexpin²!t_E1–¦f-*-“texinfo“-*-ŽŸ~¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉexpint_E1‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“expint_E1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“expMÞonenš²!tial“in˜tegral“E_1(x),Ž¤¡¯‘.ùœE_1(x)–¦f:=“Re“in•²!t_1Þ^Ýinft“y–¦fdt“exp(-xt)/t.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gexpin²!t_E2–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉexpint_E2‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“expint_E2‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“second-order“expMÞonenš²!tial“in˜tegral“E_2(x),Ž¤¡¯‘.ùœE_2(x)–¦f:=“Re“in•²!t_1Þ^Ýinft“y–¦fdt“exp(-xt)/tÞ^Ý2.ŽŸ¡®‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gexpin²!t_Ei–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉexpint_Ei‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“expint_Ei‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“expMÞonenš²!tial“in˜tegral“E_i(x),Ž¤¡¯‘.ùœEi(x)–¦f:=“-“PV(in•²!t_Þ{Ý-xÞ}^Ýinft“y–¦fdt“exp(-t)/t)Ž¡‘.ùœwhere–¦fPV“denotes“the“principal“v‘ÿdDalue“of“the“in²!tegral.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ~¦‘!GShi–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉShi‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“Shi‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“inš²!tegral“Shi(x)“=“in˜t_0Þ^Ýx“dt“sinh(t)/t.Ž¤¡¯‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™ŽŸ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹R›ŸòŽ ƒ3* ý ÌÖ‘!GÝChi–¦f-*-“texinfo“-*-Ž©Që’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉChi‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“Chi‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“in²!tegralŽ¤B‘.ùœChi(x)–¦f:=“Re[“gamma_E“+“log(x)“+“in²!t_0Þ^Ýx“dt“(cosh[t]-1)/t]“,Ž¡‘.ùœwhere–¦fgamma_E“is“the“Euler“constan²!t.ŽŸB‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gexpin²!t_3–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉexpint_3‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“expint_3‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–‰—routines“compute“the“expMÞonenš²!tial“in˜tegral‘‰–Ei_3(x)“=“in˜t_0Þ^Ýx“dt“exp(-tÞ^Ý3)“for“xŽ¡‘.ùœÞ>Ý=‘¦f0.Ž¤B‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GSi–¦f-*-“texinfo“-*-ŽŸQì’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉSi‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“Si‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“Sine“inš²!tegral“Si(x)“=“in˜t_0Þ^Ýx“dt“sin(t)/t.Ž¤B‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GCi–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉCi‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“Ci‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Qroutines›Qcompute“the“Cosine“in²!tegral˜Ci(x)“=“-in•²!t_xÞ^Ýinft“y˜dt–Qcos(t)/t“for“x˜Þ>“Ý0.Ž¤B‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸQì‘!Gatanin²!t–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉatanint‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“atanint‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–@@routines“compute“the“Arctangenš²!t“in˜tegral‘@@A˜tanIn˜t(x)“=“in˜t_0Þ^Ýx“dt“arctan(t)/t.Ž¤B‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™ŽŸ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹ _ŸòŽ ƒ3* ý ÌÖ‘!GÝfermi_dirac_mhalf–¦f-*-“texinfo“-*-Ž©Ÿ"’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉfermi_dirac_mhalf‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“fermi_dirac_mhalf‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“complete“F‘ÿeermi-Dirac“in²!tegral“F_Þ{Ý-1/2Þ}Ý(x).ŽŸW.‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸW-‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gfermi_dirac_half–¦f-*-“texinfo“-*-ŽŸŸ#’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉfermi_dirac_half‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“fermi_dirac_half‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“complete“F‘ÿeermi-Dirac“in²!tegral“F_Þ{Ý1/2Þ}Ý(x).ŽŸW-‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸW.‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gfermi_dirac_3half–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉfermi_dirac_3half‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“fermi_dirac_3half‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“complete“F‘ÿeermi-Dirac“in²!tegral“F_Þ{Ý3/2Þ}Ý(x).ŽŸW.‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸW-‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Ggamma_gsl–¦f-*-“texinfo“-*-ŽŸŸ#’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉgamma_gsl‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“gamma_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–garoutines›gbcompute“the“Gamma“function˜Gamma(x),‘— sub‘›»ject“to“x“not˜bMÞeing“aŽ¡‘.ùœnegativ•²!e›¿in“teger.‘ çThe˜function–¾is˜computed˜using˜the“real˜Lanczos˜methoMÞd.‘ çTheŽ¡‘.ùœmaxim²!um–]v‘ÿdDalue›\of“x˜suc²!h“that˜Gamma(x)“is“not˜considered“an˜o•²!v“er o“w‘]is˜giv“en‘]b“yŽ¡‘.ùœthe–¦fmacro“GSL_SF_GAMMA_XMAX“and“is“171.0.ŽŸW-‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸW.‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Glngamma_gsl–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlngamma_gsl‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“lngamma_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–gžroutines“compute›gthe“logarithm“of“the“Gamma˜function,‘t-log(Gamma(x)),‘t,sub-Ž¡‘.ùœject–£¾to“x›£½not“a“bMÞeing“negativ•²!e˜in“teger.‘ÕåF‘ÿeor˜xÞ<Ý0–£¾the“real“part˜of“log(Gamma(x))“isŽ¡‘.ùœreturned,‘rwhic•²!h›ðÖis‘ðÕequiv‘ÿdDalen“t˜to˜log(Þ|ÝGamma(x)Þ|Ý).‘½-The‘ðÕfunction˜is˜computed˜usingŽ¡‘.ùœthe–¦freal“Lanczos“methoMÞd.ŽŸW.‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸW-‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹!j“ŸòŽ ƒ3* ý ÌÖ‘!GÝgammastar–¦f-*-“texinfo“-*-Ž©ÜÌ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉgammastar‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“gammastar‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–oÙroutines›oÚcompute“the“regulated“Gamma˜F‘ÿeunction“GammaÞ^Ý*(x)“for“x˜Þ>“Ý0.‘Ë®TheŽ¡‘.ùœregulated–¦fgamma“function“is“givš²!en“b˜y‘ÿe,ŽŸg‘.ùœGammaÞ^Ý*(x)–ƒ<=›ƒ;Gamma(x)/(sqrtÞ{Ý2piÞ}“ÝxÞ^{Ý(x-1/2)Þ}“Ýexp(-x))“=˜(1“+“(1/12x)˜+“...)Ž¡‘.ùœfor–¦fx“to“inft²!yŽ¤f‘.ùœand–¦fis“a“useful“suggestion“of“T‘ÿeemme.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÜÍ‘!Ggammain²!v_gsl–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉgammainv_gsl‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“gammainv_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¤5routines›¤4compute“the˜reciproMÞcal“of˜the“gamma“function,‘ã§1/Gamma(x)“usingŽ¡‘.ùœthe–¦freal“Lanczos“methoMÞd.Ž¤f‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÜÍ‘!Glam²!bMÞert_W0–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlambert_W0‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“lambert_W0‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦fcompute“the“principal“brancš²!h“of“the“Lam˜bMÞert“W“function,“W_0(x).Ž©f‘.ùœLam²!bMÞert's›Œ³W‘Œ6functions,–FW(x),“are˜de ned˜to˜bMÞe˜solutions‘Œ´of˜the˜equation˜W(x)Ž¡‘.ùœexp(W(x))–b£=“x.‘ “This“function“has‘b¢mš²!ultiple“branc˜hes“for“x‘b¢Þ<“Ý0;‘@@Áho˜w˜ev˜er,‘ѱit“hasŽ¡‘.ùœonly›ct•²!w“o˜real-v‘ÿdDalued˜branc“hes.‘3ÓW‘ÿee˜de ne˜W_0(x)˜to˜bMÞe‘bthe˜principal˜branc“h,‘4âwhereŽ¡‘.ùœW‘}!Þ>–}+Ý-1“for“x“Þ<“Ý0,›…jand“W_Þ{Ý-1Þ}Ý(x)“to“bMÞe“the“other“real“branc²!h,˜where“W‘}!Þ<“Ý-1“for“x“Þ<“Ý0.ŽŸg‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÜÌ‘!Glam²!bMÞert_Wm1–¦f-*-“texinfo“-*-ŽŸÜÍ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlambert_Wm1‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“lambert_Wm1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–:Bcompute“the“secondary‘:Areal-v‘ÿdDalued“brancš²!h“of“the“Lam˜bMÞert“W‘:function,‘_9W_Þ{Ý-Ž¡‘.ùœ1Þ}Ý(x).Ž¦‘.ùœLam²!bMÞert's›Œ³W‘Œ6functions,–FW(x),“are˜de ned˜to˜bMÞe˜solutions‘Œ´of˜the˜equation˜W(x)Ž¡‘.ùœexp(W(x))–b£=“x.‘ “This“function“has‘b¢mš²!ultiple“branc˜hes“for“x‘b¢Þ<“Ý0;‘@@Áho˜w˜ev˜er,‘ѱit“hasŽ¡‘.ùœonly›ct•²!w“o˜real-v‘ÿdDalued˜branc“hes.‘3ÓW‘ÿee˜de ne˜W_0(x)˜to˜bMÞe‘bthe˜principal˜branc“h,‘4âwhereŽ¡‘.ùœW‘}!Þ>–}+Ý-1“for“x“Þ<“Ý0,›…jand“W_Þ{Ý-1Þ}Ý(x)“to“bMÞe“the“other“real“branc²!h,˜where“W‘}!Þ<“Ý-1“for“x“Þ<“Ý0.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŽŒ‹"x$ŸòŽ ƒ3* ý ÌÖ‘.ùœÝThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž©Šø‘!Glog_1plusx–¦f-*-“texinfo“-*-ŽŸŠù’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlog_1plusx‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“log_1plusx‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–žkroutines“compute“log(1“+›žlx)“for“x“Þ>“Ý-1“using“an“algorithm˜that“is“accurate“forŽ¡‘.ùœsmall‘¦fx.ŽŸ_‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ_‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Glog_1plusx_mx–¦f-*-“texinfo“-*-Ž©Šù’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlog_1plusx_mx‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“log_1plusx_mx‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ŸYroutines›ŸXcompute“log(1˜+“x)“-˜x“for˜x“Þ>˜Ý-1“using“an˜algorithm“that˜is“accurateŽ¡‘.ùœfor–¦fsmall“x.ŽŸ_‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ_‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gpsi–¦f-*-“texinfo“-*-ŽŸŠø’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉpsi‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“psi‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“digamma“function“psi(x)“for“general“x,“x“e“0.ŽŸ_‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ_‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gpsi_1piy–¦f-*-“texinfo“-*-ŽŸŠø’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉpsi_1piy‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“psi_1piy‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–è6routines“compute“the“real“part“of“the“digamma“function“on“the“line“1+i“y‘ÿe,Ž¡‘.ùœRe[psi(1–¦f+“i“y)].ŽŸ_‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ_‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gsync²!hrotron_1–¦f-*-“texinfo“-*-ŽŸŠø’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉsynchrotron_1‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“synchrotron_1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–GCroutines“compute‘GDthe“ rst“syncš²!hrotron“function“x“in˜t_xÞ^Ýinft˜y‘GDdt“K_Þ{Ý5/3Þ}Ý(t)“forŽ¡‘.ùœx–¦fÞ>Ý=“0.ŽŽŒ‹#…fŸòŽ ƒ3* ý ÌÖ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž©B‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸQë‘!Gsync²!hrotron_2–¦f-*-“texinfo“-*-ŽŸQì’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉsynchrotron_2‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“synchrotron_2‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“second“sync²!hrotron“function“x“K_Þ{Ý2/3Þ}Ý(x)“for“x“Þ>Ý=“0.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Që‘!GtranspMÞort_2–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉtransport_2‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“transport_2‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“transpMÞort“function“J(2,x).Ž¦‘.ùœThe–üztranspMÞort›üyfunctions“J(n,x)“are“de ned˜bš²!y“the“in˜tegral“represen˜tations‘üyJ(n,x)“:=Ž¡‘.ùœin²!t_0Þ^Ýx–¦fdt“tÞ^Ýn“eÞ^Ýt“/(eÞ^Ýt“-“1)Þ^Ý2.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸQì‘!GtranspMÞort_3–¦f-*-“texinfo“-*-ŽŸQë’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉtransport_3‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“transport_3‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“transpMÞort“function“J(3,x).Ž¦‘.ùœThe–üztranspMÞort›üyfunctions“J(n,x)“are“de ned˜bš²!y“the“in˜tegral“represen˜tations‘üyJ(n,x)“:=Ž¡‘.ùœin²!t_0Þ^Ýx–¦fdt“tÞ^Ýn“eÞ^Ýt“/(eÞ^Ýt“-“1)Þ^Ý2.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸQë‘!GtranspMÞort_4–¦f-*-“texinfo“-*-ŽŸQì’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉtransport_4‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“transport_4‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“transpMÞort“function“J(4,x).Ž¦‘.ùœThe–üztranspMÞort›üyfunctions“J(n,x)“are“de ned˜bš²!y“the“in˜tegral“represen˜tations‘üyJ(n,x)“:=Ž¡‘.ùœin²!t_0Þ^Ýx–¦fdt“tÞ^Ýn“eÞ^Ýt“/(eÞ^Ýt“-“1)Þ^Ý2.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸQë‘!GtranspMÞort_5–¦f-*-“texinfo“-*-ŽŽŒ‹$·ŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉtransport_5‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“transport_5‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“transpMÞort“function“J(5,x).Ž©•ñ‘.ùœThe–üztranspMÞort›üyfunctions“J(n,x)“are“de ned˜bš²!y“the“in˜tegral“represen˜tations‘üyJ(n,x)“:=Ž¡‘.ùœin²!t_0Þ^Ýx–¦fdt“tÞ^Ýn“eÞ^Ýt“/(eÞ^Ýt“-“1)Þ^Ý2.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸø°‘!Gsinc_gsl–¦f-*-“texinfo“-*-ŽŸø¯’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉsinc_gsl‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“sinc_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“sinc(x)“=“sin(pi“x)“/“(pi“x)“for“an²!y“v‘ÿdDalue“of“x.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ø¯‘!Glnsinh–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlnsinh‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“lnsinh‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“log(sinh(x))“for“x“Þ>“Ý0.ŽŸ•ò‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ø¯‘!Glncosh–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlncosh‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“lncosh‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“log(cosh(x))“for“an²!y“x.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸø¯‘!Gzeta–¦f-*-“texinfo“-*-ŽŸø°’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉzeta‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“zeta‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“Riemann“zeta“function“zeta(s)“for“arbitrary“s,“s“e“1.Ž¦‘.ùœThe–b¨Riemann›b©zeta“function˜is“de ned“b²!y˜the“in nite˜sum“zeta(s)˜=“sum_Þ{Ýk=1Þ}^Ýinft²!yŽ¡‘.ùœkÞ^{Ý-sÞ}Ý.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹%œ—ŸòŽ ƒ3* ý ÌÖ‘!GÝeta–¦f-*-“texinfo“-*-Ž©‰n’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉeta‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“eta‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“eta“function“eta(s)“for“arbitrary“s.Ž¤úœ‘.ùœThe–¦feta“function“is“de ned“b²!y“eta(s)“=“(1-2Þ^{Ý1-sÞ}Ý)“zeta(s).Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_Jn–¦f-*-“texinfo“-*-ŽŸ‰o’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_Jn‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_Jn‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“regular“cylindrical“Bessel“function“of“order“n,“J_n(x).Ž¤úœ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_Yn–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_Yn‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_Yn‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–&Üroutines›&Ýcompute“the“irregular˜cylindrical“Bessel“function˜of“order“n,‘FúY_n(x),Ž¡‘.ùœfor‘¦fxÞ>Ý0.Ž¤úœ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_In–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_In‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_In‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–?ºroutines›?¹compute“the“regular˜moMÞdi ed“cylindrical˜Bessel“function“of˜order“n,Ž¡‘.ùœI_n(x).ŽŸú‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸúœ‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_In_scaled–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_In_scaled‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_In_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–8©routines›8¨compute“the˜scaled“regular˜moMÞdi ed“cylindrical˜Bessel“function˜ofŽ¡‘.ùœorder–¦fn,“exp(-Þ|ÝxÞ|Ý)“I_n(x)Ž¤úœ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™ŽŸ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹&¨/ŸòŽ ƒ3* ý ÌÖ‘!GÝbMÞessel_Kn–¦f-*-“texinfo“-*-Ž©’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_Kn‘yšâ(éná,‘¦féx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_Kn‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–• routines›•!compute“the“irregular“moMÞdi ed˜cylindrical“Bessel“function“of˜order“n,Ž¡‘.ùœK_n(x),–¦ffor“x“Þ>“Ý0.Ž¤™™‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_Kn_scaled–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_Kn_scaled‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_Kn_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ™™‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_jl–¦f-*-“texinfo“-*-ŽŸÿÿ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_jl‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_jl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–>qroutines“compute“the‘>pregular“spherical“Bessel“function“of“order“l,–dsj_l(x),“for‘>qlŽ¡‘.ùœÞ>Ý=–¦f0“and“x“Þ>Ý=“0.ŽŸ™š‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ™™‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_yl–¦f-*-“texinfo“-*-ŽŸÿÿ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_yl‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_yl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–‚íroutines“compute“the“irregular“spherical“Bessel“function“of“order“l,–Šy_l(x),“for‘‚ílŽ¡‘.ùœÞ>Ý=‘¦f0.ŽŸ™š‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ™™‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_il_scaled–¦f-*-“texinfo“-*-ŽŸÿÿ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_il_scaled‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_il_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–(Òroutines›(Ócompute“the“scaled“regular˜moMÞdi ed“spherical“Bessel“function˜of“orderŽ¡‘.ùœl,–¦fexp(-Þ|ÝxÞ|Ý)“i_l(x)ŽŸ™š‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ™™‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹'´ŸòŽ ƒ3* ý ÌÖ‘!GÝbMÞessel_kl_scaled–¦f-*-“texinfo“-*-Ž©’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_kl_scaled‘yšâ(éná,‘¦féx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_kl_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–>routines“compute“the“scaled“irregular“moMÞdi ed“spherical“Bessel“function“ofŽ¡‘.ùœorder–¦fl,“exp(x)“k_l(x),“for“xÞ>Ý0.ŽŸ""‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ"!‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gexprel_n–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉexprel_n‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“exprel_n‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–“routines“compute“the“N-relativš²!e“expMÞonen˜tial,‘Ÿwhic˜h“is“the“n-th“generalizationŽ¡‘.ùœof–b÷the›bøfunctions“gsl_sf_exprel“and˜gsl_sf_exprel2.‘‘The“N-relativš²!e“expMÞonen˜tial‘bøis“giv˜enŽ¡‘.ùœb²!y‘ÿe,Ž©""‘.ùœexprel_N(x)–ÇF=“N!/xÞ^ÝN‘ƺ(exp(x)“-“sum_Þ{Ýk=0Þ}^{ÝN-1Þ}“ÝxÞ^Ýk/k!)‘ @@}=“1“+“x/(N+1)“+Ž¡‘.ùœxÞ^Ý2/((N+1)(N+2))–¦f+“...‘ÝÝ=“1F1“(1,1+N,x)Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ"!‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤‘!Gfermi_dirac_in²!t–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉfermi_dirac_int‘yšâ(éná,‘¦féx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“fermi_dirac_int‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–OÖroutines›O×compute“the˜complete“F‘ÿeermi-Dirac˜in²!tegral“with˜an“in²!teger˜index“of˜j,Ž¡‘.ùœF_j(x)–¦f=“(1/Gamma(j+1))“in•²!t_0Þ^Ýinft“y–¦fdt“(tÞ^Ýj“/(exp(t-x)+1)).Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÿÿ‘!Gta²!ylorcoMÞe –¦f-*-“texinfo“-*-ŽŸ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉtaylorcoeff‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“taylorcoeff‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“T‘ÿeaš²!ylor“coMÞecien˜t“xÞ^Ýn“/“n!‘ÝÝfor“x“Þ>Ý=“0,“n“Þ>Ý=“0.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÿÿ‘!Glegendre_Pl–¦f-*-“texinfo“-*-ŽŸ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlegendre_Pl‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“legendre_Pl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Ojfunctions›Oiev‘ÿdDaluate“the“Legendre“pMÞolynomial˜P_l(x)“for“a˜spMÞeci c“v‘ÿdDalue“of“l,‘yªxŽ¡‘.ùœsub‘›»ject–¦fto“l“Þ>Ý=“0,“Þ|ÝxÞ|“<Ý=“1ŽŽŒ‹(¿äŸòŽ ƒ3* ý ÌÖ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸC‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž© 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Rú‘!Glegendre_Ql–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlegendre_Ql‘yšâ(éná,‘¦féx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“legendre_Ql‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“Legendre“function“Q_l(x)“for“x“Þ>“Ý-1,“x“!=“1“and“l“Þ>Ý=“0.Ž¤C‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸRú‘!Gpsi_n–¦f-*-“texinfo“-*-ŽŸRû’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉpsi_n‘yšâ(éná,‘¦féx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“psi_n‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“pMÞolygamma“function“psiÞ^{Ý(m)Þ}Ý(x)“for“m“Þ>Ý=“0,“x“Þ>“Ý0.ŽŸC‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸRú‘!GbMÞessel_Jn²!u–¦f-*-“texinfo“-*-ŽŸRû’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Jnu‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Jnu‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–Ukroutines“compute›Ujthe“regular“cylindrical“Bessel“function“of˜fractional“order“n²!u,Ž¦‘.ùœJ_u(x).ŽŸC‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸRú‘!GbMÞessel_Yn²!u–¦f-*-“texinfo“-*-ŽŸRû’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Ynu‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Ynu‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–l¦routines›l¥compute“the˜irregular“cylindrical“Bessel˜function“of˜fractional“orderŽ¦‘.ùœn²!u,‘¦fY_u(x).Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸC‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸRû‘!GbMÞessel_In²!u–¦f-*-“texinfo“-*-ŽŸRú’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Inu‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Inu‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–Uroutines“compute“the“regular“moMÞdi ed‘TBessel“function“of“fractional“order“n²!u,Ž¦‘.ùœI_u(x)–¦ffor“xÞ>Ý0,“uÞ>Ý0.ŽŽŒ‹)ÌxŸòŽ ƒ3* ý ÌÖ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ“é‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž© 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ôŸ‘!GbMÞessel_In²!u_scaled–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Inu_scaled‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Inu_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–Ü_routines›Ü^compute“the“scaled“regular˜moMÞdi ed“Bessel“function“of˜fractional“orderŽ¦‘.ùœn²!u,–¦fexp(-Þ|ÝxÞ|Ý)I_u(x)“for“xÞ>Ý0,“uÞ>Ý0.Ž¤“é‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ôŸ‘!GbMÞessel_Kn²!u–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Knu‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Knu‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–q¼routines›q»compute“the˜irregular“moMÞdi ed˜Bessel“function˜of“fractional˜order“n²!u,Ž¦‘.ùœK_u(x)–¦ffor“xÞ>Ý0,“uÞ>Ý0.Ž¤“é‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸôž‘!GbMÞessel_lnKn²!u–¦f-*-“texinfo“-*-ŽŸôŸ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_lnKnu‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_lnKnu‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–Îroutines›Îcompute“the“logarithm“of˜the“irregular“moMÞdi ed“Bessel˜function“ofŽ¦‘.ùœfractional–¦forder“n²!u,“ln(K_u(x))“for“xÞ>Ý0,“uÞ>Ý0.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ôŸ‘!GbMÞessel_Kn²!u_scaled–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Knu_scaled‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Knu_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–êroutines›êcompute“the“scaled˜irregular“moMÞdi ed“Bessel“function˜of“fractionalŽ¦‘.ùœorder–¦fn²!u,“exp(+Þ|ÝxÞ|Ý)“K_u(x)“for“xÞ>Ý0,“uÞ>Ý0.Ž¤“é‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸôŸ‘!Gexp_m²!ult–¦f-*-“texinfo“-*-ŽŽŒ‹*ØNŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉexp_mult‘yšâ(éxá,‘¦féy‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“exp_mult‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ò`routines›ò_expMÞonen²!tiate“x˜and“m•²!ultiply˜b“y–ò`the“factor˜y“to˜return“the˜proMÞduct“yŽ¡‘.ùœexp(x).Ž¤ff‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÌÍ‘!Gfermi_dirac_inc_0–¦f-*-“texinfo“-*-Ž©ÌÌ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉfermi_dirac_inc_0‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“fermi_dirac_inc_0‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–FÎroutines“compute“the“incomplete“F‘ÿeermi-Dirac‘FÏin²!tegral“with“an“index“of“zero,Ž¡‘.ùœF_0(x,b)–¦f=“ln(1“+“eÞ^{Ýb-xÞ}Ý)“-“(b-x).ŽŸff‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸfg‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gp•MÞo“c²!h–¦f-*-“texinfo“-*-ŽŸÌÍ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉpoch‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“poch‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“P•²!ošMÞc“hhammer‘¦fsym“b˜olŽ¤ff‘.ùœ(a)_x–¦f:=“Gamma(a“+“x)/Gamma(a),Ž¡‘.ùœsub‘›»ject–to›a“and“a+x˜not“bMÞeing“negativ•²!e˜in“tegers.‘AàThe›P“oMÞc“hhammer˜sym“bMÞol‘is˜alsoŽ© 33‘.ùœknoš²!wn–¦fas“the“ApMÞell“sym˜bMÞol.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÌÍ‘!Glnp•MÞo“c²!h–¦f-*-“texinfo“-*-ŽŸÌÌ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉlnpoch‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“lnpoch‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–Ò-routines›Ò.compute“the“logarithm˜of“the“P•²!ošMÞc“hhammer‘Ò-sym“b˜ol,‘]log((a)_x)‘Ò-=Ž¦‘.ùœlog(Gamma(a–¦f+“x)/Gamma(a))“for“a“Þ>“Ý0,“a+x“Þ>“Ý0.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸfg‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÌÌ‘!Gp•MÞo“c²!hrel–¦f-*-“texinfo“-*-ŽŸÌÍ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉpochrel‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“pochrel‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–Kñroutines›Kòcompute“the˜relativš²!e“P˜oMÞc˜hhammer“sym˜bMÞol›Kò((a,x)“-˜1)/x“where˜(a,x)“=Ž¦‘.ùœ(a)_x–¦f:=“Gamma(a“+“x)/Gamma(a).Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹+ãÇŸòŽ ƒ3* ý ÌÖ‘!GÝgamma_inc_Q–¦f-*-“texinfo“-*-Ž©Ÿ"’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉgamma_inc_Q‘yšâ(éxá,‘¦féy‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“gamma_inc_Q‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–~øroutines›~ùcompute“the“normalized˜incomplete“Gamma“F‘ÿeunction˜Q(a,x)“=Ž¡‘.ùœ1/Gamma(a)›¦fin•²!t_xinft“y˜dt˜tÞ^{Ýa-1Þ}˜Ýexp(-t)˜for˜a˜Þ>˜Ý0,˜x˜Þ>Ý=˜0.ŽŸW.‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸW-‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Ggamma_inc_P–¦f-*-“texinfo“-*-ŽŸŸ#’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉgamma_inc_P‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“gamma_inc_P‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–(ïroutines›(ðcompute“the“complemen²!tary˜normalized“incomplete˜Gamma“F‘ÿeunctionŽ¡‘.ùœP(a,x)–¦f=“1/Gamma(a)“in²!t_0Þ^Ýx“dt“tÞ^{Ýa-1Þ}“Ýexp(-t)“for“a“Þ>“Ý0,“x“Þ>Ý=“0.ŽŸW-‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸW.‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Ggamma_inc–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉgamma_inc‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“gamma_inc‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–°functions›±compute“the“incomplete˜Gamma“F‘ÿeunction“the˜normalization“factorŽ¡‘.ùœincluded–Þ¦in›Þ¥the“previously˜de ned“functions:‘N\Gamma(a,x)˜=“in•²!t_xinft“y˜dt‘Þ¦tÞ^{Ýa-1Þ}Ž¡‘.ùœÝexp(-t)–¦ffor“a“real“and“x“Þ>Ý=“0.ŽŸW.‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸW-‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞeta_gsl–¦f-*-“texinfo“-*-ŽŸŸ#’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbeta_gsl‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“beta_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–nïroutines“compute“the“Beta“F‘ÿeunction,‘­:B(a,b)“=“Gamma(a)Gamma(b)/Gamma(a+b)Ÿ¼Ì„ ó2Ž¡‘.ùœfor–¦fa“Þ>“Ý0,“b“Þ>“Ý0.ŽŸW-‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸW.‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gln²!bMÞeta–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉlnbeta‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“lnbeta‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¸ûroutines“compute“the“logarithm“of‘¸úthe“Beta“F‘ÿeunction,›½ log(B(a,b))“for“a“Þ>“Ý0,˜bŽ¡‘.ùœÞ>‘¦fÝ0.ŽŸW.‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸW-‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹,ðŸòŽ ƒ3* ý ÌÖ‘!GÝh²!ypMÞerg_0F1–¦f-*-“texinfo“-*-Ž©)’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉhyperg_0F1‘yšâ(éxá,‘¦féy‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“hyperg_0F1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“h²!ypMÞergeometric“function“0F1(c,x).ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GconicalP_half–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉconicalP_half‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“conicalP_half‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ÍÏroutines›ÍÎcompute“the˜irregular“Spherical“Conical˜F‘ÿeunction“PÞ^{Ý1/2Þ}Ý_Þ{Ý-1/2˜+“iŽ¡‘.ùœlam²!bMÞdaÞ}Ý(x)–¦ffor“x“Þ>“Ý-1.ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GconicalP_mhalf–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉconicalP_mhalf‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“conicalP_mhalf‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–,routines›,compute“the“regular“Spherical˜Conical“F‘ÿeunction“PÞ^{Ý-1/2Þ}Ý_Þ{Ý-1/2˜+“iŽ¡‘.ùœlam²!bMÞdaÞ}Ý(x)–¦ffor“x“Þ>“Ý-1.ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GconicalP_0–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉconicalP_0‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“conicalP_0‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“conical“function“PÞ^Ý0_Þ{Ý-1/2“+“i“lam²!bMÞdaÞ}Ý(x)“for“x“Þ>“Ý-1.ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GconicalP_1–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉconicalP_1‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“conicalP_1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“conical“function“PÞ^Ý1_Þ{Ý-1/2“+“i“lam²!bMÞdaÞ}Ý(x)“for“x“Þ>“Ý-1.ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Ghzeta–¦f-*-“texinfo“-*-ŽŽŒ‹-ý‰ŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉhzeta‘yšâ(éxá,‘¦féy‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“hzeta‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“Hurwitz“zeta“function“zeta(s,q)“for“s“Þ>“Ý1,“q“Þ>“Ý0.Ž¤è‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž© 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Ø‘!Gairy_Ai–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Ai‘yšâ(éxá,‘¦fémode‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Ai‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–cMroutines›cNcompute“the˜Airy“function˜Ai(x)“with˜an“accuracy˜spMÞeci ed“b²!y˜moMÞde.ŽŸé‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸïB‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¦‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.Ž¤è‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¦‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¡‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¦‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸïC‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸè‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Ø‘!Gairy_Bi–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Bi‘yšâ(éxá,‘¦fémode‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Bi‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–m routines“compute“the›m Airy“function“Bi(x)“with“an“accuracy˜spšMÞeci ed“b²!y“mo˜de.ŽŸè‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸïC‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¦‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.Ž¤è‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¦‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¡‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¦‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸïC‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸè‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸØ‘!Gairy_Ai_scaled–¦f-*-“texinfo“-*-ŽŽŒ‹. •ŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Ai_scaled‘yšâ(éxá,‘¦fémode‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Ai_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ßKroutines›ßLcompute“a“scaled“v²!ersion˜of“the“Airy“function˜S_A(x)“Ai(x).‘ˆF‘ÿeor“xÞ>Ý0Ž¡‘.ùœthe–¦fscaling“factor“S_A(x)“is“exp(+(2/3)“xÞ^Ý(3/2)),“and“is“1“for“xÞ<Ý0.ŽŸ Ö‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽ©èz‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.ŽŸèy‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸèy‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž© Ö‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Ã‘!Gairy_Bi_scaled–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Bi_scaled‘yšâ(éxá,‘¦fémode‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Bi_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–îÞroutines“compute“a“scaled“v²!ersion“of“the‘îÝAiry“function“S_B(x)“Bi(x).‘·EF‘ÿeor“xÞ>Ý0Ž¡‘.ùœthe–¦fscaling“factor“S_B(x)“is“exp(-(2/3)“xÞ^Ý(3/2)),“and“is“1“for“xÞ<Ý0.Ž¦‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽ©èz‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.ŽŸèy‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸèy‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž© Ö‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Ã‘!Gairy_Ai_deriv–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Ai_deriv‘yšâ(éxá,‘¦fémode‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Ai_deriv‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Ýroutines›Ýcompute“the˜Airy“function˜deriv‘ÿdDativ²!e“Ai'(x)˜with“an˜accuracy“spMÞeci edŽ¡‘.ùœb²!y‘¦fmoMÞde.Ž¦‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸèz‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.ŽŸèy‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.ŽŽŒ‹/ñŸòŽ ƒ3* ý ÌÖ‘.ùœÝ2–¦f=“GSL_PREC_APPR•²!O“XŽ¤ 33‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.Ž©¶”‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸà‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ ‘!Gairy_Bi_deriv–¦f-*-“texinfo“-*-ŽŸ ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Bi_deriv‘yšâ(éxá,‘¦fémode‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Bi_deriv‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ç²routines›ç±compute“the“Airy“function˜deriv‘ÿdDativ²!e“Bi'(x)“with“an˜accuracy“spMÞeci edŽ¡‘.ùœb²!y‘¦fmoMÞde.ŽŸà‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸ¶•‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.ŽŸà‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.ŽŸà‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž©à‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ ‘!Gairy_Ai_deriv_scaled–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Ai_deriv_scaled‘yšâ(éxá,‘¦fémode‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Ai_deriv_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“deriv‘ÿdDativ²!e“of“the“scaled“Airy“function“S_A(x)“Ai(x).Ž¦‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸ¶”‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.Ž©à‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸ¶”‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸà‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ ‘!Gairy_Bi_deriv_scaled–¦f-*-“texinfo“-*-ŽŽŒ‹0tŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Bi_deriv_scaled‘yšâ(éxá,‘¦fémode‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Bi_deriv_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“deriv‘ÿdDativ²!e“of“the“scaled“Airy“function“S_B(x)“Bi(x).ŽŸDŠ‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸM5‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.Ž©DŠ‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸM5‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž©DŠ‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸUá‘!Gellin²!t_Kcomp–¦f-*-“texinfo“-*-ŽŸUà’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉellint_Kcomp‘yšâ(éxá,‘¦fémode‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“ellint_Kcomp‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“complete“elliptic“in²!tegral“K(k)ŽŸ#…eŸý b’¡RåK‘ÈÝ(åkX?Ý)ŽŽ’½ì=‘ §Ÿò&»½ZŽŸôŸ‘ ¨´@@L=®2ŽŸ@@‘˜á0ŽŽŸø—ž‘@@Ñ%ådtŽ‘“ÒŸÞȉfeP!ñŸ[rŸó¤‡½qŽ‘ Ÿó¤‡‰feF!ðŸ [yÝ(1–nìæ“åkX?ŸüÖ0®2Ž‘§ãÝsinŽ‘™Ÿû(¾®2Ž‘– Ý(åtÝ))ŽŽŽŽŽŽŽŽŽŽŽŸ&–¼‘.ùœThe–Æ«notation“used“here“is“based“on“Carlson,‘νáNumerisc²!he“Mathematik‘p¯Ý33“(1979)“andŽ¡‘.ùœdi ers–Ìûslighš²!tly“from“that“used“b˜y“Abramo˜witz“&“Stegun,‘øvwhere“the“functions“are“giv˜enŽ¡‘.ùœin–¦fterms“of“the“parameter“åm– §Ý=“åkX?Ÿü¾®2Ž‘Ô²Ý.Ž¦‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸM5‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.Ž©DŠ‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸM5‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸDŠ‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸUà‘!Gellin²!t_Ecomp–¦f-*-“texinfo“-*-ŽŸUá’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉellint_Ecomp‘yšâ(éxá,‘¦fémode‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“ellint_Ecomp‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Ùroutines“compute›Ùthe“complete“elliptic“in²!tegral“E(k)“to˜the“accuracy“spMÞeci edŽ¡‘.ùœb²!y–¦fthe“mošMÞde“v‘ÿdDariable“mo˜de.ŽŽŒ‹1)”ŸòŽ ƒ3* ý ÌÖŸ!GŸ#’ž`ÞåE‘¡’Ý(åkX?Ý)ŽŽ’¸²F=‘ §Ÿò&»½ZŽŸôŸ‘ ¨´@@L=®2ŽŸ@@‘˜á0ŽŽ‘`ŸŸóv½qŽ‘&` Ÿóv‰feF!ðŸ åŠÝ(1–nìæ“åkX?ŸüÖ0®2Ž‘§ãÝsinŽ‘™Ÿû(¾®2Ž‘– Ý(åtÝ))ŽŽŽ‘l‚ådtŽŽŽŽŽŸ:©‘.ùœÝThe–Æ«notation“used“here“is“based“on“Carlson,‘νáNumerisc²!he“Mathematik‘p¯Ý33“(1979)“andŽ¤ 33‘.ùœdi ers–Ìûslighš²!tly“from“that“used“b˜y“Abramo˜witz“&“Stegun,‘øvwhere“the“functions“are“giv˜enŽ¡‘.ùœin–¦fterms“of“the“parameter“åm– §Ý=“åkX?Ÿü¾®2Ž‘Ô²Ý.ŽŸÇ‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸ¾‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.Ž©Ç‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸ¾‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž©Ç‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ì[‘!Gairy_zero_Ai–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_zero_Ai‘yšâ(én‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_zero_Ai‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“loMÞcation“of“the“s-th“zero“of“the“Airy“function“Ai(x).Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ì[‘!Gairy_zero_Bi–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_zero_Bi‘yšâ(én‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_zero_Bi‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“loMÞcation“of“the“s-th“zero“of“the“Airy“function“Bi(x).Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ì[‘!Gairy_zero_Ai_deriv–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_zero_Ai_deriv‘yšâ(én‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_zero_Ai_deriv‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ñ¡routines“compute›ñ¢the“loMÞcation“of“the˜s-th“zero“of“the˜Airy“function“deriv‘ÿdDativ²!eŽ¡‘.ùœAi(x).Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹25ŸòŽ ƒ3* ý ÌÖ‘!GÝairy_zero_Bi_deriv–¦f-*-“texinfo“-*-Ž©ÁÔ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_zero_Bi_deriv‘yšâ(én‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_zero_Bi_deriv‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ñ¡routines“compute›ñ¢the“loMÞcation“of“the˜s-th“zero“of“the˜Airy“function“deriv‘ÿdDativ²!eŽ¡‘.ùœBi(x).ŽŸzƒ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸz„‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÁÓ‘!GbMÞessel_zero_J0–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_zero_J0‘yšâ(én‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_zero_J0‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–+routines“compute“the“lošMÞcation“of“the“s-th“p˜ositiv²!e“zero“of“the“Bessel“functionŽ¡‘.ùœJ_0(x).ŽŸz„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸzƒ‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_zero_J1–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_zero_J1‘yšâ(én‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_zero_J1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–+routines“compute“the“lošMÞcation“of“the“s-th“p˜ositiv²!e“zero“of“the“Bessel“functionŽ¡‘.ùœJ_1(x).Ž¤zƒ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gpsi_1_in²!t–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉpsi_1_int‘yšâ(én‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“psi_1_int‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“T‘ÿerigamma“function“psi(n)“for“pMÞositivš²!e“in˜teger“n.ŽŸzƒ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸz„‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÁÓ‘!Gzeta_in²!t–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉzeta_int‘yšâ(én‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“zeta_int‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“Riemann“zeta“function“zeta(n)“for“in²!teger“n,“n“e“1.ŽŸz„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸzƒ‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹3@@§ŸòŽ ƒ3* ý ÌÖ‘!GÝeta_in²!t–¦f-*-“texinfo“-*-Ž©JÔ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉeta_int‘yšâ(én‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“eta_int‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“eta“function“eta(n)“for“in²!teger“n.ŽŸ;‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ;‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸJÕ‘!Glegendre_Plm–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlegendre_Plm‘yšâ(éná,–¦fémá,“éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“legendre_Plm‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ãÎroutines“compute“the“assošMÞciated“Legendre“p˜olynomial‘ãÍP_lÞ^Ým(x)“for“m“Þ>Ý=“0,‘ó(lŽ¡‘.ùœÞ>Ý=–¦fm,“Þ|ÝxÞ|“<Ý=“1.ŽŸ;‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ;‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Glegendre_sphPlm–¦f-*-“texinfo“-*-ŽŸJÕ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlegendre_sphPlm‘yšâ(éná,–¦fémá,“éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“legendre_sphPlm‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese– *9routines“compute“the‘ *8normalized“assošMÞciated“Legendre“p˜olynomialŽ¡‘.ùœ$sqrtÞ{Ý(2l+1)/(4pi)Þ}– ØÝsqrtÞ{Ý(l-m)!/(l+m)!Þ}› ÙÝP_lÞ^Ým(x)$“suitable˜for“use˜in“sphericalŽ¡‘.ùœharmonics.‘ÎUThe–wÎparameters›wÍm²!ust“satisfy˜m“Þ>Ý=“0,‘l˜Þ>Ý=“m,‘Þ|ÝxÞ|“<Ý=˜1.‘ÎUTheses“routinesŽ¡‘.ùœa•²!v“oid–¦fthe“o•²!v“er o“ws–¦fthat“oMÞccur“for“the“standard“normalization“of“P_lÞ^Ým(x).ŽŸ;‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ;‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gh²!ypMÞerg_U–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géout‘°Yè=‘LÉhyperg_U‘yšâ(éx0á,–¦féx1á,“éx2‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éoutè,–LÉéerr‘cè]“=“hyperg_U‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝSecondary–iõCon uen²!t“Hyp•MÞergo“emetric›iôU‘iæfunction–iõA&E‘iå13.1.3“All“input˜are“double“asŽ¡‘.ùœis–¦fthe“output.ŽŸ;‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áoutÝ.a.ŽŸ;‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸJÕ‘!Gh²!ypMÞerg_1F1–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géout‘°Yè=‘LÉhyperg_1F1‘yšâ(éx0á,–¦féx1á,“éx2‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éoutè,–LÉéerr‘cè]“=“hyperg_1F1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝPrimary–ã¶Con uen²!t“Hyp•MÞergo“emetric›ã·U‘ã¦function–ã¶A&E‘ã§13.1.3“All“inputs˜are“double“asŽ¡‘.ùœis–¦fthe“output.ŽŸ;‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áoutÝ.a.ŽŸ;‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒøLcƒ’À;è…ïöïÿ 3ó>ßê ó3 cmmi10ó7m#½R ó3 cmss10ó6p®0J ó3 cmsl10ó3ßê; my $tex = 0; while ($line) { if ($line =~ /^\@@DOCSTRING/) { my $found = 0; my $func = $line; $func =~ s/\@@DOCSTRING\(//; $func =~ s/\)[\n\r]+//; my $func0 = $func; my $func1 = $func; $func0 =~ s/,.*$//; $func1 =~ s/^.*,//; if ( open(DOC,$docfile) ) { while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func0$/) { my $desc = ""; my $docline; my $doctex = 0; while (($docline = ) && ($docline !~ /^\037/)) { $docline =~ s/^\s*-[*]- texinfo -[*]-\s*//; if ($docline =~ /\@@tex/) { $doctex = 1; } if ($doctex) { $docline =~ s/\\\\/\\/g; } if ($docline =~ /\@@end tex/) { $doctex = 0; } $desc .= $docline; } $desc =~ s/$func0/$func1/g; $desc =~ s/\@@seealso\{(.*[^}])\}/See also: \1/g; print "$desc", "\n"; $found = 1; last; } } close (DOC); if (! $found) { print "\@@emph{Not implemented}\n"; } } else { print STDERR "Could not open file $docfile\n"; exit 1; } } elsif ($line =~ /^\@@REFERENCE_SECTION/) { my $secfound = 0; my $sec = $line; $sec =~ s/\@@REFERENCE_SECTION\(//; $sec =~ s/\)[\n\r]+//; my @@listfunc = (); my $nfunc = 0; my $seccat = 0; if ( open(IND,$indexfile) ) { while () { next unless /^[^ ]/; my $section = $_; $section =~ s/[\n\r]+//; if ($section =~ /^(.*?)\s*>>\s*(.*?)$/) { $section =~ s/.*>>(.*)/\1/; $seccat = 1; } $section =~ s/^ *//; $section =~ s/ *$//; if ($section =~ /^$sec$/) { if ($seccat) { print "\@@iftex\n"; print "\@@section Functions by Category\n"; # Get the list of categories to index my $firstcat = 1; my $category; while () { last if />>/; if (/^[^ ]/) { if (! $firstcat) { print "\@@end table\n"; } else { $firstcat = 0; } $category = $_; $category =~ s/[\n\r]+//; print "\@@subsection $category\n"; print "\@@table \@@asis\n"; } elsif (/^\s+(\S.*\S)\s*=\s*(\S.*\S)\s*$/) { my $func = $1; my $desc = $2; print "\@@item $func\n"; print "$desc\n"; print "\n"; } else { if ($firstcat) { print STDERR "Error parsing index file\n"; exit 1; } s/^\s+//; my @@funcs = split /\s+/; while ($#funcs >= 0) { my $func = shift @@funcs; $func =~ s/^ *//; $func =~ s/[\n\r]+//; push @@listfunc, $func; $nfunc = $nfunc + 1; print "\@@item $func\n"; print func_summary($func, $docfile); print "\n"; } } } if (! $firstcat) { print "\@@end table\n"; } print "\n\@@section Functions Alphabetically\n"; print "\@@end iftex\n\n"; } else { # Get the list of functions to index my $indline; while (($indline = ) && ($indline =~ /^ /)) { if ($indline =~ /^\s+(\S.*\S)\s*=\s*(\S.*\S)\s*$/) { next; } $indline =~ s/^\s+//; my @@funcs = split(/\s+/,$indline); while ($#funcs >= 0) { my $func = shift @@funcs; $func =~ s/^ *//; $func =~ s/[\n\r]+//; push @@listfunc, $func; $nfunc = $nfunc + 1; } } } $secfound = 1; last; } } close (IND); if (! $secfound) { print STDERR "Did not find section $sec\n"; } } else { print STDERR "Could not open file $indexfile\n"; exit 1; } @@listfunc = sort(@@listfunc); my @@listfunc2 = (); my $indent = 16 - 3; print "\@@menu\n"; foreach my $func (@@listfunc) { if ( open(DOC,$docfile) ) { my $found = 0; while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func$/) { $found = 1; last; } } close (DOC); if ($found) { push @@listfunc2, $func; my $func0 = "${func}::"; my $entry = sprintf("* %-*s %s",$indent,$func0,func_summary($func,$docfile)); print wrap("","\t\t","$entry"), "\n"; } } else { print STDERR "Could not open file $indexfile\n"; exit 1; } } print "\@@end menu\n"; my $up = "Function Reference"; my $next; my $prev; my $mfunc = 1; foreach my $func (@@listfunc2) { if ($mfunc == $nfunc) { $next = ""; } else { $next = @@listfunc2[$mfunc]; $mfunc = $mfunc + 1; } print "\n\@@node $func, $next, $prev, $up\n"; if ($seccat) { print "\@@subsection $func\n\n"; } else { print "\@@section $func\n\n"; } $prev = $func; my $found = 0; my $desc = ""; if ( open(DOC,$docfile) ) { while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func$/) { my $docline; my $doctex = 0; while (($docline = ) && ($docline !~ /^\037/)) { $docline =~ s/^\s*-[*]- texinfo -[*]-\s*//; if ($docline =~ /\@@tex/) { $doctex = 1; } if ($doctex) { $docline =~ s/\\\\/\\/g; } if ($docline =~ /\@@end tex/) { $doctex = 0; } $desc .= $docline; } $desc =~ s/\@@seealso\{(.*[^}])\}/See also: \1/g; print "$desc", "\n"; $found = 1; last; } } close (DOC); if (! $found) { print "\@@emph{Not implemented}\n"; } } else { print STDERR "Could not open file $docfile\n"; exit 1; } } } else { if ($line =~ /\@@tex/) { $tex = 1; } if ($tex) { $line =~ s/\\\\/\\/g; } print "$line"; if ($line =~ /\@@end tex/) { $tex = 0; } } $line = ; } } else { print STDERR "Could not open file $file\n"; exit 1; }; print("\@@bye"); sub func_summary { # {{{1 my ($func, # in function name $docfile # in DOCSTRINGS ) = @@_; my $desc = ""; my $found = 0; if ( open(DOC,$docfile) ) { while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func$/) { my $docline; my $doctex = 0; while (($docline = ) && ($docline !~ /^\037/)) { if ($docline =~ /\@@tex/) { $doctex = 1; } if ($doctex) { $docline =~ s/\\\\/\\/g; } if ($docline =~ /\@@end tex/) { $doctex = 0; } $desc .= $docline; } $desc =~ s/\@@seealso\{(.*[^}])\}/See also: \1/g; $found = 1; last; } } close (DOC); if (! $found) { $desc = "\@@emph{Not implemented}"; } } else { print STDERR "Could not open file $docfile\n"; exit 1; } return first_sentence($desc); } # 1}}} sub first_sentence { # {{{1 # grab the first real sentence from the function documentation my ($desc) = @@_; my $retval = ''; my $line; my $next; my @@lines; my $trace = 0; # $trace = 1 if $desc =~ /Levenberg/; return "" unless defined $desc; if ($desc =~ /^\s*-[*]- texinfo -[*]-/) { # help text contains texinfo. Strip the indicator and run it # through makeinfo. (XXX FIXME XXX this needs to be a function) $desc =~ s/^\s*-[*]- texinfo -[*]-\s*//; my $cmd = "makeinfo --fill-column 1600 --no-warn --no-validate --no-headers --force --ifinfo"; open3(*Writer, *Reader, *Errer, $cmd) or die "Could not run info"; print Writer "\@@macro seealso {args}\n\n\@@noindent\nSee also: \\args\\.\n\@@end macro\n"; print Writer "$desc"; close(Writer); @@lines = ; close(Reader); my @@err = ; close(Errer); waitpid(-1,&WNOHANG); # Display source and errors, if any if (@@err) { my $n = 1; foreach $line ( split(/\n/,$desc) ) { printf "%2d: %s\n",$n++,$line; } print ">>> @@err"; } # Print trace showing formatted output # print "\n"; # Skip prototype and blank lines while (1) { return "" unless @@lines; $line = shift @@lines; next if $line =~ /^\s*-/; next if $line =~ /^\s*$/; last; } } else { # print "\n"; # Skip prototype and blank lines @@lines = split(/\n/,$desc); while (1) { return "" if ($#lines < 0); $line = shift @@lines; next if $line =~ /^\s*[Uu][Ss][Aa][Gg][Ee]/; # skip " usage " $line =~ s/^\s*\w+\s*://; # chop " blah : " print "strip blah: $line\n" if $trace; $line =~ s/^\s*[Ff]unction\s+//; # chop " function " print "strip function $line\n" if $trace; $line =~ s/^\s*\[.*\]\s*=\s*//; # chop " [a,b] = " print "strip []= $line\n" if $trace; $line =~ s/^\s*\w+\s*=\s*//; # chop " a = " print "strip a= $line\n" if $trace; $line =~ s/^\s*\w+\s*\([^\)]*\)\s*//; # chop " f(x) " print "strip f(x) $line\n" if $trace; $line =~ s/^\s*[;:]\s*//; # chop " ; " print "strip ; $line\n" if $trace; $line =~ s/^\s*[[:upper:]][[:upper:]0-9_]+//; # chop " BLAH" print "strip BLAH $line\n" if $trace; $line =~ s/^\s*\w*\s*[-]+\s+//; # chop " blah --- " print "strip blah --- $line\n" if $trace; $line =~ s/^\s*\w+ *\t\s*//; # chop " blah " print "strip blah $line\n" if $trace; $line =~ s/^\s*\w+\s\s+//; # chop " blah " print "strip blah $line\n" if $trace; # next if $line =~ /^\s*\[/; # skip [a,b] = f(x) # next if $line =~ /^\s*\w+\s*(=|\()/; # skip a = f(x) OR f(x) next if $line =~ /^\s*or\s*$/; # skip blah \n or \n blah next if $line =~ /^\s*$/; # skip blank line next if $line =~ /^\s?!\//; # skip # !/usr/bin/octave # XXX FIXME XXX should be testing for unmatched () in proto # before going to the next line! last; } } # Try to make a complete sentence, including the '.' if ( "$line " !~ /[^.][.]\s/ && $#lines >= 0) { my $next = $lines[0]; $line =~ s/\s*$//; # trim trailing blanks on last $next =~ s/^\s*//; # trim leading blanks on next $line .= " $next" if "$next " =~ /[^.][.]\s/; # ends the sentence } # Tidy up the sentence. chomp $line; # trim trailing newline, if there is one $line =~ s/^\s*//; # trim leading blanks on line $line =~ s/([^.][.])\s.*$/$1/; # trim everything after the sentence print "Skipping:\n$desc---\n" if $line eq ""; # And return it. return $line; } # 1}}} __END__ This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, see . This program is granted to the public domain. THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. @ gsl-1.0.8/doc/RCS/gsl.ps,v0000644000175000017500000115127011201030376012702 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @% @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @%!PS-Adobe-2.0 %%Creator: dvips(k) 5.95a Copyright 2005 Radical Eye Software %%Title: gsl.dvi %%Pages: 51 %%PageOrder: Ascend %%BoundingBox: 0 0 595 842 %%DocumentFonts: CMR10 CMTT10 CMSS10 CMSLTT10 CMSL10 CMMI10 CMEX10 CMMI7 %%+ CMR7 CMSY10 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -o gsl.ps gsl.dvi %DVIPSParameters: dpi=600 %DVIPSSource: TeX output 2008.05.15:1311 %%BeginProcSet: tex.pro 0 0 %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@@landscape{/isls true N}B/@@manualfeed{ statusdict/manualfeed true put}B/@@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S /BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @@rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: texps.pro 0 0 %! TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]FontType 0 ne{/Metrics exch def dict begin Encoding{exch dup type/integertype ne{ pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def}ifelse}forall Metrics/Metrics currentdict end def}{{1 index type /nametype eq{exit}if exch pop}loop}ifelse[2 index currentdict end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[ exch{dup CharStrings exch known not{pop/.notdef/Encoding true def}if} forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def}def end %%EndProcSet %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put readonly def /FontBBox{-29 -960 1116 775}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /zero put dup 50 /two put readonly def /FontBBox{-27 -250 1122 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 25 /pi put dup 61 /slash put readonly def /FontBBox{0 -250 1171 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 90 /integraldisplay put dup 113 /radicalBig put readonly def /FontBBox{-24 -2960 1454 772}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 69 /E put dup 75 /K put dup 100 /d put dup 107 /k put dup 109 /m put dup 116 /t put readonly def /FontBBox{-32 -250 1048 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E394A533A081C36D456A09920001A3D2199583EB9B84B4DEE08E3D12939E321 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTT10 %!PS-AdobeFont-1.1: CMTT10 1.00B %%CreationDate: 1992 Apr 26 10:42:42 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTT10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def /FontName /CMTT10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 42 /asterisk put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 58 /colon put dup 60 /less put dup 61 /equal put dup 62 /greater put dup 65 /A put dup 66 /B put dup 67 /C put dup 69 /E put dup 70 /F put dup 73 /I put dup 74 /J put dup 75 /K put dup 80 /P put dup 81 /Q put dup 83 /S put dup 85 /U put dup 87 /W put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 93 /bracketright put dup 94 /asciicircum put dup 95 /underscore put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /braceleft put dup 124 /bar put dup 125 /braceright put readonly def /FontBBox{-4 -235 731 800}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F00F963068B8232429ED8B7CF6A3D879A2D19 38DD5C4467F9DD8C5D1A2000B3A6BF2F25629BAEC199AE8BD4BA6ED9BBF7DABF 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSL10 %!PS-AdobeFont-1.1: CMSL10 1.0 %%CreationDate: 1991 Aug 20 16:40:20 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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cleartomark %%EndFont %%BeginFont: CMSLTT10 %!PS-AdobeFont-1.1: CMSLTT10 1.0 %%CreationDate: 1991 Aug 20 16:41:43 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSLTT10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -9.46 def /isFixedPitch true def end readonly def /FontName /CMSLTT10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /zero put dup 49 /one put dup 50 /two put dup 100 /d put dup 101 /e put dup 109 /m put dup 110 /n put dup 111 /o put dup 114 /r put dup 116 /t put dup 117 /u put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-20 -233 617 696}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSS10 %!PS-AdobeFont-1.1: CMSS10 1.0 %%CreationDate: 1991 Aug 20 17:33:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSS10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put readonly def /FontBBox{-61 -250 999 759}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 31 /Oslash put dup 33 /exclam put dup 36 /dollar put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 55 /seven put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 93 /bracketright put dup 95 /dotaccent put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-251 -250 1009 969}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont TeXDict begin 39139632 55387786 1000 600 600 (gsl.dvi) @@start /Fa 255[71{}1 90.9091 /CMSY10 rf /Fb 205[33 1[33 48[{}2 58.1154 /CMR7 rf /Fc 194[34 35[39 25[{}2 58.1154 /CMMI7 rf /Fd 142[83 22[46 90[{}2 83.022 /CMEX10 rf /Fe 139[33 6[80 1[47 6[47 24[77 5[67 69[{}6 90.9091 /CMMI10 rf /Ff 130[48 48 48 3[48 1[48 48 48 48 1[48 48 48 1[48 3[48 48 48 48 3[48 2[48 31[48 1[48 1[48 2[48 48 48 48 1[48 48 48 48 48 48 2[48 42[{}32 90.9091 /CMTT10 rf /Fg 133[40 48 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b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 1163 42 84 v 390 1252 a Fk(for)30 b(do)s(cumen)m(tation.)275 1467 y(\037b)s(essel_il_scaled)h(-*-)h(texinfo)f(-*-)2960 1682 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(bessel_il_scaled)d Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 1791 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_il_scaled)d Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 1901 y Fk(These)26 b(routines)g(compute)h(the)f(scaled)h(regular)g(mo)s(di\014ed)e (spherical)i(Bessel)g(function)f(of)g(order)390 2011 y(l,)31 b(exp\(-)p Ff(|)p Fk(x)p Ff(|)p Fk(\))f(i_l\(x\))390 2160 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 2310 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o 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b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g (Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 929 42 84 v 390 1019 a Fk(for)30 b(do)s(cumen)m(tation.)275 1215 y(\037ta)m(ylorco)s(e\013)i(-*-)f(texinfo)g(-*-)2960 1412 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(taylorcoeff)c Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 1522 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(taylorcoeff)c Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 1631 y Fk(These)30 b(routines)g(compute)h(the)g(T)-8 b(a)m(ylor)31 b(co)s(e\016cien)m(t)h (x)p Ff(^)p Fk(n)e(/)h(n!)40 b(for)30 b(x)g Ff(>)p Fk(=)g(0,)h(n)f Ff(>)p Fk(=)g(0.)390 1772 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate) i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 1913 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 1933 V 390 2022 a 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Fi(\))2960 4736 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_il_scaled)d Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 4845 y Fk(These)26 b(routines)g(compute)h(the)f(scaled)h(regular)g(mo)s(di\014ed)e (spherical)i(Bessel)g(function)f(of)g(order)390 4955 y(l,)31 b(exp\(-)p Ff(|)p Fk(x)p Ff(|)p Fk(\))f(i_l\(x\))390 5093 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 5230 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o (re/g)o(sl/)p 3977 5251 V 390 5340 a Fk(for)30 b(do)s(cumen)m(tation.)p eop end %%Page: 39 39 TeXDict begin 39 38 bop 275 299 a Fk(\037b)s(essel_kl_scaled)31 b(-*-)g(texinfo)g(-*-)2960 482 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(bessel_kl_scaled)d Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 591 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p 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Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 3087 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(fermi_dirac_int)d Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 3197 y Fk(These)27 b(routines)h(compute)g(the)f(complete)i(F)-8 b(ermi-Dirac)30 b(in)m(tegral)f(with)f(an)f(in)m(teger)i(index)e(of)h(j,)390 3306 y(F_j\(x\))j(=)f(\(1/Gamma\(j+1\)\))k(in)m(t_0)p Ff(^)p Fk(inft)m(y)d(dt)g(\(t)p Ff(^)p Fk(j)f(/\(exp\(t-x\)+1\)\).)390 3440 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 3574 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o (re/g)o(sl/)p 3977 3595 V 390 3684 a Fk(for)30 b(do)s(cumen)m(tation.) 275 3867 y(\037ta)m(ylorco)s(e\013)i(-*-)f(texinfo)g(-*-)2960 4049 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(taylorcoeff)c Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 4159 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(taylorcoeff)c Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 4268 y Fk(These)30 b(routines)g(compute)h(the)g(T)-8 b(a)m(ylor)31 b(co)s(e\016cien)m(t)h (x)p Ff(^)p Fk(n)e(/)h(n!)40 b(for)30 b(x)g Ff(>)p Fk(=)g(0,)h(n)f Ff(>)p Fk(=)g(0.)390 4402 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate) i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 4536 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 4557 V 390 4646 a Fk(for)30 b(do)s(cumen)m(tation.)275 4829 y(\037legendre_Pl)g(-*-)i(texinfo)f(-*-)2960 5011 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(legendre_Pl)c Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 5121 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(legendre_Pl)c Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 5230 y Fk(These)36 b(functions)f(ev)-5 b(aluate)38 b(the)e(Legendre)f(p)s(olynomial)i(P_l\(x\))g(for)e(a)h(sp) s(eci\014c)g(v)-5 b(alue)36 b(of)g(l,)i(x)390 5340 y(sub)5 b(ject)30 b(to)h(l)g Ff(>)p Fk(=)f(0,)h Ff(|)p Fk(x)p Ff(|)e(<)p Fk(=)h(1)p eop end %%Page: 40 40 TeXDict begin 40 39 bop 390 299 a Fg(err)36 b Fk(con)m(tains)c(an)e (estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 434 y(This)19 b(function)h(is)h(from)f(the) g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 454 42 84 v 390 543 a Fk(for)30 b(do)s(cumen)m(tation.)275 729 y(\037legendre_Ql)g(-*-)i(texinfo)f(-*-)2960 914 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(legendre_Ql)c Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 1024 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(legendre_Ql)c Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 1133 y Fk(These)30 b(routines)g (compute)h(the)g(Legendre)f(function)g(Q_l\(x\))h(for)f(x)h Ff(>)f Fk(-1,)h(x)f(!=)h(1)f(and)g(l)h Ff(>)p Fk(=)e(0.)390 1268 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 1403 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o (re/g)o(sl/)p 3977 1424 V 390 1513 a Fk(for)30 b(do)s(cumen)m(tation.) 275 1698 y(\037psi_n)f(-*-)i(texinfo)g(-*-)2960 1884 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(psi_n)47 b Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 1993 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(psi_n)47 b Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 2103 y Fk(These)30 b(routines)g(compute)h(the)g(p)s(olygamma)g(function)f(psi)p Ff(^{)p Fk(\(m\))p Ff(})p Fk(\(x\))g(for)g(m)g Ff(>)p Fk(=)g(0,)h(x)f Ff(>)g Fk(0.)390 2238 y Fg(err)36 b Fk(con)m(tains)c (an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 2373 y(This)19 b(function)h(is)h(from)f (the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 2393 V 390 2482 a Fk(for)30 b(do)s(cumen)m(tation.)275 2668 y(\037b)s(essel_Jn)m(u)f(-*-)i(texinfo)g(-*-)2960 2853 y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53 b(bessel_Jnu)48 b Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b Fi(\))2960 2963 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_Jnu)48 b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 3072 y Fk(These)28 b(routines)f(compute)h(the)g(regular)g(cylindrical)h(Bessel)f(function) g(of)g(fractional)h(order)e(n)m(u,)390 3182 y(J_u\(x\).)390 3317 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(z)p Fk(.)390 3452 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o (re/g)o(sl/)p 3977 3472 V 390 3561 a Fk(for)30 b(do)s(cumen)m(tation.) 275 3747 y(\037b)s(essel_Yn)m(u)f(-*-)j(texinfo)f(-*-)2960 3932 y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53 b(bessel_Ynu)48 b Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b Fi(\))2960 4042 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_Ynu)48 b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 4151 y Fk(These)37 b(routines)f(compute)h(the)g(irregular)g(cylindrical)h(Bessel)g (function)e(of)h(fractional)h(order)390 4261 y(n)m(u,)30 b(Y_u\(x\).)390 4396 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of) f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(z)p Fk(.)390 4531 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 4551 V 390 4641 a Fk(for)30 b(do)s(cumen)m(tation.)275 4826 y(\037b)s(essel_In)m(u)f(-*-)i(texinfo)g(-*-)2960 5011 y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53 b(bessel_Inu)48 b Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b Fi(\))2960 5121 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_Inu)48 b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 5230 y Fk(These)34 b(routines)g(compute)h(the)f(regular)g(mo)s(di\014ed)f(Bessel)j (function)e(of)g(fractional)i(order)d(n)m(u,)390 5340 y(I_u\(x\))e(for)f(x)p Ff(>)p Fk(0,)g(u)p Ff(>)p Fk(0.)p eop end %%Page: 41 41 TeXDict begin 41 40 bop 390 299 a Fg(err)36 b Fk(con)m(tains)c(an)e (estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(z)p Fk(.)390 445 y(This)19 b(function)h(is)h(from)f(the) g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 465 42 84 v 390 554 a Fk(for)30 b(do)s(cumen)m(tation.)275 762 y(\037b)s(essel_In)m(u_scaled)g(-*-)h(texinfo)g(-*-)2960 969 y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53 b(bessel_Inu_scaled)d 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b(airy_Ai_deriv)c Fi(\()p Fh(x)p Fg(,)31 b Fh(mode)12 b Fi(\))2960 4454 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(airy_Ai_deriv)c Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 4564 y Fk(These)24 b(routines)f (compute)h(the)h(Airy)e(function)h(deriv)-5 b(ativ)m(e)25 b(Ai'\(x\))g(with)f(an)g(accuracy)h(sp)s(eci\014ed)390 4674 y(b)m(y)30 b(mo)s(de.)390 4807 y(The)g(second)g(argumen)m(t)h Fg(mo)s(de)k Fk(m)m(ust)30 b(b)s(e)g(an)g(in)m(teger)i(corresp)s (onding)e(to)390 4964 y(0)h(=)f(GSL_PREC_DOUBLE)870 5073 y(Double-precision,)i(a)e(relativ)m(e)j(accuracy)e(of)g(appro)m (ximately)h Ff(2)e(*)g(10^-16)p Fk(.)390 5230 y(1)h(=)f (GSL_PREC_SINGLE)870 5340 y(Single-precision,)h(a)g(relativ)m(e)i (accuracy)e(of)g(appro)m(ximately)h Ff(10^-7)p Fk(.)p eop end %%Page: 47 47 TeXDict begin 47 46 bop 390 299 a Fk(2)31 b(=)f(GSL_PREC_APPR)m(O)m(X) 870 408 y(Appro)m(ximate)h(v)-5 b(alues,)31 b(a)g(relativ)m(e)h (accuracy)g(of)e(appro)m(ximately)i 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y(0)h(=)f(GSL_PREC_DOUBLE)870 2038 y(Double-precision,)i(a)e(relativ)m(e)j(accuracy)e(of)g(appro)m (ximately)h Ff(2)e(*)g(10^-16)p Fk(.)390 2211 y(1)h(=)f (GSL_PREC_SINGLE)870 2321 y(Single-precision,)h(a)g(relativ)m(e)i (accuracy)e(of)g(appro)m(ximately)h Ff(10^-7)p Fk(.)390 2494 y(2)f(=)f(GSL_PREC_APPR)m(O)m(X)870 2604 y(Appro)m(ximate)h(v)-5 b(alues,)31 b(a)g(relativ)m(e)h(accuracy)g(of)e(appro)m(ximately)i Ff(5)e(*)g(10^-4)p Fk(.)390 2784 y Fg(err)36 b Fk(con)m(tains)c(an)e (estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 2932 y(This)19 b(function)h(is)h(from)f (the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 2953 V 390 3042 a Fk(for)30 b(do)s(cumen)m(tation.)275 3254 y(\037airy_Ai_deriv_scaled)i(-*-)f(texinfo)g(-*-)2960 3466 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(airy_Ai_deriv_scaled)e Fi(\()p Fh(x)p Fg(,)31 b Fh(mode)12 b Fi(\))2960 3576 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(airy_Ai_deriv_scaled)e Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 3686 y Fk(These)30 b(routines)g(compute)h(the)g (deriv)-5 b(ativ)m(e)32 b(of)e(the)h(scaled)g(Airy)f(function)g (S_A\(x\))h(Ai\(x\).)390 3834 y(The)f(second)g(argumen)m(t)h Fg(mo)s(de)k Fk(m)m(ust)30 b(b)s(e)g(an)g(in)m(teger)i(corresp)s (onding)e(to)390 4014 y(0)h(=)f(GSL_PREC_DOUBLE)870 4124 y(Double-precision,)i(a)e(relativ)m(e)j(accuracy)e(of)g(appro)m (ximately)h Ff(2)e(*)g(10^-16)p Fk(.)390 4297 y(1)h(=)f (GSL_PREC_SINGLE)870 4407 y(Single-precision,)h(a)g(relativ)m(e)i (accuracy)e(of)g(appro)m(ximately)h Ff(10^-7)p Fk(.)390 4580 y(2)f(=)f(GSL_PREC_APPR)m(O)m(X)870 4690 y(Appro)m(ximate)h(v)-5 b(alues,)31 b(a)g(relativ)m(e)h(accuracy)g(of)e(appro)m(ximately)i Ff(5)e(*)g(10^-4)p Fk(.)390 4870 y Fg(err)36 b Fk(con)m(tains)c(an)e (estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 5018 y(This)19 b(function)h(is)h(from)f (the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 5038 V 390 5128 a Fk(for)30 b(do)s(cumen)m(tation.)275 5340 y(\037airy_Bi_deriv_scaled)i(-*-)f(texinfo)g(-*-)p eop end %%Page: 48 48 TeXDict begin 48 47 bop 2960 299 a Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(airy_Bi_deriv_scaled)e Fi(\()p Fh(x)p Fg(,)31 b Fh(mode)12 b Fi(\))2960 408 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(airy_Bi_deriv_scaled)e Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 518 y Fk(These)30 b(routines)g(compute)h(the)g(deriv)-5 b(ativ)m(e)32 b(of)e(the)h (scaled)g(Airy)f(function)g(S_B\(x\))h(Bi\(x\).)390 653 y(The)f(second)g(argumen)m(t)h Fg(mo)s(de)k Fk(m)m(ust)30 b(b)s(e)g(an)g(in)m(teger)i(corresp)s(onding)e(to)390 813 y(0)h(=)f(GSL_PREC_DOUBLE)870 923 y(Double-precision,)i(a)e (relativ)m(e)j(accuracy)e(of)g(appro)m(ximately)h Ff(2)e(*)g(10^-16)p Fk(.)390 1083 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b(second)g(argumen)m(t)h Fg(mo)s(de)k Fk(m)m(ust)30 b(b)s(e)g(an)g(in)m(teger)i(corresp)s (onding)e(to)390 1213 y(0)h(=)f(GSL_PREC_DOUBLE)870 1322 y(Double-precision,)i(a)e(relativ)m(e)j(accuracy)e(of)g(appro)m (ximately)h Ff(2)e(*)g(10^-16)p Fk(.)390 1485 y(1)h(=)f (GSL_PREC_SINGLE)870 1594 y(Single-precision,)h(a)g(relativ)m(e)i (accuracy)e(of)g(appro)m(ximately)h Ff(10^-7)p Fk(.)390 1757 y(2)f(=)f(GSL_PREC_APPR)m(O)m(X)870 1866 y(Appro)m(ximate)h(v)-5 b(alues,)31 b(a)g(relativ)m(e)h(accuracy)g(of)e(appro)m(ximately)i Ff(5)e(*)g(10^-4)p Fk(.)390 2030 y Fg(err)36 b Fk(con)m(tains)c(an)e (estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 2168 y(This)19 b(function)h(is)h(from)f (the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 2188 42 84 v 390 2277 a Fk(for)30 b(do)s(cumen)m(tation.)275 2468 y(\037airy_zero_Ai)i(-*-)f(texinfo)g(-*-)2960 2658 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 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b(routines)g(compute)h(the)g(lo)s (cation)h(of)e(the)h(s-th)f(zero)h(of)g(the)f(Airy)h(function)f (Bi\(x\).)390 3999 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f (the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 4136 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 4157 V 390 4246 a Fk(for)30 b(do)s(cumen)m(tation.)275 4436 y(\037airy_zero_Ai_deriv)i(-*-)f(texinfo)g(-*-)2960 4627 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(airy_zero_Ai_deriv)e Fi(\()p Fh(n)12 b Fi(\))2960 4736 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(airy_zero_Ai_deriv)e Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 4846 y Fk(These)33 b(routines)f(compute)h(the)g(lo)s(cation)i(of)e(the)g(s-th)g(zero)g(of) g(the)g(Airy)g(function)f(deriv)-5 b(ativ)m(e)390 4955 y(Ai\(x\).)390 5093 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f (the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 5230 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 5251 V 390 5340 a Fk(for)30 b(do)s(cumen)m(tation.)p eop end %%Page: 50 50 TeXDict begin 50 49 bop 275 299 a Fk(\037airy_zero_Bi_deriv)32 b(-*-)f(texinfo)g(-*-)2960 488 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(airy_zero_Bi_deriv)e Fi(\()p Fh(n)12 b Fi(\))2960 597 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(airy_zero_Bi_deriv) e Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 707 y Fk(These)33 b(routines)f(compute)h(the)g(lo)s(cation)i(of)e(the)g(s-th)g(zero)g(of) g(the)g(Airy)g(function)f(deriv)-5 b(ativ)m(e)390 817 y(Bi\(x\).)390 953 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f (the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 1090 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 1110 42 84 v 390 1200 a Fk(for)30 b(do)s(cumen)m(tation.)275 1389 y(\037b)s(essel_zero_J0)h(-*-)g(texinfo)g(-*-)2960 1578 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(bessel_zero_J0)c Fi(\()p Fh(n)12 b Fi(\))2960 1687 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_zero_J0)d Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 1797 y Fk(These)34 b(routines)g(compute)g(the)g(lo)s(cation)i(of)e(the)g(s-th)g(p)s (ositiv)m(e)h(zero)g(of)f(the)g(Bessel)h(function)390 1906 y(J_0\(x\).)390 2043 y Fg(err)h Fk(con)m(tains)c(an)e(estimate)i (of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 2180 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 2200 V 390 2290 a Fk(for)30 b(do)s(cumen)m(tation.)275 2479 y(\037b)s(essel_zero_J1)h(-*-)g(texinfo)g(-*-)2960 2667 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(bessel_zero_J1)c Fi(\()p Fh(n)12 b Fi(\))2960 2777 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_zero_J1)d Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 2887 y Fk(These)34 b(routines)g(compute)g(the)g(lo)s(cation)i(of)e(the)g(s-th)g(p)s (ositiv)m(e)h(zero)g(of)f(the)g(Bessel)h(function)390 2996 y(J_1\(x\).)390 3133 y Fg(err)h Fk(con)m(tains)c(an)e(estimate)i (of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 3270 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 3290 V 390 3379 a Fk(for)30 b(do)s(cumen)m(tation.)275 3568 y(\037psi_1_in)m(t)h(-*-)g(texinfo)g(-*-)2960 3757 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(psi_1_int)48 b Fi(\()p Fh(n)12 b Fi(\))2960 3867 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(psi_1_int)48 b Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 3977 y Fk(These)30 b(routines)g(compute)h(the)g(T)-8 b(rigamma)31 b(function)f(psi\(n\))g(for)g(p)s(ositiv)m(e)h(in)m(teger) h(n.)390 4113 y Fg(err)k Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 4250 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o (re/g)o(sl/)p 3977 4270 V 390 4360 a Fk(for)30 b(do)s(cumen)m(tation.) 275 4549 y(\037zeta_in)m(t)i(-*-)f(texinfo)g(-*-)2960 4738 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(zeta_int)48 b Fi(\()p Fh(n)12 b Fi(\))2960 4847 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(zeta_int)48 b Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 4957 y Fk(These)30 b(routines)g(compute)h(the)g(Riemann)f(zeta)i(function)e(zeta\(n\))i (for)e(in)m(teger)i(n,)e(n)g(e)g(1.)390 5094 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g (the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 5230 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 5251 V 390 5340 a Fk(for)30 b(do)s(cumen)m(tation.)p eop end %%Page: 51 51 TeXDict begin 51 50 bop 275 299 a Fk(\037eta_in)m(t)32 b(-*-)f(texinfo)g(-*-)2960 459 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(eta_int)47 b Fi(\()p Fh(n)12 b Fi(\))2960 569 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(eta_int)47 b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 678 y Fk(These)30 b(routines)g(compute)h(the)g(eta)g(function)f(eta\(n\))i(for)e(in)m (teger)i(n.)390 805 y Fg(err)k Fk(con)m(tains)c(an)e(estimate)i(of)f (the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 931 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 951 42 84 v 390 1041 a Fk(for)30 b(do)s(cumen)m(tation.)275 1201 y(\037legendre_Plm)g(-*-)i(texinfo)f(-*-)2960 1361 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(legendre_Plm)c Fi(\()p Fh(n)p Fg(,)31 b Fh(m)p Fg(,)g Fh(x)12 b Fi(\))2960 1471 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(legendre_Plm)c Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 1580 y Fk(These)32 b(routines)g(compute)h(the)g(asso)s(ciated)g(Legendre)g(p)s(olynomial)f (P_l)p Ff(^)p Fk(m\(x\))h(for)f(m)h Ff(>)p Fk(=)e(0,)j(l)390 1690 y Ff(>)p Fk(=)c(m,)g Ff(|)p Fk(x)p Ff(|)g(<)p Fk(=)g(1.)390 1816 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 1943 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o (re/g)o(sl/)p 3977 1963 V 390 2052 a Fk(for)30 b(do)s(cumen)m(tation.) 275 2212 y(\037legendre_sphPlm)f(-*-)i(texinfo)g(-*-)2960 2373 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(legendre_sphPlm)d Fi(\()p Fh(n)p Fg(,)31 b Fh(m)p Fg(,)g Fh(x)12 b Fi(\))2960 2482 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(legendre_sphPlm)d Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 2592 y Fk(These)101 b(routines)g(compute)g(the)g (normalized)h(asso)s(ciated)h(Legendre)e(p)s(olynomial)390 2701 y($sqrt)p Ff({)p Fk(\(2l+1\)/\(4pi\))p Ff(})61 b Fk(sqrt)p Ff({)p Fk(\(l-m\)!/\(l+m\)!)p Ff(})f Fk(P_l)p Ff(^)p Fk(m\(x\)$)g(suitable)f(for)f(use)g(in)h(spherical)390 2811 y(harmonics.)40 b(The)28 b(parameters)i(m)m(ust)e(satisfy)i(m)e Ff(>)p Fk(=)g(0,)i(l)f Ff(>)p Fk(=)f(m,)i Ff(|)p Fk(x)p Ff(|)e(<)p Fk(=)g(1.)41 b(Theses)28 b(routines)390 2921 y(a)m(v)m(oid)k(the)e(o)m(v)m(er\015o)m(ws)i(that)f(o)s(ccur)f(for)g (the)h(standard)f(normalization)i(of)e(P_l)p Ff(^)p Fk(m\(x\).)390 3047 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 3173 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o (re/g)o(sl/)p 3977 3194 V 390 3283 a Fk(for)30 b(do)s(cumen)m(tation.) 275 3443 y(\037h)m(yp)s(erg_U)f(-*-)j(texinfo)f(-*-)2960 3603 y([Loadable)g(F)-8 b(unction])-3599 b Fh(out)65 b Fj(=)52 b(hyperg_U)c Fi(\()p Fh(x0)p Fg(,)32 b Fh(x1)p Fg(,)f Fh(x2)12 b Fi(\))2960 3713 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(out)p Fj(,)54 b Fh(err)12 b Fj(])53 b(=)f(hyperg_U)c Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 3823 y Fk(Secondary)28 b(Con\015uen)m(t)g(Hyp)s(ergo)s (emetric)h(U)g(function)f(A&E)g(13.1.3)i(All)f(input)f(are)h(double)f (as)390 3932 y(is)i(the)h(output.)390 4059 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g (the)g(v)-5 b(alue)31 b Fg(out)p Fk(.a.)390 4185 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 4205 V 390 4295 a Fk(for)30 b(do)s(cumen)m(tation.)275 4455 y(\037h)m(yp)s(erg_1F1)h(-*-)g(texinfo)g(-*-)2960 4615 y([Loadable)g(F)-8 b(unction])-3599 b Fh(out)65 b Fj(=)52 b(hyperg_1F1)d Fi(\()p Fh(x0)p Fg(,)31 b Fh(x1)p Fg(,)h Fh(x2)12 b Fi(\))2960 4725 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(out)p Fj(,)54 b Fh(err)12 b Fj(])53 b(=)f(hyperg_1F1)d Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 4834 y Fk(Primary)32 b(Con\015uen)m(t)f(Hyp)s(ergo)s (emetric)j(U)e(function)g(A&E)g(13.1.3)j(All)e(inputs)e(are)i(double)f (as)390 4944 y(is)e(the)h(output.)390 5070 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g (the)g(v)-5 b(alue)31 b Fg(out)p Fk(.a.)390 5197 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 5217 V 390 5306 a Fk(for)30 b(do)s(cumen)m(tation.)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF @ gsl-1.0.8/doc/RCS/gsl.log,v0000644000175000017500000244260311201030376013045 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @# @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @This is pdfeTeXk, Version 3.141592-1.21a-2.2 (Web2C 7.5.4) (format=pdfetex 2008.5.11) 15 MAY 2008 13:11 entering extended mode file:line:error style messages enabled. **\nonstopmode \input ./gsl.texi (./gsl.texi (./texinfo.tex Loading texinfo [version 2004-11-25.16]: Basics, \bindingoffset=\dimen16 \normaloffset=\dimen17 \pagewidth=\dimen18 \pageheight=\dimen19 \outerhsize=\dimen20 \outervsize=\dimen21 \cornerlong=\dimen22 \cornerthick=\dimen23 \topandbottommargin=\dimen24 \headlinebox=\box16 \footlinebox=\box17 \margin=\insert252 \EMsimple=\toks13 \groupbox=\box18 \groupinvalidhelp=\toks14 \mil=\dimen25 \exdentamount=\skip18 \inmarginspacing=\skip19 pdf, \tempnum=\count27 \lnkcount=\count28 \filename=\toks15 \filenamelength=\count29 \pgn=\count30 \toksA=\toks16 \toksB=\toks17 \toksC=\toks18 \toksD=\toks19 \boxA=\box19 \countA=\count31 (/usr/share/texmf/tex/plain/pdfcolor/pdfcolor.tex) fonts, \sffam=\fam8 \textleading=\dimen26 \fontdepth=\count32 page headings, \titlepagetopglue=\skip20 \titlepagebottomglue=\skip21 \evenheadline=\toks20 \oddheadline=\toks21 \evenfootline=\toks22 \oddfootline=\toks23 tables, \tableindent=\dimen27 \itemindent=\dimen28 \itemmargin=\dimen29 \itemmax=\dimen30 \itemno=\count33 \multitableparskip=\skip22 \multitableparindent=\skip23 \multitablecolspace=\dimen31 \multitablelinespace=\skip24 \colcount=\count34 \everytab=\toks24 conditionals, \doignorecount=\count35 indexing, \secondaryindent=\skip25 \partialpage=\box20 \doublecolumnhsize=\dimen32 sectioning, \unnumberedno=\count36 \chapno=\count37 \secno=\count38 \subsecno=\count39 \subsubsecno=\count40 \appendixno=\count41 \absseclevel=\count42 \secbase=\count43 \chapheadingskip=\skip26 \secheadingskip=\skip27 \subsecheadingskip=\skip28 toc, \tocfile=\write0 \contentsrightmargin=\skip29 \savepageno=\count44 \lastnegativepageno=\count45 \tocindent=\dimen33 environments, \errorbox=\box21 \lispnarrowing=\skip30 \envskipamount=\skip31 \circthick=\dimen34 \cartouter=\dimen35 \cartinner=\dimen36 \normbskip=\skip32 \normpskip=\skip33 \normlskip=\skip34 \lskip=\skip35 \rskip=\skip36 \tabw=\dimen37 defuns, \defbodyindent=\skip37 \defargsindent=\skip38 \deflastargmargin=\skip39 \parencount=\count46 \brackcount=\count47 macros, \paramno=\count48 \macname=\toks25 cross references, \auxfile=\write1 \savesfregister=\count49 insertions, \footnoteno=\count50 \SAVEfootins=\box22 \SAVEmargin=\box23 (/usr/share/texmf/tex/generic/epsf/epsf.tex \epsffilein=\read1 \epsfframemargin=\dimen38 \epsfframethickness=\dimen39 \epsfrsize=\dimen40 \epsftmp=\dimen41 \epsftsize=\dimen42 \epsfxsize=\dimen43 \epsfysize=\dimen44 \pspoints=\dimen45 \epsfnoopenhelp=\toks26 ) \noepsfhelp=\toks27 localization, \nolanghelp=\toks28 \defaultparindent=\dimen46 and turning on texinfo input format.) ./gsl.texi:8: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gsl_sf}{\folio }{\code {gsl_sf}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.8 @@deftypefn {Loadable Function} {} gsl_sf () A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:16: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{clausen}{\folio }{\code {clausen}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.16 ...le Function} {@@var{y} =} clausen (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:17: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{clausen}{\folio }{\code {clausen}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.17 ...{[@@var{y}, @@var{err}] =} clausen (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:21: Use of \ doesn't match its definition. l.21 Cl_2(x) = - \\ int_0^x dt \\log(2 \\sin(t/2)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:21: Use of \ doesn't match its definition. l.21 Cl_2(x) = - \\int_0^x dt \\ log(2 \\sin(t/2)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:21: Use of \ doesn't match its definition. l.21 Cl_2(x) = - \\int_0^x dt \\log(2 \\ sin(t/2)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:23: Use of \ doesn't match its definition. l.23 It is related to the dilogarithm by Cl_2(\\ theta) = \\Im Li_2(\\exp(i \... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:23: Use of \ doesn't match its definition. l.23 ...d to the dilogarithm by Cl_2(\\theta) = \\ Im Li_2(\\exp(i \\theta)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:23: Use of \ doesn't match its definition. l.23 ...ilogarithm by Cl_2(\\theta) = \\Im Li_2(\\ exp(i \\theta)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:23: Use of \ doesn't match its definition. l.23 ...hm by Cl_2(\\theta) = \\Im Li_2(\\exp(i \\ theta)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 27--29 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:34: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{dawson}{\folio }{\code {dawson}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.34 ...ble Function} {@@var{y} =} dawson (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:35: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{dawson}{\folio }{\code {dawson}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.35 ... {[@@var{y}, @@var{err}] =} dawson (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:37: Use of \ doesn't match its definition. l.37 The Dawson integral is defined by \\ exp(-x^2) \\int_0^x dt \\exp(t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:37: Use of \ doesn't match its definition. l.37 ...wson integral is defined by \\exp(-x^2) \\ int_0^x dt \\exp(t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:37: Use of \ doesn't match its definition. l.37 ... is defined by \\exp(-x^2) \\int_0^x dt \\ exp(t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 42--44 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:49: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_1}{\folio }{\code {debye_1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.49 ...le Function} {@@var{y} =} debye_1 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:50: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_1}{\folio }{\code {debye_1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.50 ...{[@@var{y}, @@var{err}] =} debye_1 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:54: Use of \ doesn't match its definition. l.54 D_n(x) = n/x^n \\ int_0^x dt (t^n/(e^t - 1)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 60--62 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:67: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_2}{\folio }{\code {debye_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.67 ...le Function} {@@var{y} =} debye_2 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:68: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_2}{\folio }{\code {debye_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.68 ...{[@@var{y}, @@var{err}] =} debye_2 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:72: Use of \ doesn't match its definition. l.72 D_n(x) = n/x^n \\ int_0^x dt (t^n/(e^t - 1)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 78--80 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:85: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_3}{\folio }{\code {debye_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.85 ...le Function} {@@var{y} =} debye_3 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [1{/usr/share/texmf-var/fonts/map/pdftex/updmap/pdftex.map} \entry{gsl_sf}{1}{\code {gsl_sf}} \entry{clausen}{1}{\code {clausen}} \entry{clausen}{1}{\code {clausen}} \entry{dawson}{1}{\code {dawson}} \entry{dawson}{1}{\code {dawson}} \entry{debye_1}{1}{\code {debye_1}} \entry{debye_1}{1}{\code {debye_1}} \entry{debye_2}{1}{\code {debye_2}} \entry{debye_2}{1}{\code {debye_2}} ] ./gsl.texi:86: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_3}{\folio }{\code {debye_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.86 ...{[@@var{y}, @@var{err}] =} debye_3 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:90: Use of \ doesn't match its definition. l.90 D_n(x) = n/x^n \\ int_0^x dt (t^n/(e^t - 1)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 96--98 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:103: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_4}{\folio }{\code {debye_4}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.103 ...e Function} {@@var{y} =} debye_4 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:104: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_4}{\folio }{\code {debye_4}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.104 ...[@@var{y}, @@var{err}] =} debye_4 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:108: Use of \ doesn't match its definition. l.108 D_n(x) = n/x^n \\ int_0^x dt (t^n/(e^t - 1)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 114--116 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:121: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_gsl}{\folio }{\code {erf_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.121 ...e Function} {@@var{y} =} erf_gsl (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:122: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_gsl}{\folio }{\code {erf_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.122 ...[@@var{y}, @@var{err}] =} erf_gsl (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:125: Use of \ doesn't match its definition. l.125 erf(x) = (2/\\ sqrt(\\pi)) \\int_0^x dt \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:125: Use of \ doesn't match its definition. l.125 erf(x) = (2/\\sqrt(\\ pi)) \\int_0^x dt \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:125: Use of \ doesn't match its definition. l.125 erf(x) = (2/\\sqrt(\\pi)) \\ int_0^x dt \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:125: Use of \ doesn't match its definition. l.125 erf(x) = (2/\\sqrt(\\pi)) \\int_0^x dt \\ exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 129--131 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:136: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erfc_gsl}{\folio }{\code {erfc_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.136 ... Function} {@@var{y} =} erfc_gsl (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:137: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erfc_gsl}{\folio }{\code {erfc_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.137 ...@@var{y}, @@var{err}] =} erfc_gsl (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:140: Use of \ doesn't match its definition. l.140 erfc(x) = 1 - erf(x) = (2/\\ sqrt(\\pi)) \\int_x^\\infty \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:140: Use of \ doesn't match its definition. l.140 erfc(x) = 1 - erf(x) = (2/\\sqrt(\\ pi)) \\int_x^\\infty \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:140: Use of \ doesn't match its definition. l.140 erfc(x) = 1 - erf(x) = (2/\\sqrt(\\pi)) \\ int_x^\\infty \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:140: Use of \ doesn't match its definition. l.140 ... 1 - erf(x) = (2/\\sqrt(\\pi)) \\int_x^\\ infty \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:140: Use of \ doesn't match its definition. l.140 ...(x) = (2/\\sqrt(\\pi)) \\int_x^\\infty \\ exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 144--146 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:151: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_erfc}{\folio }{\code {log_erfc}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.151 ... Function} {@@var{y} =} log_erfc (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:152: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_erfc}{\folio }{\code {log_erfc}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.152 ...@@var{y}, @@var{err}] =} log_erfc (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:155: Use of \ doesn't match its definition. l.155 function \\ log(\\erfc(x)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:155: Use of \ doesn't match its definition. l.155 function \\log(\\ erfc(x)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 159--161 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. [2 \entry{debye_3}{2}{\code {debye_3}} \entry{debye_3}{2}{\code {debye_3}} \entry{debye_4}{2}{\code {debye_4}} \entry{debye_4}{2}{\code {debye_4}} \entry{erf_gsl}{2}{\code {erf_gsl}} \entry{erf_gsl}{2}{\code {erf_gsl}} \entry{erfc_gsl}{2}{\code {erfc_gsl}} \entry{erfc_gsl}{2}{\code {erfc_gsl}} \entry{log_erfc}{2}{\code {log_erfc}} \entry{log_erfc}{2}{\code {log_erfc}} ] ./gsl.texi:166: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_Z}{\folio }{\code {erf_Z}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.166 ...ble Function} {@@var{y} =} erf_Z (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:167: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_Z}{\folio }{\code {erf_Z}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.167 ... {[@@var{y}, @@var{err}] =} erf_Z (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:170: Use of \ doesn't match its definition. l.170 Z(x) = (1/(2\\ pi)) \\exp(-x^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:170: Use of \ doesn't match its definition. l.170 Z(x) = (1/(2\\pi)) \\ exp(-x^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 174--176 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:181: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_Q}{\folio }{\code {erf_Q}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.181 ...ble Function} {@@var{y} =} erf_Q (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:182: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_Q}{\folio }{\code {erf_Q}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.182 ... {[@@var{y}, @@var{err}] =} erf_Q (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:185: Use of \ doesn't match its definition. l.185 function Q(x) = (1/(2\\ pi)) \\int_x^\\infty dt \\exp(-t^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:185: Use of \ doesn't match its definition. l.185 function Q(x) = (1/(2\\pi)) \\ int_x^\\infty dt \\exp(-t^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:185: Use of \ doesn't match its definition. l.185 function Q(x) = (1/(2\\pi)) \\int_x^\\ infty dt \\exp(-t^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:185: Use of \ doesn't match its definition. l.185 ... Q(x) = (1/(2\\pi)) \\int_x^\\infty dt \\ exp(-t^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 189--191 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:196: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hazard}{\folio }{\code {hazard}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.196 ...le Function} {@@var{y} =} hazard (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:197: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hazard}{\folio }{\code {hazard}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.197 ...{[@@var{y}, @@var{err}] =} hazard (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:200: Use of \ doesn't match its definition. l.200 inverse Mill\\ 's ratio, is defined as If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:201: Use of \ doesn't match its definition. l.201 h(x) = Z(x)/Q(x) = \\ sqrt@@{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2)@@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:201: Use of \ doesn't match its definition. l.201 h(x) = Z(x)/Q(x) = \\sqrt@@{2/\\ pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2)@@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:201: Use of \ doesn't match its definition. l.201 h(x) = Z(x)/Q(x) = \\sqrt@@{2/\\pi \\ exp(-x^2 / 2) / \\erfc(x/\\sqrt 2)@@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:201: Use of \ doesn't match its definition. l.201 ...(x) = \\sqrt@@{2/\\pi \\exp(-x^2 / 2) / \\ erfc(x/\\sqrt 2)@@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:201: Use of \ doesn't match its definition. l.201 ...qrt@@{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\ sqrt 2)@@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:202: Use of \ doesn't match its definition. l.202 It decreases rapidly as x approaches -\\ infty and asymptotes to If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:203: Use of \ doesn't match its definition. l.203 h(x) \\ sim x as x approaches +\\infty. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:203: Use of \ doesn't match its definition. l.203 h(x) \\sim x as x approaches +\\ infty. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 207--209 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:214: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expm1}{\folio }{\code {expm1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.214 ...ble Function} {@@var{y} =} expm1 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:215: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expm1}{\folio }{\code {expm1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.215 ... {[@@var{y}, @@var{err}] =} expm1 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:217: Use of \ doesn't match its definition. l.217 These routines compute the quantity \\ exp(x)-1 using an algorithm that If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 222--224 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:229: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel}{\folio }{\code {exprel}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.229 ...le Function} {@@var{y} =} exprel (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:230: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel}{\folio }{\code {exprel}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.230 ...{[@@var{y}, @@var{err}] =} exprel (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:232: Use of \ doesn't match its definition. l.232 These routines compute the quantity (\\ exp(x)-1)/x using an algorithm If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:234: Use of \ doesn't match its definition. l.234 the expansion (\\ exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\d... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:234: Use of \ doesn't match its definition. l.234 ... = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\ dots. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [3 \entry{erf_Z}{3}{\code {erf_Z}} \entry{erf_Z}{3}{\code {erf_Z}} \entry{erf_Q}{3}{\code {erf_Q}} \entry{erf_Q}{3}{\code {erf_Q}} \entry{hazard}{3}{\code {hazard}} \entry{hazard}{3}{\code {hazard}} \entry{expm1}{3}{\code {expm1}} \entry{expm1}{3}{\code {expm1}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 238--240 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:245: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel_2}{\folio }{\code {exprel_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.245 ... Function} {@@var{y} =} exprel_2 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:246: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel_2}{\folio }{\code {exprel_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.246 ...@@var{y}, @@var{err}] =} exprel_2 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:248: Use of \ doesn't match its definition. l.248 These routines compute the quantity 2(\\ exp(x)-1-x)/x^2 using an If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:251: Use of \ doesn't match its definition. l.251 2(\\ exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\dots. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:251: Use of \ doesn't match its definition. l.251 ... = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\ dots. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 255--257 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:262: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_E1}{\folio }{\code {expint_E1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.262 ...Function} {@@var{y} =} expint_E1 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:263: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_E1}{\folio }{\code {expint_E1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.263 ...var{y}, @@var{err}] =} expint_E1 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:267: Use of \ doesn't match its definition. l.267 E_1(x) := Re \\ int_1^\\infty dt \\exp(-xt)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:267: Use of \ doesn't match its definition. l.267 E_1(x) := Re \\int_1^\\ infty dt \\exp(-xt)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:267: Use of \ doesn't match its definition. l.267 E_1(x) := Re \\int_1^\\infty dt \\ exp(-xt)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 271--273 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:278: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_E2}{\folio }{\code {expint_E2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.278 ...Function} {@@var{y} =} expint_E2 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:279: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_E2}{\folio }{\code {expint_E2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.279 ...var{y}, @@var{err}] =} expint_E2 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:283: Use of \ doesn't match its definition. l.283 E_2(x) := \\ Re \\int_1^\\infty dt \\exp(-xt)/t^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:283: Use of \ doesn't match its definition. l.283 E_2(x) := \\Re \\ int_1^\\infty dt \\exp(-xt)/t^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:283: Use of \ doesn't match its definition. l.283 E_2(x) := \\Re \\int_1^\\ infty dt \\exp(-xt)/t^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:283: Use of \ doesn't match its definition. l.283 E_2(x) := \\Re \\int_1^\\infty dt \\ exp(-xt)/t^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 287--289 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:294: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_Ei}{\folio }{\code {expint_Ei}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.294 ...Function} {@@var{y} =} expint_Ei (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:295: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_Ei}{\folio }{\code {expint_Ei}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.295 ...var{y}, @@var{err}] =} expint_Ei (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:299: Use of \ doesn't match its definition. l.299 Ei(x) := - PV(\\ int_@@{-x@@}^\\infty dt \\exp(-t)/t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:299: Use of \ doesn't match its definition. l.299 Ei(x) := - PV(\\int_@@{-x@@}^\\ infty dt \\exp(-t)/t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:299: Use of \ doesn't match its definition. l.299 Ei(x) := - PV(\\int_@@{-x@@}^\\infty dt \\ exp(-t)/t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 305--307 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. [4 \entry{exprel}{4}{\code {exprel}} \entry{exprel}{4}{\code {exprel}} \entry{exprel_2}{4}{\code {exprel_2}} \entry{exprel_2}{4}{\code {exprel_2}} \entry{expint_E1}{4}{\code {expint_E1}} \entry{expint_E1}{4}{\code {expint_E1}} \entry{expint_E2}{4}{\code {expint_E2}} \entry{expint_E2}{4}{\code {expint_E2}} \entry{expint_Ei}{4}{\code {expint_Ei}} \entry{expint_Ei}{4}{\code {expint_Ei}} ] ./gsl.texi:312: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Shi}{\folio }{\code {Shi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.312 ...dable Function} {@@var{y} =} Shi (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:313: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Shi}{\folio }{\code {Shi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.313 ...n} {[@@var{y}, @@var{err}] =} Shi (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:315: Use of \ doesn't match its definition. l.315 ...routines compute the integral Shi(x) = \\ int_0^x dt \\sinh(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:315: Use of \ doesn't match its definition. l.315 ...ute the integral Shi(x) = \\int_0^x dt \\ sinh(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 319--321 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:326: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Chi}{\folio }{\code {Chi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.326 ...dable Function} {@@var{y} =} Chi (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:327: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Chi}{\folio }{\code {Chi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.327 ...n} {[@@var{y}, @@var{err}] =} Chi (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:331: Use of \ doesn't match its definition. l.331 Chi(x) := Re[ \\ gamma_E + \\log(x) + \\int_0^x dt (\\cosh[t]-1)/t] , If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:331: Use of \ doesn't match its definition. l.331 Chi(x) := Re[ \\gamma_E + \\ log(x) + \\int_0^x dt (\\cosh[t]-1)/t] , If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:331: Use of \ doesn't match its definition. l.331 Chi(x) := Re[ \\gamma_E + \\log(x) + \\ int_0^x dt (\\cosh[t]-1)/t] , If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:331: Use of \ doesn't match its definition. l.331 ...[ \\gamma_E + \\log(x) + \\int_0^x dt (\\ cosh[t]-1)/t] , If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:333: Use of \ doesn't match its definition. l.333 where \\ gamma_E is the Euler constant. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 337--339 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:344: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_3}{\folio }{\code {expint_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.344 ... Function} {@@var{y} =} expint_3 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:345: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_3}{\folio }{\code {expint_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.345 ...@@var{y}, @@var{err}] =} expint_3 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:348: Use of \ doesn't match its definition. l.348 Ei_3(x) = \\ int_0^x dt \\exp(-t^3) for x >= 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:348: Use of \ doesn't match its definition. l.348 Ei_3(x) = \\int_0^x dt \\ exp(-t^3) for x >= 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 352--354 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:359: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Si}{\folio }{\code {Si}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.359 ...adable Function} {@@var{y} =} Si (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:360: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Si}{\folio }{\code {Si}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.360 ...on} {[@@var{y}, @@var{err}] =} Si (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:362: Use of \ doesn't match its definition. l.362 ...ines compute the Sine integral Si(x) = \\ int_0^x dt \\sin(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:362: Use of \ doesn't match its definition. l.362 ...the Sine integral Si(x) = \\int_0^x dt \\ sin(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 366--368 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:373: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Ci}{\folio }{\code {Ci}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.373 ...adable Function} {@@var{y} =} Ci (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:374: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Ci}{\folio }{\code {Ci}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.374 ...on} {[@@var{y}, @@var{err}] =} Ci (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:377: Use of \ doesn't match its definition. l.377 Ci(x) = -\\ int_x^\\infty dt \\cos(t)/t for x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:377: Use of \ doesn't match its definition. l.377 Ci(x) = -\\int_x^\\ infty dt \\cos(t)/t for x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:377: Use of \ doesn't match its definition. l.377 Ci(x) = -\\int_x^\\infty dt \\ cos(t)/t for x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 381--383 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. [5 \entry{Shi}{5}{\code {Shi}} \entry{Shi}{5}{\code {Shi}} \entry{Chi}{5}{\code {Chi}} \entry{Chi}{5}{\code {Chi}} \entry{expint_3}{5}{\code {expint_3}} \entry{expint_3}{5}{\code {expint_3}} \entry{Si}{5}{\code {Si}} \entry{Si}{5}{\code {Si}} ] ./gsl.texi:388: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{atanint}{\folio }{\code {atanint}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.388 ...e Function} {@@var{y} =} atanint (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:389: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{atanint}{\folio }{\code {atanint}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.389 ...[@@var{y}, @@var{err}] =} atanint (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:392: Use of \ doesn't match its definition. l.392 AtanInt(x) = \\ int_0^x dt \\arctan(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:392: Use of \ doesn't match its definition. l.392 AtanInt(x) = \\int_0^x dt \\ arctan(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 396--398 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:403: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_mhalf}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.403 ...} {@@var{y} =} fermi_dirac_mhalf (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:404: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_mhalf}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.404 ...@@var{err}] =} fermi_dirac_mhalf (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 410--412 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:417: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_half}{\folio }{\code {fermi_di... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.417 ...n} {@@var{y} =} fermi_dirac_half (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:418: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_half}{\folio }{\code {fermi_di... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.418 ... @@var{err}] =} fermi_dirac_half (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 424--426 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:431: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_3half}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.431 ...} {@@var{y} =} fermi_dirac_3half (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:432: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_3half}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.432 ...@@var{err}] =} fermi_dirac_3half (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 438--440 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:445: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_gsl}{\folio }{\code {gamma_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.445 ...Function} {@@var{y} =} gamma_gsl (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:446: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_gsl}{\folio }{\code {gamma_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.446 ...var{y}, @@var{err}] =} gamma_gsl (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:448: Use of \ doesn't match its definition. l.448 These routines compute the Gamma function \\ Gamma(x), subject to x not If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:450: Use of \ doesn't match its definition. l.450 ...thod. The maximum value of x such that \\ Gamma(x) is not If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [6 \entry{Ci}{6}{\code {Ci}} \entry{Ci}{6}{\code {Ci}} \entry{atanint}{6}{\code {atanint}} \entry{atanint}{6}{\code {atanint}} \entry{fermi_dirac_mhalf}{6}{\code {fermi_dirac_mhalf}} \entry{fermi_dirac_mhalf}{6}{\code {fermi_dirac_mhalf}} \entry{fermi_dirac_half}{6}{\code {fermi_dirac_half}} \entry{fermi_dirac_half}{6}{\code {fermi_dirac_half}} \entry{fermi_dirac_3half}{6}{\code {fermi_dirac_3half}} \entry{fermi_dirac_3half}{6}{\code {fermi_dirac_3half}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 455--457 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:462: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lngamma_gsl}{\folio }{\code {lngamma_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.462 ...nction} {@@var{y} =} lngamma_gsl (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:463: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lngamma_gsl}{\folio }{\code {lngamma_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.463 ...r{y}, @@var{err}] =} lngamma_gsl (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:466: Use of \ doesn't match its definition. l.466 \\ log(\\Gamma(x)), subject to x not a being negative integer. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:466: Use of \ doesn't match its definition. l.466 \\log(\\ Gamma(x)), subject to x not a being negative integer. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:467: Use of \ doesn't match its definition. l.467 For x<0 the real part of \\ log(\\Gamma(x)) is returned, which is If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:467: Use of \ doesn't match its definition. l.467 For x<0 the real part of \\log(\\ Gamma(x)) is returned, which is If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:468: Use of \ doesn't match its definition. l.468 equivalent to \\ log(|\\Gamma(x)|). The function is computed using If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:468: Use of \ doesn't match its definition. l.468 equivalent to \\log(|\\ Gamma(x)|). The function is computed using If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 473--475 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:480: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gammastar}{\folio }{\code {gammastar}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.480 ...Function} {@@var{y} =} gammastar (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:481: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gammastar}{\folio }{\code {gammastar}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.481 ...var{y}, @@var{err}] =} gammastar (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:483: Use of \ doesn't match its definition. l.483 ...s compute the regulated Gamma Function \\ Gamma^*(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:486: Use of \ doesn't match its definition. l.486 \\ Gamma^*(x) = \\Gamma(x)/(\\sqrt@@{2\\pi@@} x^@@{(x-1/2)@@} \\exp(-x)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:486: Use of \ doesn't match its definition. l.486 \\Gamma^*(x) = \\ Gamma(x)/(\\sqrt@@{2\\pi@@} x^@@{(x-1/2)@@} \\exp(-x)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:486: Use of \ doesn't match its definition. l.486 \\Gamma^*(x) = \\Gamma(x)/(\\ sqrt@@{2\\pi@@} x^@@{(x-1/2)@@} \\exp(-x)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:486: Use of \ doesn't match its definition. l.486 \\Gamma^*(x) = \\Gamma(x)/(\\sqrt@@{2\\ pi@@} x^@@{(x-1/2)@@} \\exp(-x)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:486: Use of \ doesn't match its definition. l.486 ...amma(x)/(\\sqrt@@{2\\pi@@} x^@@{(x-1/2)@@} \\ exp(-x)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:487: Use of \ doesn't match its definition. l.487 = (1 + (1/12x) + ...) for x \\ to \\infty If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:487: Use of \ doesn't match its definition. l.487 ... = (1 + (1/12x) + ...) for x \\to \\ infty If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 493--495 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:500: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gammainv_gsl}{\folio }{\code {gammainv_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.500 ...ction} {@@var{y} =} gammainv_gsl (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:501: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gammainv_gsl}{\folio }{\code {gammainv_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.501 ...{y}, @@var{err}] =} gammainv_gsl (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:503: Use of \ doesn't match its definition. l.503 ...he reciprocal of the gamma function, 1/\\ Gamma(x) using the real La... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 507--509 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:514: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lambert_W0}{\folio }{\code {lambert_W0}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.514 ...unction} {@@var{y} =} lambert_W0 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:515: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lambert_W0}{\folio }{\code {lambert_W0}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.515 ...ar{y}, @@var{err}] =} lambert_W0 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [7 \entry{gamma_gsl}{7}{\code {gamma_gsl}} \entry{gamma_gsl}{7}{\code {gamma_gsl}} \entry{lngamma_gsl}{7}{\code {lngamma_gsl}} \entry{lngamma_gsl}{7}{\code {lngamma_gsl}} \entry{gammastar}{7}{\code {gammastar}} \entry{gammastar}{7}{\code {gammastar}} \entry{gammainv_gsl}{7}{\code {gammainv_gsl}} \entry{gammainv_gsl}{7}{\code {gammainv_gsl}} ] ./gsl.texi:519: Use of \ doesn't match its definition. l.519 Lambert\\ 's W functions, W(x), are defined to be solutions of the If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:520: Use of \ doesn't match its definition. l.520 equation W(x) \\ exp(W(x)) = x. This function has multiple branches If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 527--529 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:534: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lambert_Wm1}{\folio }{\code {lambert_Wm1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.534 ...nction} {@@var{y} =} lambert_Wm1 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:535: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lambert_Wm1}{\folio }{\code {lambert_Wm1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.535 ...r{y}, @@var{err}] =} lambert_Wm1 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:540: Use of \ doesn't match its definition. l.540 Lambert\\ 's W functions, W(x), are defined to be solutions of the If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:541: Use of \ doesn't match its definition. l.541 equation W(x) \\ exp(W(x)) = x. This function has multiple branches If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 548--550 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:555: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_1plusx}{\folio }{\code {log_1plusx}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.555 ...unction} {@@var{y} =} log_1plusx (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:556: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_1plusx}{\folio }{\code {log_1plusx}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.556 ...ar{y}, @@var{err}] =} log_1plusx (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:558: Use of \ doesn't match its definition. l.558 These routines compute \\ log(1 + x) for x > -1 using an algorithm that If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 563--565 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:570: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_1plusx_mx}{\folio }{\code {log_1plusx_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.570 ...tion} {@@var{y} =} log_1plusx_mx (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:571: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_1plusx_mx}{\folio }{\code {log_1plusx_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.571 ...y}, @@var{err}] =} log_1plusx_mx (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:573: Use of \ doesn't match its definition. l.573 These routines compute \\ log(1 + x) - x for x > -1 using an algorithm If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 578--580 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:585: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi}{\folio }{\code {psi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.585 ...dable Function} {@@var{y} =} psi (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:586: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi}{\folio }{\code {psi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.586 ...n} {[@@var{y}, @@var{err}] =} psi (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:588: Use of \ doesn't match its definition. l.588 ... routines compute the digamma function \\ psi(x) for general x, If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:589: Use of \ doesn't match its definition. l.589 x \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [8 \entry{lambert_W0}{8}{\code {lambert_W0}} \entry{lambert_W0}{8}{\code {lambert_W0}} \entry{lambert_Wm1}{8}{\code {lambert_Wm1}} \entry{lambert_Wm1}{8}{\code {lambert_Wm1}} \entry{log_1plusx}{8}{\code {log_1plusx}} \entry{log_1plusx}{8}{\code {log_1plusx}} \entry{log_1plusx_mx}{8}{\code {log_1plusx_mx}} \entry{log_1plusx_mx}{8}{\code {log_1plusx_mx}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 594--596 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:601: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_1piy}{\folio }{\code {psi_1piy}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.601 ... Function} {@@var{y} =} psi_1piy (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:602: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_1piy}{\folio }{\code {psi_1piy}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.602 ...@@var{y}, @@var{err}] =} psi_1piy (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:605: Use of \ doesn't match its definition. l.605 the line 1+i y, Re[\\ psi(1 + i y)]. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 609--611 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:616: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{synchrotron_1}{\folio }{\code {synchrotron... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.616 ...tion} {@@var{y} =} synchrotron_1 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:617: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{synchrotron_1}{\folio }{\code {synchrotron... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.617 ...y}, @@var{err}] =} synchrotron_1 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:620: Use of \ doesn't match its definition. l.620 x \\ int_x^\\infty dt K_@@{5/3@@}(t) for x >= 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:620: Use of \ doesn't match its definition. l.620 x \\int_x^\\ infty dt K_@@{5/3@@}(t) for x >= 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 624--626 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:631: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{synchrotron_2}{\folio }{\code {synchrotron... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.631 ...tion} {@@var{y} =} synchrotron_2 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:632: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{synchrotron_2}{\folio }{\code {synchrotron... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.632 ...y}, @@var{err}] =} synchrotron_2 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 639--641 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:646: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_2}{\folio }{\code {transport_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.646 ...nction} {@@var{y} =} transport_2 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:647: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_2}{\folio }{\code {transport_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.647 ...r{y}, @@var{err}] =} transport_2 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:652: Use of \ doesn't match its definition. l.652 representations J(n,x) := \\ int_0^x dt t^n e^t /(e^t - 1)^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 656--658 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:663: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_3}{\folio }{\code {transport_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.663 ...nction} {@@var{y} =} transport_3 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:664: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_3}{\folio }{\code {transport_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.664 ...r{y}, @@var{err}] =} transport_3 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [9 \entry{psi}{9}{\code {psi}} \entry{psi}{9}{\code {psi}} \entry{psi_1piy}{9}{\code {psi_1piy}} \entry{psi_1piy}{9}{\code {psi_1piy}} \entry{synchrotron_1}{9}{\code {synchrotron_1}} \entry{synchrotron_1}{9}{\code {synchrotron_1}} \entry{synchrotron_2}{9}{\code {synchrotron_2}} \entry{synchrotron_2}{9}{\code {synchrotron_2}} \entry{transport_2}{9}{\code {transport_2}} \entry{transport_2}{9}{\code {transport_2}} ] ./gsl.texi:669: Use of \ doesn't match its definition. l.669 representations J(n,x) := \\ int_0^x dt t^n e^t /(e^t - 1)^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 673--675 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:680: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_4}{\folio }{\code {transport_4}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.680 ...nction} {@@var{y} =} transport_4 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:681: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_4}{\folio }{\code {transport_4}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.681 ...r{y}, @@var{err}] =} transport_4 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:686: Use of \ doesn't match its definition. l.686 representations J(n,x) := \\ int_0^x dt t^n e^t /(e^t - 1)^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 690--692 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:697: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_5}{\folio }{\code {transport_5}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.697 ...nction} {@@var{y} =} transport_5 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:698: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_5}{\folio }{\code {transport_5}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.698 ...r{y}, @@var{err}] =} transport_5 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:703: Use of \ doesn't match its definition. l.703 representations J(n,x) := \\ int_0^x dt t^n e^t /(e^t - 1)^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 707--709 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:714: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{sinc_gsl}{\folio }{\code {sinc_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.714 ... Function} {@@var{y} =} sinc_gsl (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:715: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{sinc_gsl}{\folio }{\code {sinc_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.715 ...@@var{y}, @@var{err}] =} sinc_gsl (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:717: Use of \ doesn't match its definition. l.717 These routines compute \\ sinc(x) = \\sin(\\pi x) / (\\pi x) for any va... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:717: Use of \ doesn't match its definition. l.717 These routines compute \\sinc(x) = \\ sin(\\pi x) / (\\pi x) for any va... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:717: Use of \ doesn't match its definition. l.717 These routines compute \\sinc(x) = \\sin(\\ pi x) / (\\pi x) for any va... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:717: Use of \ doesn't match its definition. l.717 ...s compute \\sinc(x) = \\sin(\\pi x) / (\\ pi x) for any value of x. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 721--723 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:728: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnsinh}{\folio }{\code {lnsinh}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.728 ...le Function} {@@var{y} =} lnsinh (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:729: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnsinh}{\folio }{\code {lnsinh}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.729 ...{[@@var{y}, @@var{err}] =} lnsinh (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:731: Use of \ doesn't match its definition. l.731 These routines compute \\ log(\\sinh(x)) for x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:731: Use of \ doesn't match its definition. l.731 These routines compute \\log(\\ sinh(x)) for x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 735--737 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. [10 \entry{transport_3}{10}{\code {transport_3}} \entry{transport_3}{10}{\code {transport_3}} \entry{transport_4}{10}{\code {transport_4}} \entry{transport_4}{10}{\code {transport_4}} \entry{transport_5}{10}{\code {transport_5}} \entry{transport_5}{10}{\code {transport_5}} \entry{sinc_gsl}{10}{\code {sinc_gsl}} \entry{sinc_gsl}{10}{\code {sinc_gsl}} \entry{lnsinh}{10}{\code {lnsinh}} \entry{lnsinh}{10}{\code {lnsinh}} ] ./gsl.texi:742: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lncosh}{\folio }{\code {lncosh}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.742 ...le Function} {@@var{y} =} lncosh (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:743: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lncosh}{\folio }{\code {lncosh}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.743 ...{[@@var{y}, @@var{err}] =} lncosh (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:745: Use of \ doesn't match its definition. l.745 These routines compute \\ log(\\cosh(x)) for any x. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:745: Use of \ doesn't match its definition. l.745 These routines compute \\log(\\ cosh(x)) for any x. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 749--751 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:756: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{zeta}{\folio }{\code {zeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.756 ...able Function} {@@var{y} =} zeta (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:757: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{zeta}{\folio }{\code {zeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.757 ...} {[@@var{y}, @@var{err}] =} zeta (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:759: Use of \ doesn't match its definition. l.759 ...ines compute the Riemann zeta function \\ zeta(s) for If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:760: Use of \ doesn't match its definition. l.760 arbitrary s, s \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:764: Use of \ doesn't match its definition. l.764 \\ zeta(s) = \\sum_@@{k=1@@}^\\infty k^@@{-s@@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:764: Use of \ doesn't match its definition. l.764 \\zeta(s) = \\ sum_@@{k=1@@}^\\infty k^@@{-s@@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:764: Use of \ doesn't match its definition. l.764 \\zeta(s) = \\sum_@@{k=1@@}^\\ infty k^@@{-s@@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 768--770 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:775: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{eta}{\folio }{\code {eta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.775 ...dable Function} {@@var{y} =} eta (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:776: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{eta}{\folio }{\code {eta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.776 ...n} {[@@var{y}, @@var{err}] =} eta (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:778: Use of \ doesn't match its definition. l.778 These routines compute the eta function \\ eta(s) for arbitrary s. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:780: Use of \ doesn't match its definition. l.780 The eta function is defined by \\ eta(s) = (1-2^@@{1-s@@}) \\zeta(s). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:780: Use of \ doesn't match its definition. l.780 ...is defined by \\eta(s) = (1-2^@@{1-s@@}) \\ zeta(s). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 784--786 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:791: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Jn}{\folio }{\code {bessel_Jn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.791 ... {@@var{y} =} bessel_Jn (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:792: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Jn}{\folio }{\code {bessel_Jn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.792 ...var{y}, @@var{err}] =} bessel_Jn (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 799--801 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:806: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Yn}{\folio }{\code {bessel_Yn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.806 ... {@@var{y} =} bessel_Yn (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:807: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Yn}{\folio }{\code {bessel_Yn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.807 ...var{y}, @@var{err}] =} bessel_Yn (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 814--816 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:821: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_In}{\folio }{\code {bessel_In}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.821 ... {@@var{y} =} bessel_In (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [11 \entry{lncosh}{11}{\code {lncosh}} \entry{lncosh}{11}{\code {lncosh}} \entry{zeta}{11}{\code {zeta}} \entry{zeta}{11}{\code {zeta}} \entry{eta}{11}{\code {eta}} \entry{eta}{11}{\code {eta}} \entry{bessel_Jn}{11}{\code {bessel_Jn}} \entry{bessel_Jn}{11}{\code {bessel_Jn}} \entry{bessel_Yn}{11}{\code {bessel_Yn}} \entry{bessel_Yn}{11}{\code {bessel_Yn}} ] ./gsl.texi:822: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_In}{\folio }{\code {bessel_In}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.822 ...var{y}, @@var{err}] =} bessel_In (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 829--831 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:836: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_In_scaled}{\folio }{\code {bessel_I... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.836 ...y} =} bessel_In_scaled (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:837: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_In_scaled}{\folio }{\code {bessel_I... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.837 ... @@var{err}] =} bessel_In_scaled (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:840: Use of \ doesn't match its definition. l.840 function of order n, \\ exp(-|x|) I_n(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 844--846 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:851: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Kn}{\folio }{\code {bessel_Kn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.851 ... {@@var{y} =} bessel_Kn (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:852: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Kn}{\folio }{\code {bessel_Kn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.852 ...var{y}, @@var{err}] =} bessel_Kn (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 859--861 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:866: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Kn_scaled}{\folio }{\code {bessel_K... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.866 ...y} =} bessel_Kn_scaled (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:867: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Kn_scaled}{\folio }{\code {bessel_K... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.867 ... @@var{err}] =} bessel_Kn_scaled (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 873--875 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:880: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_jl}{\folio }{\code {bessel_jl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.880 ... {@@var{y} =} bessel_jl (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:881: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_jl}{\folio }{\code {bessel_jl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.881 ...var{y}, @@var{err}] =} bessel_jl (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 888--890 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:895: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_yl}{\folio }{\code {bessel_yl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.895 ... {@@var{y} =} bessel_yl (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:896: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_yl}{\folio }{\code {bessel_yl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.896 ...var{y}, @@var{err}] =} bessel_yl (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [12 \entry{bessel_In}{12}{\code {bessel_In}} \entry{bessel_In}{12}{\code {bessel_In}} \entry{bessel_In_scaled}{12}{\code {bessel_In_scaled}} \entry{bessel_In_scaled}{12}{\code {bessel_In_scaled}} \entry{bessel_Kn}{12}{\code {bessel_Kn}} \entry{bessel_Kn}{12}{\code {bessel_Kn}} \entry{bessel_Kn_scaled}{12}{\code {bessel_Kn_scaled}} \entry{bessel_Kn_scaled}{12}{\code {bessel_Kn_scaled}} \entry{bessel_jl}{12}{\code {bessel_jl}} \entry{bessel_jl}{12}{\code {bessel_jl}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 903--905 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:910: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_il_scaled}{\folio }{\code {bessel_i... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.910 ...y} =} bessel_il_scaled (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:911: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_il_scaled}{\folio }{\code {bessel_i... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.911 ... @@var{err}] =} bessel_il_scaled (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:914: Use of \ doesn't match its definition. l.914 function of order l, \\ exp(-|x|) i_l(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 918--920 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:925: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_kl_scaled}{\folio }{\code {bessel_k... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.925 ...y} =} bessel_kl_scaled (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:926: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_kl_scaled}{\folio }{\code {bessel_k... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.926 ... @@var{err}] =} bessel_kl_scaled (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:929: Use of \ doesn't match its definition. l.929 function of order l, \\ exp(x) k_l(x), for x>0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 933--935 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:940: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel_n}{\folio }{\code {exprel_n}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.940 ...} {@@var{y} =} exprel_n (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:941: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel_n}{\folio }{\code {exprel_n}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.941 ...@@var{y}, @@var{err}] =} exprel_n (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:947: Use of \ doesn't match its definition. l.947 exprel_N(x) = N!/x^N (\\ exp(x) - \\sum_@@{k=0@@}^@@{N-1@@} x^k/k!) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:947: Use of \ doesn't match its definition. l.947 exprel_N(x) = N!/x^N (\\exp(x) - \\ sum_@@{k=0@@}^@@{N-1@@} x^k/k!) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 953--955 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:960: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_int}{\folio }{\code {fermi_dir... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.960 ...{y} =} fermi_dirac_int (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:961: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_int}{\folio }{\code {fermi_dir... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.961 ..., @@var{err}] =} fermi_dirac_int (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:964: Use of \ doesn't match its definition. l.964 integer index of j, F_j(x) = (1/\\ Gamma(j+1)) \\int_0^\\infty dt (t^j If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:964: Use of \ doesn't match its definition. l.964 ... index of j, F_j(x) = (1/\\Gamma(j+1)) \\ int_0^\\infty dt (t^j If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:964: Use of \ doesn't match its definition. l.964 ...f j, F_j(x) = (1/\\Gamma(j+1)) \\int_0^\\ infty dt (t^j If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:965: Use of \ doesn't match its definition. l.965 /(\\ exp(t-x)+1)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 969--971 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. [13 \entry{bessel_yl}{13}{\code {bessel_yl}} \entry{bessel_yl}{13}{\code {bessel_yl}} \entry{bessel_il_scaled}{13}{\code {bessel_il_scaled}} \entry{bessel_il_scaled}{13}{\code {bessel_il_scaled}} \entry{bessel_kl_scaled}{13}{\code {bessel_kl_scaled}} \entry{bessel_kl_scaled}{13}{\code {bessel_kl_scaled}} \entry{exprel_n}{13}{\code {exprel_n}} \entry{exprel_n}{13}{\code {exprel_n}} ] ./gsl.texi:976: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{taylorcoeff}{\folio }{\code {taylorcoeff}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.976 ...@@var{y} =} taylorcoeff (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:977: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{taylorcoeff}{\folio }{\code {taylorcoeff}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.977 ...r{y}, @@var{err}] =} taylorcoeff (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 984--986 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:991: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Pl}{\folio }{\code {legendre_Pl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.991 ...@@var{y} =} legendre_Pl (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:992: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Pl}{\folio }{\code {legendre_Pl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.992 ...r{y}, @@var{err}] =} legendre_Pl (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 999--1001 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1006: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Ql}{\folio }{\code {legendre_Ql}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1006 ...var{y} =} legendre_Ql (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1007: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Ql}{\folio }{\code {legendre_Ql}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1007 ...{y}, @@var{err}] =} legendre_Ql (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1014--1016 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1021: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_n}{\folio }{\code {psi_n}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1021 ...on} {@@var{y} =} psi_n (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1022: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_n}{\folio }{\code {psi_n}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1022 ...{[@@var{y}, @@var{err}] =} psi_n (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1024: Use of \ doesn't match its definition. l.1024 ...utines compute the polygamma function \\ psi^@@{(m)@@}(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1029--1031 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1036: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Jnu}{\folio }{\code {bessel_Jnu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1036 ...@@var{z} =} bessel_Jnu (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1037: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Jnu}{\folio }{\code {bessel_Jnu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1037 ...r{z}, @@var{err}] =} bessel_Jnu (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1040: Use of \ doesn't match its definition. l.1040 fractional order nu, J_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [14 \entry{fermi_dirac_int}{14}{\code {fermi_dirac_int}} \entry{fermi_dirac_int}{14}{\code {fermi_dirac_int}} \entry{taylorcoeff}{14}{\code {taylorcoeff}} \entry{taylorcoeff}{14}{\code {taylorcoeff}} \entry{legendre_Pl}{14}{\code {legendre_Pl}} \entry{legendre_Pl}{14}{\code {legendre_Pl}} \entry{legendre_Ql}{14}{\code {legendre_Ql}} \entry{legendre_Ql}{14}{\code {legendre_Ql}} \entry{psi_n}{14}{\code {psi_n}} \entry{psi_n}{14}{\code {psi_n}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 1045--1047 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1052: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Ynu}{\folio }{\code {bessel_Ynu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1052 ...@@var{z} =} bessel_Ynu (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1053: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Ynu}{\folio }{\code {bessel_Ynu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1053 ...r{z}, @@var{err}] =} bessel_Ynu (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1056: Use of \ doesn't match its definition. l.1056 fractional order nu, Y_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1061--1063 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1068: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Inu}{\folio }{\code {bessel_Inu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1068 ...@@var{z} =} bessel_Inu (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1069: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Inu}{\folio }{\code {bessel_Inu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1069 ...r{z}, @@var{err}] =} bessel_Inu (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1072: Use of \ doesn't match its definition. l.1072 fractional order nu, I_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1073: Use of \ doesn't match its definition. l.1073 u(x) for x>0, \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1078--1080 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1085: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Inu_scaled}{\folio }{\code {bessel_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1085 ... =} bessel_Inu_scaled (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1086: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Inu_scaled}{\folio }{\code {bessel_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1086 ...var{err}] =} bessel_Inu_scaled (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1089: Use of \ doesn't match its definition. l.1089 fractional order nu, \\ exp(-|x|)I_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1089: Use of \ doesn't match its definition. l.1089 fractional order nu, \\exp(-|x|)I_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1090: Use of \ doesn't match its definition. l.1090 u(x) for x>0, \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1095--1097 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1102: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Knu}{\folio }{\code {bessel_Knu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1102 ...@@var{z} =} bessel_Knu (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1103: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Knu}{\folio }{\code {bessel_Knu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1103 ...r{z}, @@var{err}] =} bessel_Knu (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1106: Use of \ doesn't match its definition. l.1106 fractional order nu, K_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1107: Use of \ doesn't match its definition. l.1107 u(x) for x>0, \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1112--1114 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1119: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_lnKnu}{\folio }{\code {bessel_lnKnu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1119 ...ar{z} =} bessel_lnKnu (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [15 \entry{bessel_Jnu}{15}{\code {bessel_Jnu}} \entry{bessel_Jnu}{15}{\code {bessel_Jnu}} \entry{bessel_Ynu}{15}{\code {bessel_Ynu}} \entry{bessel_Ynu}{15}{\code {bessel_Ynu}} \entry{bessel_Inu}{15}{\code {bessel_Inu}} \entry{bessel_Inu}{15}{\code {bessel_Inu}} \entry{bessel_Inu_scaled}{15}{\code {bessel_Inu_scaled}} \entry{bessel_Inu_scaled}{15}{\code {bessel_Inu_scaled}} \entry{bessel_Knu}{15}{\code {bessel_Knu}} \entry{bessel_Knu}{15}{\code {bessel_Knu}} ] ./gsl.texi:1120: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_lnKnu}{\folio }{\code {bessel_lnKnu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1120 ...z}, @@var{err}] =} bessel_lnKnu (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1123: Use of \ doesn't match its definition. l.1123 function of fractional order nu, \\ ln(K_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1123: Use of \ doesn't match its definition. l.1123 function of fractional order nu, \\ln(K_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1124: Use of \ doesn't match its definition. l.1124 u(x)) for x>0, \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1129--1131 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1136: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Knu_scaled}{\folio }{\code {bessel_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1136 ... =} bessel_Knu_scaled (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1137: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Knu_scaled}{\folio }{\code {bessel_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1137 ...var{err}] =} bessel_Knu_scaled (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1140: Use of \ doesn't match its definition. l.1140 of fractional order nu, \\ exp(+|x|) K_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1140: Use of \ doesn't match its definition. l.1140 of fractional order nu, \\exp(+|x|) K_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1141: Use of \ doesn't match its definition. l.1141 u(x) for x>0, \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1146--1148 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1153: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exp_mult}{\folio }{\code {exp_mult}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1153 ... {@@var{z} =} exp_mult (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1154: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exp_mult}{\folio }{\code {exp_mult}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1154 ...var{z}, @@var{err}] =} exp_mult (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1157: Use of \ doesn't match its definition. l.1157 the product y \\ exp(x). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1161--1163 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1168: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_inc_0}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1168 ... =} fermi_dirac_inc_0 (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1169: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_inc_0}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1169 ...var{err}] =} fermi_dirac_inc_0 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1172: Use of \ doesn't match its definition. l.1172 index of zero, F_0(x,b) = \\ ln(1 + e^@@{b-x@@}) - (b-x). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1176--1178 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1183: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{poch}{\folio }{\code {poch}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1183 ...ion} {@@var{z} =} poch (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1184: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{poch}{\folio }{\code {poch}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1184 ... {[@@var{z}, @@var{err}] =} poch (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1188: Use of \ doesn't match its definition. l.1188 (a)_x := \\ Gamma(a + x)/\\Gamma(a), If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1188: Use of \ doesn't match its definition. l.1188 (a)_x := \\Gamma(a + x)/\\ Gamma(a), If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1195--1197 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. [16 \entry{bessel_lnKnu}{16}{\code {bessel_lnKnu}} \entry{bessel_lnKnu}{16}{\code {bessel_lnKnu}} \entry{bessel_Knu_scaled}{16}{\code {bessel_Knu_scaled}} \entry{bessel_Knu_scaled}{16}{\code {bessel_Knu_scaled}} \entry{exp_mult}{16}{\code {exp_mult}} \entry{exp_mult}{16}{\code {exp_mult}} \entry{fermi_dirac_inc_0}{16}{\code {fermi_dirac_inc_0}} \entry{fermi_dirac_inc_0}{16}{\code {fermi_dirac_inc_0}} \entry{poch}{16}{\code {poch}} \entry{poch}{16}{\code {poch}} ] ./gsl.texi:1202: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnpoch}{\folio }{\code {lnpoch}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1202 ...n} {@@var{z} =} lnpoch (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1203: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnpoch}{\folio }{\code {lnpoch}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1203 ...[@@var{z}, @@var{err}] =} lnpoch (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1206: Use of \ doesn't match its definition. l.1206 \\ log((a)_x) = \\log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1206: Use of \ doesn't match its definition. l.1206 \\log((a)_x) = \\ log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1206: Use of \ doesn't match its definition. l.1206 \\log((a)_x) = \\log(\\ Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1206: Use of \ doesn't match its definition. l.1206 \\log((a)_x) = \\log(\\Gamma(a + x)/\\ Gamma(a)) for a > 0, a+x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1210--1212 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1217: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{pochrel}{\folio }{\code {pochrel}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1217 ...} {@@var{z} =} pochrel (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1218: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{pochrel}{\folio }{\code {pochrel}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1218 ...@@var{z}, @@var{err}] =} pochrel (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1221: Use of \ doesn't match its definition. l.1221 where (a,x) = (a)_x := \\ Gamma(a + x)/\\Gamma(a). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1221: Use of \ doesn't match its definition. l.1221 where (a,x) = (a)_x := \\Gamma(a + x)/\\ Gamma(a). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1225--1227 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1232: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc_Q}{\folio }{\code {gamma_inc_Q}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1232 ...var{z} =} gamma_inc_Q (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1233: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc_Q}{\folio }{\code {gamma_inc_Q}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1233 ...{z}, @@var{err}] =} gamma_inc_Q (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1236: Use of \ doesn't match its definition. l.1236 Q(a,x) = 1/\\ Gamma(a) \\int_x\\infty dt t^@@{a-1@@} \\exp(-t) for a > 0... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1236: Use of \ doesn't match its definition. l.1236 Q(a,x) = 1/\\Gamma(a) \\ int_x\\infty dt t^@@{a-1@@} \\exp(-t) for a > 0... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1236: Use of \ doesn't match its definition. l.1236 Q(a,x) = 1/\\Gamma(a) \\int_x\\ infty dt t^@@{a-1@@} \\exp(-t) for a > 0... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1236: Use of \ doesn't match its definition. l.1236 ...\Gamma(a) \\int_x\\infty dt t^@@{a-1@@} \\ exp(-t) for a > 0, x >= 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1240--1242 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1247: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc_P}{\folio }{\code {gamma_inc_P}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1247 ...var{z} =} gamma_inc_P (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1248: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc_P}{\folio }{\code {gamma_inc_P}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1248 ...{z}, @@var{err}] =} gamma_inc_P (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1251: Use of \ doesn't match its definition. l.1251 Function P(a,x) = 1/\\ Gamma(a) \\int_0^x dt t^@@{a-1@@} \\exp(-t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1251: Use of \ doesn't match its definition. l.1251 Function P(a,x) = 1/\\Gamma(a) \\ int_0^x dt t^@@{a-1@@} \\exp(-t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1251: Use of \ doesn't match its definition. l.1251 ...= 1/\\Gamma(a) \\int_0^x dt t^@@{a-1@@} \\ exp(-t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1256--1258 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1263: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc}{\folio }{\code {gamma_inc}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1263 ...{@@var{z} =} gamma_inc (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1264: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc}{\folio }{\code {gamma_inc}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1264 ...ar{z}, @@var{err}] =} gamma_inc (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1268: Use of \ doesn't match its definition. l.1268 \\ Gamma(a,x) = \\int_x\\infty dt t^@@{a-1@@} \\exp(-t) for a real and x... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1268: Use of \ doesn't match its definition. l.1268 \\Gamma(a,x) = \\ int_x\\infty dt t^@@{a-1@@} \\exp(-t) for a real and x... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1268: Use of \ doesn't match its definition. l.1268 \\Gamma(a,x) = \\int_x\\ infty dt t^@@{a-1@@} \\exp(-t) for a real and x... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1268: Use of \ doesn't match its definition. l.1268 ...ma(a,x) = \\int_x\\infty dt t^@@{a-1@@} \\ exp(-t) for a real and x >... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [17 \entry{lnpoch}{17}{\code {lnpoch}} \entry{lnpoch}{17}{\code {lnpoch}} \entry{pochrel}{17}{\code {pochrel}} \entry{pochrel}{17}{\code {pochrel}} \entry{gamma_inc_Q}{17}{\code {gamma_inc_Q}} \entry{gamma_inc_Q}{17}{\code {gamma_inc_Q}} \entry{gamma_inc_P}{17}{\code {gamma_inc_P}} \entry{gamma_inc_P}{17}{\code {gamma_inc_P}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 1272--1274 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1279: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{beta_gsl}{\folio }{\code {beta_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1279 ... {@@var{z} =} beta_gsl (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1280: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{beta_gsl}{\folio }{\code {beta_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1280 ...var{z}, @@var{err}] =} beta_gsl (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1283: Use of \ doesn't match its definition. l.1283 B(a,b) = \\ Gamma(a)\\Gamma(b)/\\Gamma(a+b) for a > 0, b > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1283: Use of \ doesn't match its definition. l.1283 B(a,b) = \\Gamma(a)\\ Gamma(b)/\\Gamma(a+b) for a > 0, b > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1283: Use of \ doesn't match its definition. l.1283 B(a,b) = \\Gamma(a)\\Gamma(b)/\\ Gamma(a+b) for a > 0, b > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (20.37637pt too wide) in paragraph at lines 1282--1284 []@@textrm These rou-tines com-pute the Beta Func-tion, B(a,b) = Gamma(a)Gamma( b)/Gamma(a+b)| @@hbox(8.2125+2.73749)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm e .etc. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1287--1289 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1294: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnbeta}{\folio }{\code {lnbeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1294 ...n} {@@var{z} =} lnbeta (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1295: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnbeta}{\folio }{\code {lnbeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1295 ...[@@var{z}, @@var{err}] =} lnbeta (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1298: Use of \ doesn't match its definition. l.1298 \\ log(B(a,b)) for a > 0, b > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1302--1304 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1309: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_0F1}{\folio }{\code {hyperg_0F1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1309 ...@@var{z} =} hyperg_0F1 (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1310: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_0F1}{\folio }{\code {hyperg_0F1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1310 ...r{z}, @@var{err}] =} hyperg_0F1 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1316--1318 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1323: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_half}{\folio }{\code {conicalP_ha... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1323 ...r{z} =} conicalP_half (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1324: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_half}{\folio }{\code {conicalP_ha... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1324 ...}, @@var{err}] =} conicalP_half (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1327: Use of \ doesn't match its definition. l.1327 P^@@{1/2@@}_@@{-1/2 + i \\ lambda@@}(x) for x > -1. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1331--1333 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1338: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_mhalf}{\folio }{\code {conicalP_m... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1338 ...{z} =} conicalP_mhalf (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [18 \entry{gamma_inc}{18}{\code {gamma_inc}} \entry{gamma_inc}{18}{\code {gamma_inc}} \entry{beta_gsl}{18}{\code {beta_gsl}} \entry{beta_gsl}{18}{\code {beta_gsl}} \entry{lnbeta}{18}{\code {lnbeta}} \entry{lnbeta}{18}{\code {lnbeta}} \entry{hyperg_0F1}{18}{\code {hyperg_0F1}} \entry{hyperg_0F1}{18}{\code {hyperg_0F1}} \entry{conicalP_half}{18}{\code {conicalP_half}} \entry{conicalP_half}{18}{\code {conicalP_half}} ] ./gsl.texi:1339: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_mhalf}{\folio }{\code {conicalP_m... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1339 ..., @@var{err}] =} conicalP_mhalf (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1342: Use of \ doesn't match its definition. l.1342 P^@@{-1/2@@}_@@{-1/2 + i \\ lambda@@}(x) for x > -1. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1346--1348 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1353: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_0}{\folio }{\code {conicalP_0}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1353 ...@@var{z} =} conicalP_0 (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1354: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_0}{\folio }{\code {conicalP_0}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1354 ...r{z}, @@var{err}] =} conicalP_0 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1356: Use of \ doesn't match its definition. l.1356 ...e the conical function P^0_@@{-1/2 + i \\ lambda@@}(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1361--1363 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1368: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_1}{\folio }{\code {conicalP_1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1368 ...@@var{z} =} conicalP_1 (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1369: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_1}{\folio }{\code {conicalP_1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1369 ...r{z}, @@var{err}] =} conicalP_1 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1371: Use of \ doesn't match its definition. l.1371 ...e the conical function P^1_@@{-1/2 + i \\ lambda@@}(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1376--1378 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1383: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hzeta}{\folio }{\code {hzeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1383 ...on} {@@var{z} =} hzeta (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1384: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hzeta}{\folio }{\code {hzeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1384 ...{[@@var{z}, @@var{err}] =} hzeta (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1386: Use of \ doesn't match its definition. l.1386 ...nes compute the Hurwitz zeta function \\ zeta(s,q) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1391--1393 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1398: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai}{\folio }{\code {airy_Ai}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1398 ...@@var{y} =} airy_Ai (@@var{x}, @@var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1399: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai}{\folio }{\code {airy_Ai}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1399 ...@@var{y}, @@var{err}] =} airy_Ai (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [19 \entry{conicalP_mhalf}{19}{\code {conicalP_mhalf}} \entry{conicalP_mhalf}{19}{\code {conicalP_mhalf}} \entry{conicalP_0}{19}{\code {conicalP_0}} \entry{conicalP_0}{19}{\code {conicalP_0}} \entry{conicalP_1}{19}{\code {conicalP_1}} \entry{conicalP_1}{19}{\code {conicalP_1}} \entry{hzeta}{19}{\code {hzeta}} \entry{hzeta}{19}{\code {hzeta}} \entry{airy_Ai}{19}{\code {airy_Ai}} \entry{airy_Ai}{19}{\code {airy_Ai}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 1417--1419 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1424: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi}{\folio }{\code {airy_Bi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1424 ...@@var{y} =} airy_Bi (@@var{x}, @@var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1425: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi}{\folio }{\code {airy_Bi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1425 ...@@var{y}, @@var{err}] =} airy_Bi (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1443--1445 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1450: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_scaled}{\folio }{\code {airy_Ai_sc... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1450 ... =} airy_Ai_scaled (@@var{x}, @@var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1451: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_scaled}{\folio }{\code {airy_Ai_sc... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1451 ..., @@var{err}] =} airy_Ai_scaled (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1454: Use of \ doesn't match its definition. l.1454 ... For x>0 the scaling factor S_A(x) is \\ exp(+(2/3) x^(3/2)), and If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1470--1472 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1477: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_scaled}{\folio }{\code {airy_Bi_sc... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1477 ... =} airy_Bi_scaled (@@var{x}, @@var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1478: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_scaled}{\folio }{\code {airy_Bi_sc... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1478 ..., @@var{err}] =} airy_Bi_scaled (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [20 \entry{airy_Bi}{20}{\code {airy_Bi}} \entry{airy_Bi}{20}{\code {airy_Bi}} \entry{airy_Ai_scaled}{20}{\code {airy_Ai_scaled}} \entry{airy_Ai_scaled}{20}{\code {airy_Ai_scaled}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 1497--1499 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1504: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_deriv}{\folio }{\code {airy_Ai_der... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1504 ...} =} airy_Ai_deriv (@@var{x}, @@var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1505: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_deriv}{\folio }{\code {airy_Ai_der... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1505 ...}, @@var{err}] =} airy_Ai_deriv (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1523--1525 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1530: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_deriv}{\folio }{\code {airy_Bi_der... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1530 ...} =} airy_Bi_deriv (@@var{x}, @@var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1531: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_deriv}{\folio }{\code {airy_Bi_der... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1531 ...}, @@var{err}] =} airy_Bi_deriv (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [21 \entry{airy_Bi_scaled}{21}{\code {airy_Bi_scaled}} \entry{airy_Bi_scaled}{21}{\code {airy_Bi_scaled}} \entry{airy_Ai_deriv}{21}{\code {airy_Ai_deriv}} \entry{airy_Ai_deriv}{21}{\code {airy_Ai_deriv}} \entry{airy_Bi_deriv}{21}{\code {airy_Bi_deriv}} \entry{airy_Bi_deriv}{21}{\code {airy_Bi_deriv}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 1549--1551 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1556: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_deriv_scaled}{\folio }{\code {airy... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1556 ...ry_Ai_deriv_scaled (@@var{x}, @@var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1557: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_deriv_scaled}{\folio }{\code {airy... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1557 ...{err}] =} airy_Ai_deriv_scaled (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1575--1577 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1582: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_deriv_scaled}{\folio }{\code {airy... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1582 ...ry_Bi_deriv_scaled (@@var{x}, @@var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1583: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_deriv_scaled}{\folio }{\code {airy... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1583 ...{err}] =} airy_Bi_deriv_scaled (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1601--1603 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1608: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{ellint_Kcomp}{\folio }{\code {ellint_Kcomp}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1608 ...y} =} ellint_Kcomp (@@var{x}, @@var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1609: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{ellint_Kcomp}{\folio }{\code {ellint_Kcomp}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1609 ...y}, @@var{err}] =} ellint_Kcomp (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1613: Undefined control sequence. l.1613 \beforedisplay The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ./gsl.texi:1619: Undefined control sequence. l.1619 \afterdisplay The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. [22 \entry{airy_Ai_deriv_scaled}{22}{\code {airy_Ai_deriv_scaled}} \entry{airy_Ai_deriv_scaled}{22}{\code {airy_Ai_deriv_scaled}} \entry{airy_Bi_deriv_scaled}{22}{\code {airy_Bi_deriv_scaled}} \entry{airy_Bi_deriv_scaled}{22}{\code {airy_Bi_deriv_scaled}} \entry{ellint_Kcomp}{22}{\code {ellint_Kcomp}} \entry{ellint_Kcomp}{22}{\code {ellint_Kcomp}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 1641--1643 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1648: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{ellint_Ecomp}{\folio }{\code {ellint_Ecomp}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1648 ...y} =} ellint_Ecomp (@@var{x}, @@var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1649: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{ellint_Ecomp}{\folio }{\code {ellint_Ecomp}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1649 ...y}, @@var{err}] =} ellint_Ecomp (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1655: Undefined control sequence. l.1655 \beforedisplay The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ./gsl.texi:1661: Undefined control sequence. l.1661 \afterdisplay The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1683--1685 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1690: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Ai}{\folio }{\code {airy_zero_Ai}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1690 ...tion} {@@var{y} =} airy_zero_Ai (@@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1691: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Ai}{\folio }{\code {airy_zero_Ai}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1691 ...y}, @@var{err}] =} airy_zero_Ai (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [23 \entry{ellint_Ecomp}{23}{\code {ellint_Ecomp}} \entry{ellint_Ecomp}{23}{\code {ellint_Ecomp}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 1698--1700 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1705: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Bi}{\folio }{\code {airy_zero_Bi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1705 ...tion} {@@var{y} =} airy_zero_Bi (@@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1706: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Bi}{\folio }{\code {airy_zero_Bi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1706 ...y}, @@var{err}] =} airy_zero_Bi (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1713--1715 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1720: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Ai_deriv}{\folio }{\code {airy_z... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1720 ...{@@var{y} =} airy_zero_Ai_deriv (@@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1721: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Ai_deriv}{\folio }{\code {airy_z... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1721 ...ar{err}] =} airy_zero_Ai_deriv (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1728--1730 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1735: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Bi_deriv}{\folio }{\code {airy_z... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1735 ...{@@var{y} =} airy_zero_Bi_deriv (@@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1736: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Bi_deriv}{\folio }{\code {airy_z... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1736 ...ar{err}] =} airy_zero_Bi_deriv (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1743--1745 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1750: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_zero_J0}{\folio }{\code {bessel_zer... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1750 ...on} {@@var{y} =} bessel_zero_J0 (@@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1751: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_zero_J0}{\folio }{\code {bessel_zer... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1751 ..., @@var{err}] =} bessel_zero_J0 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1758--1760 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1765: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_zero_J1}{\folio }{\code {bessel_zer... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1765 ...on} {@@var{y} =} bessel_zero_J1 (@@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1766: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_zero_J1}{\folio }{\code {bessel_zer... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1766 ..., @@var{err}] =} bessel_zero_J1 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [24 \entry{airy_zero_Ai}{24}{\code {airy_zero_Ai}} \entry{airy_zero_Ai}{24}{\code {airy_zero_Ai}} \entry{airy_zero_Bi}{24}{\code {airy_zero_Bi}} \entry{airy_zero_Bi}{24}{\code {airy_zero_Bi}} \entry{airy_zero_Ai_deriv}{24}{\code {airy_zero_Ai_deriv}} \entry{airy_zero_Ai_deriv}{24}{\code {airy_zero_Ai_deriv}} \entry{airy_zero_Bi_deriv}{24}{\code {airy_zero_Bi_deriv}} \entry{airy_zero_Bi_deriv}{24}{\code {airy_zero_Bi_deriv}} \entry{bessel_zero_J0}{24}{\code {bessel_zero_J0}} \entry{bessel_zero_J0}{24}{\code {bessel_zero_J0}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 1773--1775 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1780: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_1_int}{\folio }{\code {psi_1_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1780 ...unction} {@@var{y} =} psi_1_int (@@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1781: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_1_int}{\folio }{\code {psi_1_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1781 ...ar{y}, @@var{err}] =} psi_1_int (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1783: Use of \ doesn't match its definition. l.1783 ...outines compute the Trigamma function \\ psi(n) for positive If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1788--1790 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1795: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{zeta_int}{\folio }{\code {zeta_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1795 ...Function} {@@var{y} =} zeta_int (@@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1796: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{zeta_int}{\folio }{\code {zeta_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1796 ...var{y}, @@var{err}] =} zeta_int (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1798: Use of \ doesn't match its definition. l.1798 ...nes compute the Riemann zeta function \\ zeta(n) for If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1799: Use of \ doesn't match its definition. l.1799 integer n, n \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1804--1806 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1811: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{eta_int}{\folio }{\code {eta_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1811 ... Function} {@@var{y} =} eta_int (@@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1812: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{eta_int}{\folio }{\code {eta_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1812 ...@@var{y}, @@var{err}] =} eta_int (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1814: Use of \ doesn't match its definition. l.1814 These routines compute the eta function \\ eta(n) for integer n. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1818--1820 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1825: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Plm}{\folio }{\code {legendre_Plm}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1825 ...legendre_Plm (@@var{n}, @@var{m}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1826: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Plm}{\folio }{\code {legendre_Plm}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1826 ...y}, @@var{err}] =} legendre_Plm (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1833--1835 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1840: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_sphPlm}{\folio }{\code {legendre_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1840 ...endre_sphPlm (@@var{n}, @@var{m}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1841: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_sphPlm}{\folio }{\code {legendre_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1841 ... @@var{err}] =} legendre_sphPlm (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1844: Use of \ doesn't match its definition. l.1844 $\\ sqrt@@{(2l+1)/(4\\pi)@@} \\sqrt@@{(l-m)!/(l+m)!@@} P_l^m(x)$ suitable ... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1844: Use of \ doesn't match its definition. l.1844 $\\sqrt@@{(2l+1)/(4\\ pi)@@} \\sqrt@@{(l-m)!/(l+m)!@@} P_l^m(x)$ suitable ... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1844: Use of \ doesn't match its definition. l.1844 $\\sqrt@@{(2l+1)/(4\\pi)@@} \\ sqrt@@{(l-m)!/(l+m)!@@} P_l^m(x)$ suitable ... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Underfull \hbox (badness 10000) in paragraph at lines 1843--1848 []@@textrm These rou-tines com-pute the nor-mal-ized as-so-ci-ated Leg-en-dre p oly-no-mial @@hbox(7.60416+2.12917)x433.62, glue set 4.66573 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm e .etc. [25 \entry{bessel_zero_J1}{25}{\code {bessel_zero_J1}} \entry{bessel_zero_J1}{25}{\code {bessel_zero_J1}} \entry{psi_1_int}{25}{\code {psi_1_int}} \entry{psi_1_int}{25}{\code {psi_1_int}} \entry{zeta_int}{25}{\code {zeta_int}} \entry{zeta_int}{25}{\code {zeta_int}} \entry{eta_int}{25}{\code {eta_int}} \entry{eta_int}{25}{\code {eta_int}} \entry{legendre_Plm}{25}{\code {legendre_Plm}} \entry{legendre_Plm}{25}{\code {legendre_Plm}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 1851--1853 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1858: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_U}{\folio }{\code {hyperg_U}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1858 ... hyperg_U (@@var{x0}, @@var{x1}, @@var{x2}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1859: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_U}{\folio }{\code {hyperg_U}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1859 ...r{out}, @@var{err}] =} hyperg_U (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1866--1868 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1873: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_1F1}{\folio }{\code {hyperg_1F1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1873 ...yperg_1F1 (@@var{x0}, @@var{x1}, @@var{x2}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1874: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_1F1}{\folio }{\code {hyperg_1F1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1874 ...out}, @@var{err}] =} hyperg_1F1 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 1881--1883 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1888: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gsl_sf}{\folio }{\code {gsl_sf}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1888 @@deftypefn {Loadable Function} {} gsl_sf () A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1896: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{clausen}{\folio }{\code {clausen}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1896 ... Function} {@@var{y} =} clausen (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1897: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{clausen}{\folio }{\code {clausen}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1897 ...@@var{y}, @@var{err}] =} clausen (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1901: Use of \ doesn't match its definition. l.1901 Cl_2(x) = - \\ int_0^x dt \\log(2 \\sin(t/2)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1901: Use of \ doesn't match its definition. l.1901 Cl_2(x) = - \\int_0^x dt \\ log(2 \\sin(t/2)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1901: Use of \ doesn't match its definition. l.1901 Cl_2(x) = - \\int_0^x dt \\log(2 \\ sin(t/2)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1903: Use of \ doesn't match its definition. l.1903 It is related to the dilogarithm by Cl_2(\\ theta) = \\Im Li_2(\\exp(i... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1903: Use of \ doesn't match its definition. l.1903 ...to the dilogarithm by Cl_2(\\theta) = \\ Im Li_2(\\exp(i \\theta)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1903: Use of \ doesn't match its definition. l.1903 ...ogarithm by Cl_2(\\theta) = \\Im Li_2(\\ exp(i \\theta)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1903: Use of \ doesn't match its definition. l.1903 ... by Cl_2(\\theta) = \\Im Li_2(\\exp(i \\ theta)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1907--1909 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1914: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{dawson}{\folio }{\code {dawson}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1914 ...e Function} {@@var{y} =} dawson (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1915: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{dawson}{\folio }{\code {dawson}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1915 ...[@@var{y}, @@var{err}] =} dawson (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1917: Use of \ doesn't match its definition. l.1917 The Dawson integral is defined by \\ exp(-x^2) \\int_0^x dt \\exp(t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1917: Use of \ doesn't match its definition. l.1917 ...on integral is defined by \\exp(-x^2) \\ int_0^x dt \\exp(t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:1917: Use of \ doesn't match its definition. l.1917 ...s defined by \\exp(-x^2) \\int_0^x dt \\ exp(t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [26 \entry{legendre_sphPlm}{26}{\code {legendre_sphPlm}} \entry{legendre_sphPlm}{26}{\code {legendre_sphPlm}} \entry{hyperg_U}{26}{\code {hyperg_U}} \entry{hyperg_U}{26}{\code {hyperg_U}} \entry{hyperg_1F1}{26}{\code {hyperg_1F1}} \entry{hyperg_1F1}{26}{\code {hyperg_1F1}} \entry{gsl_sf}{26}{\code {gsl_sf}} \entry{clausen}{26}{\code {clausen}} \entry{clausen}{26}{\code {clausen}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 1922--1924 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1929: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_1}{\folio }{\code {debye_1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1929 ... Function} {@@var{y} =} debye_1 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1930: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_1}{\folio }{\code {debye_1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1930 ...@@var{y}, @@var{err}] =} debye_1 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1934: Use of \ doesn't match its definition. l.1934 D_n(x) = n/x^n \\ int_0^x dt (t^n/(e^t - 1)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1940--1942 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1947: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_2}{\folio }{\code {debye_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1947 ... Function} {@@var{y} =} debye_2 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1948: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_2}{\folio }{\code {debye_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1948 ...@@var{y}, @@var{err}] =} debye_2 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1952: Use of \ doesn't match its definition. l.1952 D_n(x) = n/x^n \\ int_0^x dt (t^n/(e^t - 1)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1958--1960 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1965: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_3}{\folio }{\code {debye_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1965 ... Function} {@@var{y} =} debye_3 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1966: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_3}{\folio }{\code {debye_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1966 ...@@var{y}, @@var{err}] =} debye_3 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1970: Use of \ doesn't match its definition. l.1970 D_n(x) = n/x^n \\ int_0^x dt (t^n/(e^t - 1)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 1976--1978 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:1983: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_4}{\folio }{\code {debye_4}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1983 ... Function} {@@var{y} =} debye_4 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1984: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{debye_4}{\folio }{\code {debye_4}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.1984 ...@@var{y}, @@var{err}] =} debye_4 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:1988: Use of \ doesn't match its definition. l.1988 D_n(x) = n/x^n \\ int_0^x dt (t^n/(e^t - 1)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [27 \entry{dawson}{27}{\code {dawson}} \entry{dawson}{27}{\code {dawson}} \entry{debye_1}{27}{\code {debye_1}} \entry{debye_1}{27}{\code {debye_1}} \entry{debye_2}{27}{\code {debye_2}} \entry{debye_2}{27}{\code {debye_2}} \entry{debye_3}{27}{\code {debye_3}} \entry{debye_3}{27}{\code {debye_3}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 1994--1996 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2001: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_gsl}{\folio }{\code {erf_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2001 ... Function} {@@var{y} =} erf_gsl (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2002: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_gsl}{\folio }{\code {erf_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2002 ...@@var{y}, @@var{err}] =} erf_gsl (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2005: Use of \ doesn't match its definition. l.2005 erf(x) = (2/\\ sqrt(\\pi)) \\int_0^x dt \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2005: Use of \ doesn't match its definition. l.2005 erf(x) = (2/\\sqrt(\\ pi)) \\int_0^x dt \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2005: Use of \ doesn't match its definition. l.2005 erf(x) = (2/\\sqrt(\\pi)) \\ int_0^x dt \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2005: Use of \ doesn't match its definition. l.2005 erf(x) = (2/\\sqrt(\\pi)) \\int_0^x dt \\ exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2009--2011 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2016: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erfc_gsl}{\folio }{\code {erfc_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2016 ...Function} {@@var{y} =} erfc_gsl (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2017: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erfc_gsl}{\folio }{\code {erfc_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2017 ...var{y}, @@var{err}] =} erfc_gsl (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2020: Use of \ doesn't match its definition. l.2020 erfc(x) = 1 - erf(x) = (2/\\ sqrt(\\pi)) \\int_x^\\infty \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2020: Use of \ doesn't match its definition. l.2020 erfc(x) = 1 - erf(x) = (2/\\sqrt(\\ pi)) \\int_x^\\infty \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2020: Use of \ doesn't match its definition. l.2020 erfc(x) = 1 - erf(x) = (2/\\sqrt(\\pi)) \\ int_x^\\infty \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2020: Use of \ doesn't match its definition. l.2020 ...1 - erf(x) = (2/\\sqrt(\\pi)) \\int_x^\\ infty \\exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2020: Use of \ doesn't match its definition. l.2020 ...x) = (2/\\sqrt(\\pi)) \\int_x^\\infty \\ exp(-t^2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2024--2026 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2031: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_erfc}{\folio }{\code {log_erfc}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2031 ...Function} {@@var{y} =} log_erfc (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2032: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_erfc}{\folio }{\code {log_erfc}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2032 ...var{y}, @@var{err}] =} log_erfc (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2035: Use of \ doesn't match its definition. l.2035 function \\ log(\\erfc(x)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2035: Use of \ doesn't match its definition. l.2035 function \\log(\\ erfc(x)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2039--2041 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2046: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_Z}{\folio }{\code {erf_Z}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2046 ...le Function} {@@var{y} =} erf_Z (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2047: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_Z}{\folio }{\code {erf_Z}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2047 ...{[@@var{y}, @@var{err}] =} erf_Z (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2050: Use of \ doesn't match its definition. l.2050 Z(x) = (1/(2\\ pi)) \\exp(-x^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2050: Use of \ doesn't match its definition. l.2050 Z(x) = (1/(2\\pi)) \\ exp(-x^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2054--2056 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2061: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_Q}{\folio }{\code {erf_Q}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2061 ...le Function} {@@var{y} =} erf_Q (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [28 \entry{debye_4}{28}{\code {debye_4}} \entry{debye_4}{28}{\code {debye_4}} \entry{erf_gsl}{28}{\code {erf_gsl}} \entry{erf_gsl}{28}{\code {erf_gsl}} \entry{erfc_gsl}{28}{\code {erfc_gsl}} \entry{erfc_gsl}{28}{\code {erfc_gsl}} \entry{log_erfc}{28}{\code {log_erfc}} \entry{log_erfc}{28}{\code {log_erfc}} \entry{erf_Z}{28}{\code {erf_Z}} \entry{erf_Z}{28}{\code {erf_Z}} ] ./gsl.texi:2062: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{erf_Q}{\folio }{\code {erf_Q}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2062 ...{[@@var{y}, @@var{err}] =} erf_Q (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2065: Use of \ doesn't match its definition. l.2065 function Q(x) = (1/(2\\ pi)) \\int_x^\\infty dt \\exp(-t^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2065: Use of \ doesn't match its definition. l.2065 function Q(x) = (1/(2\\pi)) \\ int_x^\\infty dt \\exp(-t^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2065: Use of \ doesn't match its definition. l.2065 function Q(x) = (1/(2\\pi)) \\int_x^\\ infty dt \\exp(-t^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2065: Use of \ doesn't match its definition. l.2065 ...Q(x) = (1/(2\\pi)) \\int_x^\\infty dt \\ exp(-t^2/2). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2069--2071 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2076: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hazard}{\folio }{\code {hazard}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2076 ...e Function} {@@var{y} =} hazard (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2077: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hazard}{\folio }{\code {hazard}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2077 ...[@@var{y}, @@var{err}] =} hazard (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2080: Use of \ doesn't match its definition. l.2080 inverse Mill\\ 's ratio, is defined as If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2081: Use of \ doesn't match its definition. l.2081 h(x) = Z(x)/Q(x) = \\ sqrt@@{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2081: Use of \ doesn't match its definition. l.2081 h(x) = Z(x)/Q(x) = \\sqrt@@{2/\\ pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2081: Use of \ doesn't match its definition. l.2081 h(x) = Z(x)/Q(x) = \\sqrt@@{2/\\pi \\ exp(-x^2 / 2) / \\erfc(x/\\sqrt 2... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2081: Use of \ doesn't match its definition. l.2081 ...x) = \\sqrt@@{2/\\pi \\exp(-x^2 / 2) / \\ erfc(x/\\sqrt 2)@@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2081: Use of \ doesn't match its definition. l.2081 ...rt@@{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\ sqrt 2)@@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2082: Use of \ doesn't match its definition. l.2082 It decreases rapidly as x approaches -\\ infty and asymptotes to If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2083: Use of \ doesn't match its definition. l.2083 h(x) \\ sim x as x approaches +\\infty. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2083: Use of \ doesn't match its definition. l.2083 h(x) \\sim x as x approaches +\\ infty. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2087--2089 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2094: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expm1}{\folio }{\code {expm1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2094 ...le Function} {@@var{y} =} expm1 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2095: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expm1}{\folio }{\code {expm1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2095 ...{[@@var{y}, @@var{err}] =} expm1 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2097: Use of \ doesn't match its definition. l.2097 These routines compute the quantity \\ exp(x)-1 using an algorithm that If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2102--2104 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2109: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel}{\folio }{\code {exprel}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2109 ...e Function} {@@var{y} =} exprel (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2110: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel}{\folio }{\code {exprel}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2110 ...[@@var{y}, @@var{err}] =} exprel (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2112: Use of \ doesn't match its definition. l.2112 These routines compute the quantity (\\ exp(x)-1)/x using an algorithm If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2114: Use of \ doesn't match its definition. l.2114 the expansion (\\ exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2114: Use of \ doesn't match its definition. l.2114 ...= 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\ dots. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2118--2120 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2125: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel_2}{\folio }{\code {exprel_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2125 ...Function} {@@var{y} =} exprel_2 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2126: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel_2}{\folio }{\code {exprel_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2126 ...var{y}, @@var{err}] =} exprel_2 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2128: Use of \ doesn't match its definition. l.2128 These routines compute the quantity 2(\\ exp(x)-1-x)/x^2 using an If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2131: Use of \ doesn't match its definition. l.2131 2(\\ exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\dots. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2131: Use of \ doesn't match its definition. l.2131 ...= 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\ dots. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [29 \entry{erf_Q}{29}{\code {erf_Q}} \entry{erf_Q}{29}{\code {erf_Q}} \entry{hazard}{29}{\code {hazard}} \entry{hazard}{29}{\code {hazard}} \entry{expm1}{29}{\code {expm1}} \entry{expm1}{29}{\code {expm1}} \entry{exprel}{29}{\code {exprel}} \entry{exprel}{29}{\code {exprel}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 2135--2137 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2142: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_E1}{\folio }{\code {expint_E1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2142 ...unction} {@@var{y} =} expint_E1 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2143: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_E1}{\folio }{\code {expint_E1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2143 ...ar{y}, @@var{err}] =} expint_E1 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2147: Use of \ doesn't match its definition. l.2147 E_1(x) := Re \\ int_1^\\infty dt \\exp(-xt)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2147: Use of \ doesn't match its definition. l.2147 E_1(x) := Re \\int_1^\\ infty dt \\exp(-xt)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2147: Use of \ doesn't match its definition. l.2147 E_1(x) := Re \\int_1^\\infty dt \\ exp(-xt)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2151--2153 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2158: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_E2}{\folio }{\code {expint_E2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2158 ...unction} {@@var{y} =} expint_E2 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2159: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_E2}{\folio }{\code {expint_E2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2159 ...ar{y}, @@var{err}] =} expint_E2 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2163: Use of \ doesn't match its definition. l.2163 E_2(x) := \\ Re \\int_1^\\infty dt \\exp(-xt)/t^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2163: Use of \ doesn't match its definition. l.2163 E_2(x) := \\Re \\ int_1^\\infty dt \\exp(-xt)/t^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2163: Use of \ doesn't match its definition. l.2163 E_2(x) := \\Re \\int_1^\\ infty dt \\exp(-xt)/t^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2163: Use of \ doesn't match its definition. l.2163 E_2(x) := \\Re \\int_1^\\infty dt \\ exp(-xt)/t^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2167--2169 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2174: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_Ei}{\folio }{\code {expint_Ei}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2174 ...unction} {@@var{y} =} expint_Ei (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2175: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_Ei}{\folio }{\code {expint_Ei}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2175 ...ar{y}, @@var{err}] =} expint_Ei (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2179: Use of \ doesn't match its definition. l.2179 Ei(x) := - PV(\\ int_@@{-x@@}^\\infty dt \\exp(-t)/t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2179: Use of \ doesn't match its definition. l.2179 Ei(x) := - PV(\\int_@@{-x@@}^\\ infty dt \\exp(-t)/t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2179: Use of \ doesn't match its definition. l.2179 Ei(x) := - PV(\\int_@@{-x@@}^\\infty dt \\ exp(-t)/t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2185--2187 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2192: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Shi}{\folio }{\code {Shi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2192 ...able Function} {@@var{y} =} Shi (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2193: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Shi}{\folio }{\code {Shi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2193 ...} {[@@var{y}, @@var{err}] =} Shi (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2195: Use of \ doesn't match its definition. l.2195 ...outines compute the integral Shi(x) = \\ int_0^x dt \\sinh(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2195: Use of \ doesn't match its definition. l.2195 ...te the integral Shi(x) = \\int_0^x dt \\ sinh(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2199--2201 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. [30 \entry{exprel_2}{30}{\code {exprel_2}} \entry{exprel_2}{30}{\code {exprel_2}} \entry{expint_E1}{30}{\code {expint_E1}} \entry{expint_E1}{30}{\code {expint_E1}} \entry{expint_E2}{30}{\code {expint_E2}} \entry{expint_E2}{30}{\code {expint_E2}} \entry{expint_Ei}{30}{\code {expint_Ei}} \entry{expint_Ei}{30}{\code {expint_Ei}} \entry{Shi}{30}{\code {Shi}} \entry{Shi}{30}{\code {Shi}} ] ./gsl.texi:2206: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Chi}{\folio }{\code {Chi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2206 ...able Function} {@@var{y} =} Chi (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2207: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Chi}{\folio }{\code {Chi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2207 ...} {[@@var{y}, @@var{err}] =} Chi (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2211: Use of \ doesn't match its definition. l.2211 Chi(x) := Re[ \\ gamma_E + \\log(x) + \\int_0^x dt (\\cosh[t]-1)/t] , If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2211: Use of \ doesn't match its definition. l.2211 Chi(x) := Re[ \\gamma_E + \\ log(x) + \\int_0^x dt (\\cosh[t]-1)/t] , If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2211: Use of \ doesn't match its definition. l.2211 Chi(x) := Re[ \\gamma_E + \\log(x) + \\ int_0^x dt (\\cosh[t]-1)/t] , If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2211: Use of \ doesn't match its definition. l.2211 ... \\gamma_E + \\log(x) + \\int_0^x dt (\\ cosh[t]-1)/t] , If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2213: Use of \ doesn't match its definition. l.2213 where \\ gamma_E is the Euler constant. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2217--2219 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2224: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_3}{\folio }{\code {expint_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2224 ...Function} {@@var{y} =} expint_3 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2225: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{expint_3}{\folio }{\code {expint_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2225 ...var{y}, @@var{err}] =} expint_3 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2228: Use of \ doesn't match its definition. l.2228 Ei_3(x) = \\ int_0^x dt \\exp(-t^3) for x >= 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2228: Use of \ doesn't match its definition. l.2228 Ei_3(x) = \\int_0^x dt \\ exp(-t^3) for x >= 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2232--2234 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2239: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Si}{\folio }{\code {Si}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2239 ...dable Function} {@@var{y} =} Si (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2240: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Si}{\folio }{\code {Si}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2240 ...n} {[@@var{y}, @@var{err}] =} Si (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2242: Use of \ doesn't match its definition. l.2242 ...nes compute the Sine integral Si(x) = \\ int_0^x dt \\sin(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2242: Use of \ doesn't match its definition. l.2242 ...he Sine integral Si(x) = \\int_0^x dt \\ sin(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2246--2248 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2253: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Ci}{\folio }{\code {Ci}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2253 ...dable Function} {@@var{y} =} Ci (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2254: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{Ci}{\folio }{\code {Ci}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2254 ...n} {[@@var{y}, @@var{err}] =} Ci (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2257: Use of \ doesn't match its definition. l.2257 Ci(x) = -\\ int_x^\\infty dt \\cos(t)/t for x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2257: Use of \ doesn't match its definition. l.2257 Ci(x) = -\\int_x^\\ infty dt \\cos(t)/t for x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2257: Use of \ doesn't match its definition. l.2257 Ci(x) = -\\int_x^\\infty dt \\ cos(t)/t for x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2261--2263 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2268: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{atanint}{\folio }{\code {atanint}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2268 ... Function} {@@var{y} =} atanint (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2269: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{atanint}{\folio }{\code {atanint}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2269 ...@@var{y}, @@var{err}] =} atanint (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2272: Use of \ doesn't match its definition. l.2272 AtanInt(x) = \\ int_0^x dt \\arctan(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2272: Use of \ doesn't match its definition. l.2272 AtanInt(x) = \\int_0^x dt \\ arctan(t)/t. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2276--2278 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2283: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_mhalf}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2283 ... {@@var{y} =} fermi_dirac_mhalf (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2284: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_mhalf}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2284 ...var{err}] =} fermi_dirac_mhalf (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [31 \entry{Chi}{31}{\code {Chi}} \entry{Chi}{31}{\code {Chi}} \entry{expint_3}{31}{\code {expint_3}} \entry{expint_3}{31}{\code {expint_3}} \entry{Si}{31}{\code {Si}} \entry{Si}{31}{\code {Si}} \entry{Ci}{31}{\code {Ci}} \entry{Ci}{31}{\code {Ci}} \entry{atanint}{31}{\code {atanint}} \entry{atanint}{31}{\code {atanint}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 2290--2292 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2297: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_half}{\folio }{\code {fermi_di... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2297 ...} {@@var{y} =} fermi_dirac_half (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2298: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_half}{\folio }{\code {fermi_di... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2298 ...@@var{err}] =} fermi_dirac_half (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2304--2306 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2311: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_3half}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2311 ... {@@var{y} =} fermi_dirac_3half (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2312: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_3half}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2312 ...var{err}] =} fermi_dirac_3half (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2318--2320 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2325: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_gsl}{\folio }{\code {gamma_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2325 ...unction} {@@var{y} =} gamma_gsl (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2326: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_gsl}{\folio }{\code {gamma_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2326 ...ar{y}, @@var{err}] =} gamma_gsl (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2328: Use of \ doesn't match its definition. l.2328 ...e routines compute the Gamma function \\ Gamma(x), subject to x not If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2330: Use of \ doesn't match its definition. l.2330 ...hod. The maximum value of x such that \\ Gamma(x) is not If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2335--2337 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2342: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lngamma_gsl}{\folio }{\code {lngamma_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2342 ...ction} {@@var{y} =} lngamma_gsl (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2343: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lngamma_gsl}{\folio }{\code {lngamma_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2343 ...{y}, @@var{err}] =} lngamma_gsl (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2346: Use of \ doesn't match its definition. l.2346 \\ log(\\Gamma(x)), subject to x not a being negative integer. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2346: Use of \ doesn't match its definition. l.2346 \\log(\\ Gamma(x)), subject to x not a being negative integer. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2347: Use of \ doesn't match its definition. l.2347 For x<0 the real part of \\ log(\\Gamma(x)) is returned, which is If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2347: Use of \ doesn't match its definition. l.2347 For x<0 the real part of \\log(\\ Gamma(x)) is returned, which is If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2348: Use of \ doesn't match its definition. l.2348 equivalent to \\ log(|\\Gamma(x)|). The function is computed using If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2348: Use of \ doesn't match its definition. l.2348 equivalent to \\log(|\\ Gamma(x)|). The function is computed using If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2353--2355 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. [32 \entry{fermi_dirac_mhalf}{32}{\code {fermi_dirac_mhalf}} \entry{fermi_dirac_mhalf}{32}{\code {fermi_dirac_mhalf}} \entry{fermi_dirac_half}{32}{\code {fermi_dirac_half}} \entry{fermi_dirac_half}{32}{\code {fermi_dirac_half}} \entry{fermi_dirac_3half}{32}{\code {fermi_dirac_3half}} \entry{fermi_dirac_3half}{32}{\code {fermi_dirac_3half}} \entry{gamma_gsl}{32}{\code {gamma_gsl}} \entry{gamma_gsl}{32}{\code {gamma_gsl}} \entry{lngamma_gsl}{32}{\code {lngamma_gsl}} \entry{lngamma_gsl}{32}{\code {lngamma_gsl}} ] ./gsl.texi:2360: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gammastar}{\folio }{\code {gammastar}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2360 ...unction} {@@var{y} =} gammastar (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2361: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gammastar}{\folio }{\code {gammastar}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2361 ...ar{y}, @@var{err}] =} gammastar (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2363: Use of \ doesn't match its definition. l.2363 ... compute the regulated Gamma Function \\ Gamma^*(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2366: Use of \ doesn't match its definition. l.2366 \\ Gamma^*(x) = \\Gamma(x)/(\\sqrt@@{2\\pi@@} x^@@{(x-1/2)@@} \\exp(-x)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2366: Use of \ doesn't match its definition. l.2366 \\Gamma^*(x) = \\ Gamma(x)/(\\sqrt@@{2\\pi@@} x^@@{(x-1/2)@@} \\exp(-x)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2366: Use of \ doesn't match its definition. l.2366 \\Gamma^*(x) = \\Gamma(x)/(\\ sqrt@@{2\\pi@@} x^@@{(x-1/2)@@} \\exp(-x)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2366: Use of \ doesn't match its definition. l.2366 \\Gamma^*(x) = \\Gamma(x)/(\\sqrt@@{2\\ pi@@} x^@@{(x-1/2)@@} \\exp(-x)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2366: Use of \ doesn't match its definition. l.2366 ...mma(x)/(\\sqrt@@{2\\pi@@} x^@@{(x-1/2)@@} \\ exp(-x)) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2367: Use of \ doesn't match its definition. l.2367 = (1 + (1/12x) + ...) for x \\ to \\infty If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2367: Use of \ doesn't match its definition. l.2367 ... = (1 + (1/12x) + ...) for x \\to \\ infty If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2373--2375 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2380: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gammainv_gsl}{\folio }{\code {gammainv_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2380 ...tion} {@@var{y} =} gammainv_gsl (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2381: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gammainv_gsl}{\folio }{\code {gammainv_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2381 ...y}, @@var{err}] =} gammainv_gsl (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2383: Use of \ doesn't match its definition. l.2383 ...e reciprocal of the gamma function, 1/\\ Gamma(x) using the real La... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2387--2389 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2394: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lambert_W0}{\folio }{\code {lambert_W0}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2394 ...nction} {@@var{y} =} lambert_W0 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2395: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lambert_W0}{\folio }{\code {lambert_W0}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2395 ...r{y}, @@var{err}] =} lambert_W0 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2399: Use of \ doesn't match its definition. l.2399 Lambert\\ 's W functions, W(x), are defined to be solutions of the If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2400: Use of \ doesn't match its definition. l.2400 equation W(x) \\ exp(W(x)) = x. This function has multiple branches If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2407--2409 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2414: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lambert_Wm1}{\folio }{\code {lambert_Wm1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2414 ...ction} {@@var{y} =} lambert_Wm1 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2415: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lambert_Wm1}{\folio }{\code {lambert_Wm1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2415 ...{y}, @@var{err}] =} lambert_Wm1 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2420: Use of \ doesn't match its definition. l.2420 Lambert\\ 's W functions, W(x), are defined to be solutions of the If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2421: Use of \ doesn't match its definition. l.2421 equation W(x) \\ exp(W(x)) = x. This function has multiple branches If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2428--2430 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. [33 \entry{gammastar}{33}{\code {gammastar}} \entry{gammastar}{33}{\code {gammastar}} \entry{gammainv_gsl}{33}{\code {gammainv_gsl}} \entry{gammainv_gsl}{33}{\code {gammainv_gsl}} \entry{lambert_W0}{33}{\code {lambert_W0}} \entry{lambert_W0}{33}{\code {lambert_W0}} \entry{lambert_Wm1}{33}{\code {lambert_Wm1}} \entry{lambert_Wm1}{33}{\code {lambert_Wm1}} ] ./gsl.texi:2435: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_1plusx}{\folio }{\code {log_1plusx}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2435 ...nction} {@@var{y} =} log_1plusx (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2436: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_1plusx}{\folio }{\code {log_1plusx}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2436 ...r{y}, @@var{err}] =} log_1plusx (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2438: Use of \ doesn't match its definition. l.2438 These routines compute \\ log(1 + x) for x > -1 using an algorithm that If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2443--2445 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2450: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_1plusx_mx}{\folio }{\code {log_1plusx_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2450 ...ion} {@@var{y} =} log_1plusx_mx (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2451: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{log_1plusx_mx}{\folio }{\code {log_1plusx_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2451 ...}, @@var{err}] =} log_1plusx_mx (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2453: Use of \ doesn't match its definition. l.2453 These routines compute \\ log(1 + x) - x for x > -1 using an algorithm If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2458--2460 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2465: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi}{\folio }{\code {psi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2465 ...able Function} {@@var{y} =} psi (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2466: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi}{\folio }{\code {psi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2466 ...} {[@@var{y}, @@var{err}] =} psi (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2468: Use of \ doesn't match its definition. l.2468 ...routines compute the digamma function \\ psi(x) for general x, If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2469: Use of \ doesn't match its definition. l.2469 x \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2474--2476 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2481: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_1piy}{\folio }{\code {psi_1piy}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2481 ...Function} {@@var{y} =} psi_1piy (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2482: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_1piy}{\folio }{\code {psi_1piy}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2482 ...var{y}, @@var{err}] =} psi_1piy (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2485: Use of \ doesn't match its definition. l.2485 the line 1+i y, Re[\\ psi(1 + i y)]. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2489--2491 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2496: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{synchrotron_1}{\folio }{\code {synchrotron... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2496 ...ion} {@@var{y} =} synchrotron_1 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2497: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{synchrotron_1}{\folio }{\code {synchrotron... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2497 ...}, @@var{err}] =} synchrotron_1 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2500: Use of \ doesn't match its definition. l.2500 x \\ int_x^\\infty dt K_@@{5/3@@}(t) for x >= 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2500: Use of \ doesn't match its definition. l.2500 x \\int_x^\\ infty dt K_@@{5/3@@}(t) for x >= 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2504--2506 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. [34 \entry{log_1plusx}{34}{\code {log_1plusx}} \entry{log_1plusx}{34}{\code {log_1plusx}} \entry{log_1plusx_mx}{34}{\code {log_1plusx_mx}} \entry{log_1plusx_mx}{34}{\code {log_1plusx_mx}} \entry{psi}{34}{\code {psi}} \entry{psi}{34}{\code {psi}} \entry{psi_1piy}{34}{\code {psi_1piy}} \entry{psi_1piy}{34}{\code {psi_1piy}} \entry{synchrotron_1}{34}{\code {synchrotron_1}} \entry{synchrotron_1}{34}{\code {synchrotron_1}} ] ./gsl.texi:2511: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{synchrotron_2}{\folio }{\code {synchrotron... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2511 ...ion} {@@var{y} =} synchrotron_2 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2512: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{synchrotron_2}{\folio }{\code {synchrotron... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2512 ...}, @@var{err}] =} synchrotron_2 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2519--2521 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2526: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_2}{\folio }{\code {transport_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2526 ...ction} {@@var{y} =} transport_2 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2527: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_2}{\folio }{\code {transport_2}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2527 ...{y}, @@var{err}] =} transport_2 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2532: Use of \ doesn't match its definition. l.2532 representations J(n,x) := \\ int_0^x dt t^n e^t /(e^t - 1)^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2536--2538 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2543: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_3}{\folio }{\code {transport_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2543 ...ction} {@@var{y} =} transport_3 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2544: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_3}{\folio }{\code {transport_3}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2544 ...{y}, @@var{err}] =} transport_3 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2549: Use of \ doesn't match its definition. l.2549 representations J(n,x) := \\ int_0^x dt t^n e^t /(e^t - 1)^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2553--2555 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2560: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_4}{\folio }{\code {transport_4}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2560 ...ction} {@@var{y} =} transport_4 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2561: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_4}{\folio }{\code {transport_4}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2561 ...{y}, @@var{err}] =} transport_4 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2566: Use of \ doesn't match its definition. l.2566 representations J(n,x) := \\ int_0^x dt t^n e^t /(e^t - 1)^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2570--2572 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2577: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_5}{\folio }{\code {transport_5}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2577 ...ction} {@@var{y} =} transport_5 (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2578: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{transport_5}{\folio }{\code {transport_5}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2578 ...{y}, @@var{err}] =} transport_5 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [35 \entry{synchrotron_2}{35}{\code {synchrotron_2}} \entry{synchrotron_2}{35}{\code {synchrotron_2}} \entry{transport_2}{35}{\code {transport_2}} \entry{transport_2}{35}{\code {transport_2}} \entry{transport_3}{35}{\code {transport_3}} \entry{transport_3}{35}{\code {transport_3}} \entry{transport_4}{35}{\code {transport_4}} \entry{transport_4}{35}{\code {transport_4}} ] ./gsl.texi:2583: Use of \ doesn't match its definition. l.2583 representations J(n,x) := \\ int_0^x dt t^n e^t /(e^t - 1)^2. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2587--2589 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2594: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{sinc_gsl}{\folio }{\code {sinc_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2594 ...Function} {@@var{y} =} sinc_gsl (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2595: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{sinc_gsl}{\folio }{\code {sinc_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2595 ...var{y}, @@var{err}] =} sinc_gsl (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2597: Use of \ doesn't match its definition. l.2597 These routines compute \\ sinc(x) = \\sin(\\pi x) / (\\pi x) for any v... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2597: Use of \ doesn't match its definition. l.2597 These routines compute \\sinc(x) = \\ sin(\\pi x) / (\\pi x) for any v... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2597: Use of \ doesn't match its definition. l.2597 These routines compute \\sinc(x) = \\sin(\\ pi x) / (\\pi x) for any v... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2597: Use of \ doesn't match its definition. l.2597 ... compute \\sinc(x) = \\sin(\\pi x) / (\\ pi x) for any value of x. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2601--2603 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2608: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnsinh}{\folio }{\code {lnsinh}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2608 ...e Function} {@@var{y} =} lnsinh (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2609: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnsinh}{\folio }{\code {lnsinh}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2609 ...[@@var{y}, @@var{err}] =} lnsinh (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2611: Use of \ doesn't match its definition. l.2611 These routines compute \\ log(\\sinh(x)) for x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2611: Use of \ doesn't match its definition. l.2611 These routines compute \\log(\\ sinh(x)) for x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2615--2617 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2622: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lncosh}{\folio }{\code {lncosh}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2622 ...e Function} {@@var{y} =} lncosh (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2623: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lncosh}{\folio }{\code {lncosh}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2623 ...[@@var{y}, @@var{err}] =} lncosh (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2625: Use of \ doesn't match its definition. l.2625 These routines compute \\ log(\\cosh(x)) for any x. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2625: Use of \ doesn't match its definition. l.2625 These routines compute \\log(\\ cosh(x)) for any x. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2629--2631 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2636: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{zeta}{\folio }{\code {zeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2636 ...ble Function} {@@var{y} =} zeta (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2637: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{zeta}{\folio }{\code {zeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2637 ... {[@@var{y}, @@var{err}] =} zeta (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2639: Use of \ doesn't match its definition. l.2639 ...nes compute the Riemann zeta function \\ zeta(s) for If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2640: Use of \ doesn't match its definition. l.2640 arbitrary s, s \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2644: Use of \ doesn't match its definition. l.2644 \\ zeta(s) = \\sum_@@{k=1@@}^\\infty k^@@{-s@@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2644: Use of \ doesn't match its definition. l.2644 \\zeta(s) = \\ sum_@@{k=1@@}^\\infty k^@@{-s@@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2644: Use of \ doesn't match its definition. l.2644 \\zeta(s) = \\sum_@@{k=1@@}^\\ infty k^@@{-s@@}. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2648--2650 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2655: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{eta}{\folio }{\code {eta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2655 ...able Function} {@@var{y} =} eta (@@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2656: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{eta}{\folio }{\code {eta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2656 ...} {[@@var{y}, @@var{err}] =} eta (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2658: Use of \ doesn't match its definition. l.2658 These routines compute the eta function \\ eta(s) for arbitrary s. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [36 \entry{transport_5}{36}{\code {transport_5}} \entry{transport_5}{36}{\code {transport_5}} \entry{sinc_gsl}{36}{\code {sinc_gsl}} \entry{sinc_gsl}{36}{\code {sinc_gsl}} \entry{lnsinh}{36}{\code {lnsinh}} \entry{lnsinh}{36}{\code {lnsinh}} \entry{lncosh}{36}{\code {lncosh}} \entry{lncosh}{36}{\code {lncosh}} \entry{zeta}{36}{\code {zeta}} \entry{zeta}{36}{\code {zeta}} ] ./gsl.texi:2660: Use of \ doesn't match its definition. l.2660 The eta function is defined by \\ eta(s) = (1-2^@@{1-s@@}) \\zeta(s). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2660: Use of \ doesn't match its definition. l.2660 ...s defined by \\eta(s) = (1-2^@@{1-s@@}) \\ zeta(s). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2664--2666 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2671: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Jn}{\folio }{\code {bessel_Jn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2671 ...{@@var{y} =} bessel_Jn (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2672: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Jn}{\folio }{\code {bessel_Jn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2672 ...ar{y}, @@var{err}] =} bessel_Jn (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2679--2681 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2686: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Yn}{\folio }{\code {bessel_Yn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2686 ...{@@var{y} =} bessel_Yn (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2687: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Yn}{\folio }{\code {bessel_Yn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2687 ...ar{y}, @@var{err}] =} bessel_Yn (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2694--2696 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2701: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_In}{\folio }{\code {bessel_In}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2701 ...{@@var{y} =} bessel_In (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2702: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_In}{\folio }{\code {bessel_In}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2702 ...ar{y}, @@var{err}] =} bessel_In (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2709--2711 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2716: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_In_scaled}{\folio }{\code {bessel_I... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2716 ...} =} bessel_In_scaled (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2717: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_In_scaled}{\folio }{\code {bessel_I... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2717 ...@@var{err}] =} bessel_In_scaled (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2720: Use of \ doesn't match its definition. l.2720 function of order n, \\ exp(-|x|) I_n(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2724--2726 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2731: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Kn}{\folio }{\code {bessel_Kn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2731 ...{@@var{y} =} bessel_Kn (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [37 \entry{eta}{37}{\code {eta}} \entry{eta}{37}{\code {eta}} \entry{bessel_Jn}{37}{\code {bessel_Jn}} \entry{bessel_Jn}{37}{\code {bessel_Jn}} \entry{bessel_Yn}{37}{\code {bessel_Yn}} \entry{bessel_Yn}{37}{\code {bessel_Yn}} \entry{bessel_In}{37}{\code {bessel_In}} \entry{bessel_In}{37}{\code {bessel_In}} \entry{bessel_In_scaled}{37}{\code {bessel_In_scaled}} \entry{bessel_In_scaled}{37}{\code {bessel_In_scaled}} ] ./gsl.texi:2732: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Kn}{\folio }{\code {bessel_Kn}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2732 ...ar{y}, @@var{err}] =} bessel_Kn (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2739--2741 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2746: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Kn_scaled}{\folio }{\code {bessel_K... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2746 ...} =} bessel_Kn_scaled (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2747: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Kn_scaled}{\folio }{\code {bessel_K... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2747 ...@@var{err}] =} bessel_Kn_scaled (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2753--2755 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2760: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_jl}{\folio }{\code {bessel_jl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2760 ...{@@var{y} =} bessel_jl (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2761: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_jl}{\folio }{\code {bessel_jl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2761 ...ar{y}, @@var{err}] =} bessel_jl (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2768--2770 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2775: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_yl}{\folio }{\code {bessel_yl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2775 ...{@@var{y} =} bessel_yl (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2776: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_yl}{\folio }{\code {bessel_yl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2776 ...ar{y}, @@var{err}] =} bessel_yl (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2783--2785 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2790: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_il_scaled}{\folio }{\code {bessel_i... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2790 ...} =} bessel_il_scaled (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2791: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_il_scaled}{\folio }{\code {bessel_i... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2791 ...@@var{err}] =} bessel_il_scaled (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2794: Use of \ doesn't match its definition. l.2794 function of order l, \\ exp(-|x|) i_l(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2798--2800 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2805: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_kl_scaled}{\folio }{\code {bessel_k... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2805 ...} =} bessel_kl_scaled (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2806: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_kl_scaled}{\folio }{\code {bessel_k... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2806 ...@@var{err}] =} bessel_kl_scaled (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2809: Use of \ doesn't match its definition. l.2809 function of order l, \\ exp(x) k_l(x), for x>0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [38 \entry{bessel_Kn}{38}{\code {bessel_Kn}} \entry{bessel_Kn}{38}{\code {bessel_Kn}} \entry{bessel_Kn_scaled}{38}{\code {bessel_Kn_scaled}} \entry{bessel_Kn_scaled}{38}{\code {bessel_Kn_scaled}} \entry{bessel_jl}{38}{\code {bessel_jl}} \entry{bessel_jl}{38}{\code {bessel_jl}} \entry{bessel_yl}{38}{\code {bessel_yl}} \entry{bessel_yl}{38}{\code {bessel_yl}} \entry{bessel_il_scaled}{38}{\code {bessel_il_scaled}} \entry{bessel_il_scaled}{38}{\code {bessel_il_scaled}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 2813--2815 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2820: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel_n}{\folio }{\code {exprel_n}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2820 ... {@@var{y} =} exprel_n (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2821: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exprel_n}{\folio }{\code {exprel_n}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2821 ...var{y}, @@var{err}] =} exprel_n (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2827: Use of \ doesn't match its definition. l.2827 exprel_N(x) = N!/x^N (\\ exp(x) - \\sum_@@{k=0@@}^@@{N-1@@} x^k/k!) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2827: Use of \ doesn't match its definition. l.2827 exprel_N(x) = N!/x^N (\\exp(x) - \\ sum_@@{k=0@@}^@@{N-1@@} x^k/k!) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2833--2835 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2840: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_int}{\folio }{\code {fermi_dir... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2840 ...y} =} fermi_dirac_int (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2841: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_int}{\folio }{\code {fermi_dir... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2841 ... @@var{err}] =} fermi_dirac_int (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2844: Use of \ doesn't match its definition. l.2844 integer index of j, F_j(x) = (1/\\ Gamma(j+1)) \\int_0^\\infty dt (t^j If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2844: Use of \ doesn't match its definition. l.2844 ...index of j, F_j(x) = (1/\\Gamma(j+1)) \\ int_0^\\infty dt (t^j If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2844: Use of \ doesn't match its definition. l.2844 ... j, F_j(x) = (1/\\Gamma(j+1)) \\int_0^\\ infty dt (t^j If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2845: Use of \ doesn't match its definition. l.2845 /(\\ exp(t-x)+1)). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2849--2851 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2856: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{taylorcoeff}{\folio }{\code {taylorcoeff}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2856 ...var{y} =} taylorcoeff (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2857: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{taylorcoeff}{\folio }{\code {taylorcoeff}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2857 ...{y}, @@var{err}] =} taylorcoeff (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2864--2866 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2871: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Pl}{\folio }{\code {legendre_Pl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2871 ...var{y} =} legendre_Pl (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2872: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Pl}{\folio }{\code {legendre_Pl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2872 ...{y}, @@var{err}] =} legendre_Pl (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2879--2881 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. [39 \entry{bessel_kl_scaled}{39}{\code {bessel_kl_scaled}} \entry{bessel_kl_scaled}{39}{\code {bessel_kl_scaled}} \entry{exprel_n}{39}{\code {exprel_n}} \entry{exprel_n}{39}{\code {exprel_n}} \entry{fermi_dirac_int}{39}{\code {fermi_dirac_int}} \entry{fermi_dirac_int}{39}{\code {fermi_dirac_int}} \entry{taylorcoeff}{39}{\code {taylorcoeff}} \entry{taylorcoeff}{39}{\code {taylorcoeff}} \entry{legendre_Pl}{39}{\code {legendre_Pl}} \entry{legendre_Pl}{39}{\code {legendre_Pl}} ] ./gsl.texi:2886: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Ql}{\folio }{\code {legendre_Ql}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2886 ...var{y} =} legendre_Ql (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2887: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Ql}{\folio }{\code {legendre_Ql}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2887 ...{y}, @@var{err}] =} legendre_Ql (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 2894--2896 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2901: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_n}{\folio }{\code {psi_n}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2901 ...on} {@@var{y} =} psi_n (@@var{n}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2902: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_n}{\folio }{\code {psi_n}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2902 ...{[@@var{y}, @@var{err}] =} psi_n (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2904: Use of \ doesn't match its definition. l.2904 ...utines compute the polygamma function \\ psi^@@{(m)@@}(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2909--2911 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2916: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Jnu}{\folio }{\code {bessel_Jnu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2916 ...@@var{z} =} bessel_Jnu (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2917: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Jnu}{\folio }{\code {bessel_Jnu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2917 ...r{z}, @@var{err}] =} bessel_Jnu (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2920: Use of \ doesn't match its definition. l.2920 fractional order nu, J_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2925--2927 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2932: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Ynu}{\folio }{\code {bessel_Ynu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2932 ...@@var{z} =} bessel_Ynu (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2933: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Ynu}{\folio }{\code {bessel_Ynu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2933 ...r{z}, @@var{err}] =} bessel_Ynu (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2936: Use of \ doesn't match its definition. l.2936 fractional order nu, Y_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2941--2943 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2948: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Inu}{\folio }{\code {bessel_Inu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2948 ...@@var{z} =} bessel_Inu (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2949: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Inu}{\folio }{\code {bessel_Inu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2949 ...r{z}, @@var{err}] =} bessel_Inu (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2952: Use of \ doesn't match its definition. l.2952 fractional order nu, I_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2953: Use of \ doesn't match its definition. l.2953 u(x) for x>0, \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2958--2960 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. [40 \entry{legendre_Ql}{40}{\code {legendre_Ql}} \entry{legendre_Ql}{40}{\code {legendre_Ql}} \entry{psi_n}{40}{\code {psi_n}} \entry{psi_n}{40}{\code {psi_n}} \entry{bessel_Jnu}{40}{\code {bessel_Jnu}} \entry{bessel_Jnu}{40}{\code {bessel_Jnu}} \entry{bessel_Ynu}{40}{\code {bessel_Ynu}} \entry{bessel_Ynu}{40}{\code {bessel_Ynu}} \entry{bessel_Inu}{40}{\code {bessel_Inu}} \entry{bessel_Inu}{40}{\code {bessel_Inu}} ] ./gsl.texi:2965: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Inu_scaled}{\folio }{\code {bessel_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2965 ... =} bessel_Inu_scaled (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2966: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Inu_scaled}{\folio }{\code {bessel_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2966 ...var{err}] =} bessel_Inu_scaled (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2969: Use of \ doesn't match its definition. l.2969 fractional order nu, \\ exp(-|x|)I_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2969: Use of \ doesn't match its definition. l.2969 fractional order nu, \\exp(-|x|)I_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2970: Use of \ doesn't match its definition. l.2970 u(x) for x>0, \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2975--2977 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2982: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Knu}{\folio }{\code {bessel_Knu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2982 ...@@var{z} =} bessel_Knu (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2983: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Knu}{\folio }{\code {bessel_Knu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2983 ...r{z}, @@var{err}] =} bessel_Knu (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:2986: Use of \ doesn't match its definition. l.2986 fractional order nu, K_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:2987: Use of \ doesn't match its definition. l.2987 u(x) for x>0, \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 2992--2994 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:2999: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_lnKnu}{\folio }{\code {bessel_lnKnu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.2999 ...ar{z} =} bessel_lnKnu (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3000: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_lnKnu}{\folio }{\code {bessel_lnKnu}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3000 ...z}, @@var{err}] =} bessel_lnKnu (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3003: Use of \ doesn't match its definition. l.3003 function of fractional order nu, \\ ln(K_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3003: Use of \ doesn't match its definition. l.3003 function of fractional order nu, \\ln(K_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3004: Use of \ doesn't match its definition. l.3004 u(x)) for x>0, \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3009--3011 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3016: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Knu_scaled}{\folio }{\code {bessel_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3016 ... =} bessel_Knu_scaled (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3017: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_Knu_scaled}{\folio }{\code {bessel_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3017 ...var{err}] =} bessel_Knu_scaled (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3020: Use of \ doesn't match its definition. l.3020 of fractional order nu, \\ exp(+|x|) K_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3020: Use of \ doesn't match its definition. l.3020 of fractional order nu, \\exp(+|x|) K_\ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3021: Use of \ doesn't match its definition. l.3021 u(x) for x>0, \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3026--3028 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3033: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exp_mult}{\folio }{\code {exp_mult}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3033 ... {@@var{z} =} exp_mult (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3034: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{exp_mult}{\folio }{\code {exp_mult}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3034 ...var{z}, @@var{err}] =} exp_mult (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3037: Use of \ doesn't match its definition. l.3037 the product y \\ exp(x). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [41 \entry{bessel_Inu_scaled}{41}{\code {bessel_Inu_scaled}} \entry{bessel_Inu_scaled}{41}{\code {bessel_Inu_scaled}} \entry{bessel_Knu}{41}{\code {bessel_Knu}} \entry{bessel_Knu}{41}{\code {bessel_Knu}} \entry{bessel_lnKnu}{41}{\code {bessel_lnKnu}} \entry{bessel_lnKnu}{41}{\code {bessel_lnKnu}} \entry{bessel_Knu_scaled}{41}{\code {bessel_Knu_scaled}} \entry{bessel_Knu_scaled}{41}{\code {bessel_Knu_scaled}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 3041--3043 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3048: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_inc_0}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3048 ... =} fermi_dirac_inc_0 (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3049: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{fermi_dirac_inc_0}{\folio }{\code {fermi_d... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3049 ...var{err}] =} fermi_dirac_inc_0 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3052: Use of \ doesn't match its definition. l.3052 index of zero, F_0(x,b) = \\ ln(1 + e^@@{b-x@@}) - (b-x). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3056--3058 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3063: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{poch}{\folio }{\code {poch}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3063 ...ion} {@@var{z} =} poch (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3064: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{poch}{\folio }{\code {poch}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3064 ... {[@@var{z}, @@var{err}] =} poch (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3068: Use of \ doesn't match its definition. l.3068 (a)_x := \\ Gamma(a + x)/\\Gamma(a), If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3068: Use of \ doesn't match its definition. l.3068 (a)_x := \\Gamma(a + x)/\\ Gamma(a), If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3075--3077 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3082: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnpoch}{\folio }{\code {lnpoch}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3082 ...n} {@@var{z} =} lnpoch (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3083: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnpoch}{\folio }{\code {lnpoch}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3083 ...[@@var{z}, @@var{err}] =} lnpoch (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3086: Use of \ doesn't match its definition. l.3086 \\ log((a)_x) = \\log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3086: Use of \ doesn't match its definition. l.3086 \\log((a)_x) = \\ log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3086: Use of \ doesn't match its definition. l.3086 \\log((a)_x) = \\log(\\ Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3086: Use of \ doesn't match its definition. l.3086 \\log((a)_x) = \\log(\\Gamma(a + x)/\\ Gamma(a)) for a > 0, a+x > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3090--3092 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3097: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{pochrel}{\folio }{\code {pochrel}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3097 ...} {@@var{z} =} pochrel (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3098: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{pochrel}{\folio }{\code {pochrel}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3098 ...@@var{z}, @@var{err}] =} pochrel (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3101: Use of \ doesn't match its definition. l.3101 where (a,x) = (a)_x := \\ Gamma(a + x)/\\Gamma(a). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3101: Use of \ doesn't match its definition. l.3101 where (a,x) = (a)_x := \\Gamma(a + x)/\\ Gamma(a). If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3105--3107 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. [42 \entry{exp_mult}{42}{\code {exp_mult}} \entry{exp_mult}{42}{\code {exp_mult}} \entry{fermi_dirac_inc_0}{42}{\code {fermi_dirac_inc_0}} \entry{fermi_dirac_inc_0}{42}{\code {fermi_dirac_inc_0}} \entry{poch}{42}{\code {poch}} \entry{poch}{42}{\code {poch}} \entry{lnpoch}{42}{\code {lnpoch}} \entry{lnpoch}{42}{\code {lnpoch}} \entry{pochrel}{42}{\code {pochrel}} \entry{pochrel}{42}{\code {pochrel}} ] ./gsl.texi:3112: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc_Q}{\folio }{\code {gamma_inc_Q}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3112 ...var{z} =} gamma_inc_Q (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3113: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc_Q}{\folio }{\code {gamma_inc_Q}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3113 ...{z}, @@var{err}] =} gamma_inc_Q (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3116: Use of \ doesn't match its definition. l.3116 Q(a,x) = 1/\\ Gamma(a) \\int_x\\infty dt t^@@{a-1@@} \\exp(-t) for a > 0... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3116: Use of \ doesn't match its definition. l.3116 Q(a,x) = 1/\\Gamma(a) \\ int_x\\infty dt t^@@{a-1@@} \\exp(-t) for a > 0... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3116: Use of \ doesn't match its definition. l.3116 Q(a,x) = 1/\\Gamma(a) \\int_x\\ infty dt t^@@{a-1@@} \\exp(-t) for a > 0... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3116: Use of \ doesn't match its definition. l.3116 ...\Gamma(a) \\int_x\\infty dt t^@@{a-1@@} \\ exp(-t) for a > 0, x >= 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3120--3122 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3127: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc_P}{\folio }{\code {gamma_inc_P}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3127 ...var{z} =} gamma_inc_P (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3128: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc_P}{\folio }{\code {gamma_inc_P}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3128 ...{z}, @@var{err}] =} gamma_inc_P (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3131: Use of \ doesn't match its definition. l.3131 Function P(a,x) = 1/\\ Gamma(a) \\int_0^x dt t^@@{a-1@@} \\exp(-t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3131: Use of \ doesn't match its definition. l.3131 Function P(a,x) = 1/\\Gamma(a) \\ int_0^x dt t^@@{a-1@@} \\exp(-t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3131: Use of \ doesn't match its definition. l.3131 ...= 1/\\Gamma(a) \\int_0^x dt t^@@{a-1@@} \\ exp(-t) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3136--3138 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3143: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc}{\folio }{\code {gamma_inc}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3143 ...{@@var{z} =} gamma_inc (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3144: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{gamma_inc}{\folio }{\code {gamma_inc}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3144 ...ar{z}, @@var{err}] =} gamma_inc (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3148: Use of \ doesn't match its definition. l.3148 \\ Gamma(a,x) = \\int_x\\infty dt t^@@{a-1@@} \\exp(-t) for a real and x... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3148: Use of \ doesn't match its definition. l.3148 \\Gamma(a,x) = \\ int_x\\infty dt t^@@{a-1@@} \\exp(-t) for a real and x... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3148: Use of \ doesn't match its definition. l.3148 \\Gamma(a,x) = \\int_x\\ infty dt t^@@{a-1@@} \\exp(-t) for a real and x... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3148: Use of \ doesn't match its definition. l.3148 ...ma(a,x) = \\int_x\\infty dt t^@@{a-1@@} \\ exp(-t) for a real and x >... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3152--3154 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3159: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{beta_gsl}{\folio }{\code {beta_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3159 ... {@@var{z} =} beta_gsl (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3160: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{beta_gsl}{\folio }{\code {beta_gsl}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3160 ...var{z}, @@var{err}] =} beta_gsl (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3163: Use of \ doesn't match its definition. l.3163 B(a,b) = \\ Gamma(a)\\Gamma(b)/\\Gamma(a+b) for a > 0, b > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3163: Use of \ doesn't match its definition. l.3163 B(a,b) = \\Gamma(a)\\ Gamma(b)/\\Gamma(a+b) for a > 0, b > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3163: Use of \ doesn't match its definition. l.3163 B(a,b) = \\Gamma(a)\\Gamma(b)/\\ Gamma(a+b) for a > 0, b > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (20.37637pt too wide) in paragraph at lines 3162--3164 []@@textrm These rou-tines com-pute the Beta Func-tion, B(a,b) = Gamma(a)Gamma( b)/Gamma(a+b)| @@hbox(8.2125+2.73749)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm e .etc. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3167--3169 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3174: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnbeta}{\folio }{\code {lnbeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3174 ...n} {@@var{z} =} lnbeta (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3175: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{lnbeta}{\folio }{\code {lnbeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3175 ...[@@var{z}, @@var{err}] =} lnbeta (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3178: Use of \ doesn't match its definition. l.3178 \\ log(B(a,b)) for a > 0, b > 0. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3182--3184 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. [43 \entry{gamma_inc_Q}{43}{\code {gamma_inc_Q}} \entry{gamma_inc_Q}{43}{\code {gamma_inc_Q}} \entry{gamma_inc_P}{43}{\code {gamma_inc_P}} \entry{gamma_inc_P}{43}{\code {gamma_inc_P}} \entry{gamma_inc}{43}{\code {gamma_inc}} \entry{gamma_inc}{43}{\code {gamma_inc}} \entry{beta_gsl}{43}{\code {beta_gsl}} \entry{beta_gsl}{43}{\code {beta_gsl}} \entry{lnbeta}{43}{\code {lnbeta}} \entry{lnbeta}{43}{\code {lnbeta}} ] ./gsl.texi:3189: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_0F1}{\folio }{\code {hyperg_0F1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3189 ...@@var{z} =} hyperg_0F1 (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3190: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_0F1}{\folio }{\code {hyperg_0F1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3190 ...r{z}, @@var{err}] =} hyperg_0F1 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3196--3198 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3203: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_half}{\folio }{\code {conicalP_ha... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3203 ...r{z} =} conicalP_half (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3204: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_half}{\folio }{\code {conicalP_ha... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3204 ...}, @@var{err}] =} conicalP_half (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3207: Use of \ doesn't match its definition. l.3207 P^@@{1/2@@}_@@{-1/2 + i \\ lambda@@}(x) for x > -1. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3211--3213 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3218: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_mhalf}{\folio }{\code {conicalP_m... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3218 ...{z} =} conicalP_mhalf (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3219: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_mhalf}{\folio }{\code {conicalP_m... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3219 ..., @@var{err}] =} conicalP_mhalf (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3222: Use of \ doesn't match its definition. l.3222 P^@@{-1/2@@}_@@{-1/2 + i \\ lambda@@}(x) for x > -1. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3226--3228 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3233: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_0}{\folio }{\code {conicalP_0}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3233 ...@@var{z} =} conicalP_0 (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3234: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_0}{\folio }{\code {conicalP_0}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3234 ...r{z}, @@var{err}] =} conicalP_0 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3236: Use of \ doesn't match its definition. l.3236 ...e the conical function P^0_@@{-1/2 + i \\ lambda@@}(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3241--3243 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3248: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_1}{\folio }{\code {conicalP_1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3248 ...@@var{z} =} conicalP_1 (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3249: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{conicalP_1}{\folio }{\code {conicalP_1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3249 ...r{z}, @@var{err}] =} conicalP_1 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3251: Use of \ doesn't match its definition. l.3251 ...e the conical function P^1_@@{-1/2 + i \\ lambda@@}(x) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3256--3258 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3263: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hzeta}{\folio }{\code {hzeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3263 ...on} {@@var{z} =} hzeta (@@var{x}, @@var{y}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3264: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hzeta}{\folio }{\code {hzeta}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3264 ...{[@@var{z}, @@var{err}] =} hzeta (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3266: Use of \ doesn't match its definition. l.3266 ...nes compute the Hurwitz zeta function \\ zeta(s,q) If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [44 \entry{hyperg_0F1}{44}{\code {hyperg_0F1}} \entry{hyperg_0F1}{44}{\code {hyperg_0F1}} \entry{conicalP_half}{44}{\code {conicalP_half}} \entry{conicalP_half}{44}{\code {conicalP_half}} \entry{conicalP_mhalf}{44}{\code {conicalP_mhalf}} \entry{conicalP_mhalf}{44}{\code {conicalP_mhalf}} \entry{conicalP_0}{44}{\code {conicalP_0}} \entry{conicalP_0}{44}{\code {conicalP_0}} \entry{conicalP_1}{44}{\code {conicalP_1}} \entry{conicalP_1}{44}{\code {conicalP_1}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 3271--3273 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3278: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai}{\folio }{\code {airy_Ai}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3278 ...@@var{y} =} airy_Ai (@@var{x}, @@var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3279: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai}{\folio }{\code {airy_Ai}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3279 ...@@var{y}, @@var{err}] =} airy_Ai (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3297--3299 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3304: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi}{\folio }{\code {airy_Bi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3304 ...@@var{y} =} airy_Bi (@@var{x}, @@var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3305: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi}{\folio }{\code {airy_Bi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3305 ...@@var{y}, @@var{err}] =} airy_Bi (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3323--3325 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3330: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_scaled}{\folio }{\code {airy_Ai_sc... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3330 ... =} airy_Ai_scaled (@@var{x}, @@var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3331: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_scaled}{\folio }{\code {airy_Ai_sc... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3331 ..., @@var{err}] =} airy_Ai_scaled (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3334: Use of \ doesn't match its definition. l.3334 ... For x>0 the scaling factor S_A(x) is \\ exp(+(2/3) x^(3/2)), and If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [45 \entry{hzeta}{45}{\code {hzeta}} \entry{hzeta}{45}{\code {hzeta}} \entry{airy_Ai}{45}{\code {airy_Ai}} \entry{airy_Ai}{45}{\code {airy_Ai}} \entry{airy_Bi}{45}{\code {airy_Bi}} \entry{airy_Bi}{45}{\code {airy_Bi}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 3350--3352 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3357: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_scaled}{\folio }{\code {airy_Bi_sc... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3357 ... =} airy_Bi_scaled (@@var{x}, @@var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3358: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_scaled}{\folio }{\code {airy_Bi_sc... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3358 ..., @@var{err}] =} airy_Bi_scaled (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3377--3379 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3384: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_deriv}{\folio }{\code {airy_Ai_der... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3384 ...} =} airy_Ai_deriv (@@var{x}, @@var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3385: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_deriv}{\folio }{\code {airy_Ai_der... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3385 ...}, @@var{err}] =} airy_Ai_deriv (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [46 \entry{airy_Ai_scaled}{46}{\code {airy_Ai_scaled}} \entry{airy_Ai_scaled}{46}{\code {airy_Ai_scaled}} \entry{airy_Bi_scaled}{46}{\code {airy_Bi_scaled}} \entry{airy_Bi_scaled}{46}{\code {airy_Bi_scaled}} \entry{airy_Ai_deriv}{46}{\code {airy_Ai_deriv}} \entry{airy_Ai_deriv}{46}{\code {airy_Ai_deriv}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 3403--3405 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3410: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_deriv}{\folio }{\code {airy_Bi_der... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3410 ...} =} airy_Bi_deriv (@@var{x}, @@var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3411: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_deriv}{\folio }{\code {airy_Bi_der... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3411 ...}, @@var{err}] =} airy_Bi_deriv (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3429--3431 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3436: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_deriv_scaled}{\folio }{\code {airy... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3436 ...ry_Ai_deriv_scaled (@@var{x}, @@var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3437: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Ai_deriv_scaled}{\folio }{\code {airy... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3437 ...{err}] =} airy_Ai_deriv_scaled (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3455--3457 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3462: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_deriv_scaled}{\folio }{\code {airy... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3462 ...ry_Bi_deriv_scaled (@@var{x}, @@var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3463: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_Bi_deriv_scaled}{\folio }{\code {airy... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3463 ...{err}] =} airy_Bi_deriv_scaled (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [47 \entry{airy_Bi_deriv}{47}{\code {airy_Bi_deriv}} \entry{airy_Bi_deriv}{47}{\code {airy_Bi_deriv}} \entry{airy_Ai_deriv_scaled}{47}{\code {airy_Ai_deriv_scaled}} \entry{airy_Ai_deriv_scaled}{47}{\code {airy_Ai_deriv_scaled}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 3481--3483 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3488: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{ellint_Kcomp}{\folio }{\code {ellint_Kcomp}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3488 ...y} =} ellint_Kcomp (@@var{x}, @@var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3489: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{ellint_Kcomp}{\folio }{\code {ellint_Kcomp}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3489 ...y}, @@var{err}] =} ellint_Kcomp (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3493: Undefined control sequence. l.3493 \beforedisplay The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ./gsl.texi:3499: Undefined control sequence. l.3499 \afterdisplay The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3521--3523 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3528: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{ellint_Ecomp}{\folio }{\code {ellint_Ecomp}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3528 ...y} =} ellint_Ecomp (@@var{x}, @@var{mode}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3529: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{ellint_Ecomp}{\folio }{\code {ellint_Ecomp}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3529 ...y}, @@var{err}] =} ellint_Ecomp (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3535: Undefined control sequence. l.3535 \beforedisplay The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ./gsl.texi:3541: Undefined control sequence. l.3541 \afterdisplay The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. [48 \entry{airy_Bi_deriv_scaled}{48}{\code {airy_Bi_deriv_scaled}} \entry{airy_Bi_deriv_scaled}{48}{\code {airy_Bi_deriv_scaled}} \entry{ellint_Kcomp}{48}{\code {ellint_Kcomp}} \entry{ellint_Kcomp}{48}{\code {ellint_Kcomp}} \entry{ellint_Ecomp}{48}{\code {ellint_Ecomp}} \entry{ellint_Ecomp}{48}{\code {ellint_Ecomp}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 3563--3565 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3570: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Ai}{\folio }{\code {airy_zero_Ai}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3570 ...tion} {@@var{y} =} airy_zero_Ai (@@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3571: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Ai}{\folio }{\code {airy_zero_Ai}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3571 ...y}, @@var{err}] =} airy_zero_Ai (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3578--3580 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3585: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Bi}{\folio }{\code {airy_zero_Bi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3585 ...tion} {@@var{y} =} airy_zero_Bi (@@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3586: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Bi}{\folio }{\code {airy_zero_Bi}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3586 ...y}, @@var{err}] =} airy_zero_Bi (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3593--3595 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3600: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Ai_deriv}{\folio }{\code {airy_z... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3600 ...{@@var{y} =} airy_zero_Ai_deriv (@@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3601: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Ai_deriv}{\folio }{\code {airy_z... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3601 ...ar{err}] =} airy_zero_Ai_deriv (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3608--3610 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3615: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Bi_deriv}{\folio }{\code {airy_z... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3615 ...{@@var{y} =} airy_zero_Bi_deriv (@@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3616: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{airy_zero_Bi_deriv}{\folio }{\code {airy_z... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3616 ...ar{err}] =} airy_zero_Bi_deriv (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) [49 \entry{airy_zero_Ai}{49}{\code {airy_zero_Ai}} \entry{airy_zero_Ai}{49}{\code {airy_zero_Ai}} \entry{airy_zero_Bi}{49}{\code {airy_zero_Bi}} \entry{airy_zero_Bi}{49}{\code {airy_zero_Bi}} \entry{airy_zero_Ai_deriv}{49}{\code {airy_zero_Ai_deriv}} \entry{airy_zero_Ai_deriv}{49}{\code {airy_zero_Ai_deriv}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 3623--3625 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3630: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_zero_J0}{\folio }{\code {bessel_zer... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3630 ...on} {@@var{y} =} bessel_zero_J0 (@@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3631: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_zero_J0}{\folio }{\code {bessel_zer... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3631 ..., @@var{err}] =} bessel_zero_J0 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3638--3640 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3645: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_zero_J1}{\folio }{\code {bessel_zer... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3645 ...on} {@@var{y} =} bessel_zero_J1 (@@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3646: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{bessel_zero_J1}{\folio }{\code {bessel_zer... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3646 ..., @@var{err}] =} bessel_zero_J1 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3653--3655 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3660: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_1_int}{\folio }{\code {psi_1_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3660 ...unction} {@@var{y} =} psi_1_int (@@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3661: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{psi_1_int}{\folio }{\code {psi_1_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3661 ...ar{y}, @@var{err}] =} psi_1_int (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3663: Use of \ doesn't match its definition. l.3663 ...outines compute the Trigamma function \\ psi(n) for positive If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3668--3670 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3675: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{zeta_int}{\folio }{\code {zeta_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3675 ...Function} {@@var{y} =} zeta_int (@@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3676: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{zeta_int}{\folio }{\code {zeta_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3676 ...var{y}, @@var{err}] =} zeta_int (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3678: Use of \ doesn't match its definition. l.3678 ...nes compute the Riemann zeta function \\ zeta(n) for If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3679: Use of \ doesn't match its definition. l.3679 integer n, n \ If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3684--3686 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3691: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{eta_int}{\folio }{\code {eta_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3691 ... Function} {@@var{y} =} eta_int (@@var{n}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3692: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{eta_int}{\folio }{\code {eta_int}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3692 ...@@var{y}, @@var{err}] =} eta_int (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3694: Use of \ doesn't match its definition. l.3694 These routines compute the eta function \\ eta(n) for integer n. If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. [50 \entry{airy_zero_Bi_deriv}{50}{\code {airy_zero_Bi_deriv}} \entry{airy_zero_Bi_deriv}{50}{\code {airy_zero_Bi_deriv}} \entry{bessel_zero_J0}{50}{\code {bessel_zero_J0}} \entry{bessel_zero_J0}{50}{\code {bessel_zero_J0}} \entry{bessel_zero_J1}{50}{\code {bessel_zero_J1}} \entry{bessel_zero_J1}{50}{\code {bessel_zero_J1}} \entry{psi_1_int}{50}{\code {psi_1_int}} \entry{psi_1_int}{50}{\code {psi_1_int}} \entry{zeta_int}{50}{\code {zeta_int}} \entry{zeta_int}{50}{\code {zeta_int}} ] Overfull \hbox (26.66904pt too wide) in paragraph at lines 3698--3700 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3705: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Plm}{\folio }{\code {legendre_Plm}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3705 ...legendre_Plm (@@var{n}, @@var{m}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3706: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_Plm}{\folio }{\code {legendre_Plm}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3706 ...y}, @@var{err}] =} legendre_Plm (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3713--3715 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3720: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_sphPlm}{\folio }{\code {legendre_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3720 ...endre_sphPlm (@@var{n}, @@var{m}, @@var{x}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3721: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{legendre_sphPlm}{\folio }{\code {legendre_... \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3721 ... @@var{err}] =} legendre_sphPlm (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3724: Use of \ doesn't match its definition. l.3724 $\\ sqrt@@{(2l+1)/(4\\pi)@@} \\sqrt@@{(l-m)!/(l+m)!@@} P_l^m(x)$ suitable ... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3724: Use of \ doesn't match its definition. l.3724 $\\sqrt@@{(2l+1)/(4\\ pi)@@} \\sqrt@@{(l-m)!/(l+m)!@@} P_l^m(x)$ suitable ... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. ./gsl.texi:3724: Use of \ doesn't match its definition. l.3724 $\\sqrt@@{(2l+1)/(4\\pi)@@} \\ sqrt@@{(l-m)!/(l+m)!@@} P_l^m(x)$ suitable ... If you say, e.g., `\def\a1{...}', then you must always put `1' after `\a', since control sequence names are made up of letters only. The macro here has not been followed by the required stuff, so I'm ignoring it. Underfull \hbox (badness 10000) in paragraph at lines 3723--3728 []@@textrm These rou-tines com-pute the nor-mal-ized as-so-ci-ated Leg-en-dre p oly-no-mial @@hbox(7.60416+2.12917)x433.62, glue set 4.66573 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm e .etc. Overfull \hbox (26.66904pt too wide) in paragraph at lines 3731--3733 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3738: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_U}{\folio }{\code {hyperg_U}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3738 ... hyperg_U (@@var{x0}, @@var{x1}, @@var{x2}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3739: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_U}{\folio }{\code {hyperg_U}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3739 ...r{out}, @@var{err}] =} hyperg_U (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3746--3748 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. ./gsl.texi:3753: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_1F1}{\folio }{\code {hyperg_1F1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3753 ...yperg_1F1 (@@var{x0}, @@var{x1}, @@var{x2}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ./gsl.texi:3754: Missing number, treated as zero. \fnindfile \temp ->\write \fnindfile {\entry{hyperg_1F1}{\folio }{\code {hyperg_1F1}}} \dosubindsanitize ... -\skip 0 \fi \dosubindwrite \ifx \lastskipmacro \zeros... \dosubind ...ndcsname }\ifvmode \dosubindsanitize \else \dosubindwrite \fi }... \deftypefngeneral ...dosubind {fn}{\code {#4}}{#1} \defname {#2}{#3}{#4}\defu... \printdefunline #1#2->\begingroup #1#2 \endheader \interlinepenalty = 10000 ... l.3754 ...out}, @@var{err}] =} hyperg_1F1 (@@dots{}) A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) Overfull \hbox (26.66904pt too wide) in paragraph at lines 3761--3763 []@@textrm This func-tion is from the GNU Sci-en-tific Li-brary, see [][]@@textt t http://www.gnu.org/software/gsl/[][][]| @@hbox(7.60416+2.43333)x433.62, glue set - 1.0 .@@glue(@@leftskip) 28.90755 .@@hbox(0.0+0.0)x0.0 .@@textrm T .@@textrm h .@@textrm i .etc. [51 \entry{eta_int}{51}{\code {eta_int}} \entry{eta_int}{51}{\code {eta_int}} \entry{legendre_Plm}{51}{\code {legendre_Plm}} \entry{legendre_Plm}{51}{\code {legendre_Plm}} \entry{legendre_sphPlm}{51}{\code {legendre_sphPlm}} \entry{legendre_sphPlm}{51}{\code {legendre_sphPlm}} \entry{hyperg_U}{51}{\code {hyperg_U}} \entry{hyperg_U}{51}{\code {hyperg_U}} \entry{hyperg_1F1}{51}{\code {hyperg_1F1}} \entry{hyperg_1F1}{51}{\code {hyperg_1F1}} ] ) Here is how much of TeX's memory you used: 1576 strings out of 97341 16795 string characters out of 1211892 40064 words of memory out of 1000000 2682 multiletter control sequences out of 10000+50000 32127 words of font info for 112 fonts, out of 500000 for 2000 51 hyphenation exceptions out of 1000 12i,9n,16p,235b,419s stack positions out of 1500i,500n,5000p,200000b,5000s PDF statistics: 412 PDF objects out of 300000 0 named destinations out of 131072 1 words of extra memory for PDF output out of 65536 Output written on gsl.pdf (51 pages, 207536 bytes). @ gsl-1.0.8/doc/RCS/texinfo.tex,v0000644000175000017500000067477311201030376013770 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @% @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @% texinfo.tex -- TeX macros to handle Texinfo files. % % Load plain if necessary, i.e., if running under initex. \expandafter\ifx\csname fmtname\endcsname\relax\input plain\fi % \def\texinfoversion{2004-11-25.16} % % Copyright (C) 1985, 1986, 1988, 1990, 1991, 1992, 1993, 1994, 1995, % 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004 Free Software % Foundation, Inc. % % This texinfo.tex file is free software; you can redistribute it and/or % modify it under the terms of the GNU General Public License as % published by the Free Software Foundation; either version 2, or (at % your option) any later version. % % This texinfo.tex file is distributed in the hope that it will be % useful, but WITHOUT ANY WARRANTY; without even the implied warranty % of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU % General Public License for more details. % % You should have received a copy of the GNU General Public License % along with this texinfo.tex file; see the file COPYING. If not, write % to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, % Boston, MA 02111-1307, USA. % % As a special exception, when this file is read by TeX when processing % a Texinfo source document, you may use the result without % restriction. (This has been our intent since Texinfo was invented.) % % Please try the latest version of texinfo.tex before submitting bug % reports; you can get the latest version from: % http://www.gnu.org/software/texinfo/ (the Texinfo home page), or % ftp://tug.org/tex/texinfo.tex % (and all CTAN mirrors, see http://www.ctan.org). % The texinfo.tex in any given distribution could well be out % of date, so if that's what you're using, please check. % % Send bug reports to bug-texinfo@@gnu.org. Please include including a % complete document in each bug report with which we can reproduce the % problem. Patches are, of course, greatly appreciated. % % To process a Texinfo manual with TeX, it's most reliable to use the % texi2dvi shell script that comes with the distribution. For a simple % manual foo.texi, however, you can get away with this: % tex foo.texi % texindex foo.?? % tex foo.texi % tex foo.texi % dvips foo.dvi -o # or whatever; this makes foo.ps. % The extra TeX runs get the cross-reference information correct. % Sometimes one run after texindex suffices, and sometimes you need more % than two; texi2dvi does it as many times as necessary. % % It is possible to adapt texinfo.tex for other languages, to some % extent. You can get the existing language-specific files from the % full Texinfo distribution. % % The GNU Texinfo home page is http://www.gnu.org/software/texinfo. \message{Loading texinfo [version \texinfoversion]:} % If in a .fmt file, print the version number % and turn on active characters that we couldn't do earlier because % they might have appeared in the input file name. \everyjob{\message{[Texinfo version \texinfoversion]}% \catcode`+=\active \catcode`\_=\active} \message{Basics,} \chardef\other=12 % We never want plain's \outer definition of \+ in Texinfo. % For @@tex, we can use \tabalign. \let\+ = \relax % Save some plain tex macros whose names we will redefine. \let\ptexb=\b \let\ptexbullet=\bullet \let\ptexc=\c \let\ptexcomma=\, \let\ptexdot=\. \let\ptexdots=\dots \let\ptexend=\end \let\ptexequiv=\equiv \let\ptexexclam=\! \let\ptexfootnote=\footnote \let\ptexgtr=> \let\ptexhat=^ \let\ptexi=\i \let\ptexindent=\indent \let\ptexinsert=\insert \let\ptexlbrace=\{ \let\ptexless=< \let\ptexnewwrite\newwrite \let\ptexnoindent=\noindent \let\ptexplus=+ \let\ptexrbrace=\} \let\ptexslash=\/ \let\ptexstar=\* \let\ptext=\t % If this character appears in an error message or help string, it % starts a new line in the output. \newlinechar = `^^J % Use TeX 3.0's \inputlineno to get the line number, for better error % messages, but if we're using an old version of TeX, don't do anything. % \ifx\inputlineno\thisisundefined \let\linenumber = \empty % Pre-3.0. \else \def\linenumber{l.\the\inputlineno:\space} \fi % Set up fixed words for English if not already set. \ifx\putwordAppendix\undefined \gdef\putwordAppendix{Appendix}\fi \ifx\putwordChapter\undefined \gdef\putwordChapter{Chapter}\fi \ifx\putwordfile\undefined \gdef\putwordfile{file}\fi \ifx\putwordin\undefined \gdef\putwordin{in}\fi \ifx\putwordIndexIsEmpty\undefined \gdef\putwordIndexIsEmpty{(Index is empty)}\fi \ifx\putwordIndexNonexistent\undefined \gdef\putwordIndexNonexistent{(Index is nonexistent)}\fi \ifx\putwordInfo\undefined \gdef\putwordInfo{Info}\fi \ifx\putwordInstanceVariableof\undefined \gdef\putwordInstanceVariableof{Instance Variable of}\fi \ifx\putwordMethodon\undefined \gdef\putwordMethodon{Method on}\fi \ifx\putwordNoTitle\undefined \gdef\putwordNoTitle{No Title}\fi \ifx\putwordof\undefined \gdef\putwordof{of}\fi \ifx\putwordon\undefined \gdef\putwordon{on}\fi \ifx\putwordpage\undefined \gdef\putwordpage{page}\fi \ifx\putwordsection\undefined \gdef\putwordsection{section}\fi \ifx\putwordSection\undefined \gdef\putwordSection{Section}\fi \ifx\putwordsee\undefined \gdef\putwordsee{see}\fi \ifx\putwordSee\undefined \gdef\putwordSee{See}\fi \ifx\putwordShortTOC\undefined \gdef\putwordShortTOC{Short Contents}\fi \ifx\putwordTOC\undefined \gdef\putwordTOC{Table of Contents}\fi % \ifx\putwordMJan\undefined \gdef\putwordMJan{January}\fi \ifx\putwordMFeb\undefined \gdef\putwordMFeb{February}\fi \ifx\putwordMMar\undefined \gdef\putwordMMar{March}\fi \ifx\putwordMApr\undefined \gdef\putwordMApr{April}\fi \ifx\putwordMMay\undefined \gdef\putwordMMay{May}\fi \ifx\putwordMJun\undefined \gdef\putwordMJun{June}\fi \ifx\putwordMJul\undefined \gdef\putwordMJul{July}\fi \ifx\putwordMAug\undefined \gdef\putwordMAug{August}\fi \ifx\putwordMSep\undefined \gdef\putwordMSep{September}\fi \ifx\putwordMOct\undefined \gdef\putwordMOct{October}\fi \ifx\putwordMNov\undefined \gdef\putwordMNov{November}\fi \ifx\putwordMDec\undefined \gdef\putwordMDec{December}\fi % \ifx\putwordDefmac\undefined \gdef\putwordDefmac{Macro}\fi \ifx\putwordDefspec\undefined \gdef\putwordDefspec{Special Form}\fi \ifx\putwordDefvar\undefined \gdef\putwordDefvar{Variable}\fi \ifx\putwordDefopt\undefined \gdef\putwordDefopt{User Option}\fi \ifx\putwordDeffunc\undefined \gdef\putwordDeffunc{Function}\fi % In some macros, we cannot use the `\? notation---the left quote is % in some cases the escape char. \chardef\colonChar = `\: \chardef\commaChar = `\, \chardef\dotChar = `\. \chardef\exclamChar= `\! \chardef\questChar = `\? \chardef\semiChar = `\; \chardef\underChar = `\_ \chardef\spaceChar = `\ % \chardef\spacecat = 10 \def\spaceisspace{\catcode\spaceChar=\spacecat} % Ignore a token. % \def\gobble#1{} % The following is used inside several \edef's. \def\makecsname#1{\expandafter\noexpand\csname#1\endcsname} % Hyphenation fixes. \hyphenation{ Flor-i-da Ghost-script Ghost-view Mac-OS Post-Script ap-pen-dix bit-map bit-maps data-base data-bases eshell fall-ing half-way long-est man-u-script man-u-scripts mini-buf-fer mini-buf-fers over-view par-a-digm par-a-digms rath-er rec-tan-gu-lar ro-bot-ics se-vere-ly set-up spa-ces spell-ing spell-ings stand-alone strong-est time-stamp time-stamps which-ever white-space wide-spread wrap-around } % Margin to add to right of even pages, to left of odd pages. \newdimen\bindingoffset \newdimen\normaloffset \newdimen\pagewidth \newdimen\pageheight % For a final copy, take out the rectangles % that mark overfull boxes (in case you have decided % that the text looks ok even though it passes the margin). % \def\finalout{\overfullrule=0pt} % @@| inserts a changebar to the left of the current line. It should % surround any changed text. This approach does *not* work if the % change spans more than two lines of output. To handle that, we would % have adopt a much more difficult approach (putting marks into the main % vertical list for the beginning and end of each change). % \def\|{% % \vadjust can only be used in horizontal mode. \leavevmode % % Append this vertical mode material after the current line in the output. \vadjust{% % We want to insert a rule with the height and depth of the current % leading; that is exactly what \strutbox is supposed to record. \vskip-\baselineskip % % \vadjust-items are inserted at the left edge of the type. So % the \llap here moves out into the left-hand margin. \llap{% % % For a thicker or thinner bar, change the `1pt'. \vrule height\baselineskip width1pt % % This is the space between the bar and the text. \hskip 12pt }% }% } % Sometimes it is convenient to have everything in the transcript file % and nothing on the terminal. We don't just call \tracingall here, % since that produces some useless output on the terminal. We also make % some effort to order the tracing commands to reduce output in the log % file; cf. trace.sty in LaTeX. % \def\gloggingall{\begingroup \globaldefs = 1 \loggingall \endgroup}% \def\loggingall{% \tracingstats2 \tracingpages1 \tracinglostchars2 % 2 gives us more in etex \tracingparagraphs1 \tracingoutput1 \tracingmacros2 \tracingrestores1 \showboxbreadth\maxdimen \showboxdepth\maxdimen \ifx\eTeXversion\undefined\else % etex gives us more logging \tracingscantokens1 \tracingifs1 \tracinggroups1 \tracingnesting2 \tracingassigns1 \fi \tracingcommands3 % 3 gives us more in etex \errorcontextlines16 }% % add check for \lastpenalty to plain's definitions. If the last thing % we did was a \nobreak, we don't want to insert more space. % \def\smallbreak{\ifnum\lastpenalty<10000\par\ifdim\lastskip<\smallskipamount \removelastskip\penalty-50\smallskip\fi\fi} \def\medbreak{\ifnum\lastpenalty<10000\par\ifdim\lastskip<\medskipamount \removelastskip\penalty-100\medskip\fi\fi} \def\bigbreak{\ifnum\lastpenalty<10000\par\ifdim\lastskip<\bigskipamount \removelastskip\penalty-200\bigskip\fi\fi} % For @@cropmarks command. % Do @@cropmarks to get crop marks. % \newif\ifcropmarks \let\cropmarks = \cropmarkstrue % % Dimensions to add cropmarks at corners. % Added by P. A. MacKay, 12 Nov. 1986 % \newdimen\outerhsize \newdimen\outervsize % set by the paper size routines \newdimen\cornerlong \cornerlong=1pc \newdimen\cornerthick \cornerthick=.3pt \newdimen\topandbottommargin \topandbottommargin=.75in % Main output routine. \chardef\PAGE = 255 \output = {\onepageout{\pagecontents\PAGE}} \newbox\headlinebox \newbox\footlinebox % \onepageout takes a vbox as an argument. Note that \pagecontents % does insertions, but you have to call it yourself. \def\onepageout#1{% \ifcropmarks \hoffset=0pt \else \hoffset=\normaloffset \fi % \ifodd\pageno \advance\hoffset by \bindingoffset \else \advance\hoffset by -\bindingoffset\fi % % Do this outside of the \shipout so @@code etc. will be expanded in % the headline as they should be, not taken literally (outputting ''code). \setbox\headlinebox = \vbox{\let\hsize=\pagewidth \makeheadline}% \setbox\footlinebox = \vbox{\let\hsize=\pagewidth \makefootline}% % {% % Have to do this stuff outside the \shipout because we want it to % take effect in \write's, yet the group defined by the \vbox ends % before the \shipout runs. % \escapechar = `\\ % use backslash in output files. \indexdummies % don't expand commands in the output. \normalturnoffactive % \ in index entries must not stay \, e.g., if % the page break happens to be in the middle of an example. \shipout\vbox{% % Do this early so pdf references go to the beginning of the page. \ifpdfmakepagedest \pdfdest name{\the\pageno} xyz\fi % \ifcropmarks \vbox to \outervsize\bgroup \hsize = \outerhsize \vskip-\topandbottommargin \vtop to0pt{% \line{\ewtop\hfil\ewtop}% \nointerlineskip \line{% \vbox{\moveleft\cornerthick\nstop}% \hfill \vbox{\moveright\cornerthick\nstop}% }% \vss}% \vskip\topandbottommargin \line\bgroup \hfil % center the page within the outer (page) hsize. \ifodd\pageno\hskip\bindingoffset\fi \vbox\bgroup \fi % \unvbox\headlinebox \pagebody{#1}% \ifdim\ht\footlinebox > 0pt % Only leave this space if the footline is nonempty. % (We lessened \vsize for it in \oddfootingxxx.) % The \baselineskip=24pt in plain's \makefootline has no effect. \vskip 2\baselineskip \unvbox\footlinebox \fi % \ifcropmarks \egroup % end of \vbox\bgroup \hfil\egroup % end of (centering) \line\bgroup \vskip\topandbottommargin plus1fill minus1fill \boxmaxdepth = \cornerthick \vbox to0pt{\vss \line{% \vbox{\moveleft\cornerthick\nsbot}% \hfill \vbox{\moveright\cornerthick\nsbot}% }% \nointerlineskip \line{\ewbot\hfil\ewbot}% }% \egroup % \vbox from first cropmarks clause \fi }% end of \shipout\vbox }% end of group with \normalturnoffactive \advancepageno \ifnum\outputpenalty>-20000 \else\dosupereject\fi } \newinsert\margin \dimen\margin=\maxdimen \def\pagebody#1{\vbox to\pageheight{\boxmaxdepth=\maxdepth #1}} {\catcode`\@@ =11 \gdef\pagecontents#1{\ifvoid\topins\else\unvbox\topins\fi % marginal hacks, juha@@viisa.uucp (Juha Takala) \ifvoid\margin\else % marginal info is present \rlap{\kern\hsize\vbox to\z@@{\kern1pt\box\margin \vss}}\fi \dimen@@=\dp#1 \unvbox#1 \ifvoid\footins\else\vskip\skip\footins\footnoterule \unvbox\footins\fi \ifr@@ggedbottom \kern-\dimen@@ \vfil \fi} } % Here are the rules for the cropmarks. Note that they are % offset so that the space between them is truly \outerhsize or \outervsize % (P. A. MacKay, 12 November, 1986) % \def\ewtop{\vrule height\cornerthick depth0pt width\cornerlong} \def\nstop{\vbox {\hrule height\cornerthick depth\cornerlong width\cornerthick}} \def\ewbot{\vrule height0pt depth\cornerthick width\cornerlong} \def\nsbot{\vbox {\hrule height\cornerlong depth\cornerthick width\cornerthick}} % Parse an argument, then pass it to #1. The argument is the rest of % the input line (except we remove a trailing comment). #1 should be a % macro which expects an ordinary undelimited TeX argument. % \def\parsearg{\parseargusing{}} \def\parseargusing#1#2{% \def\next{#2}% \begingroup \obeylines \spaceisspace #1% \parseargline\empty% Insert the \empty token, see \finishparsearg below. } {\obeylines % \gdef\parseargline#1^^M{% \endgroup % End of the group started in \parsearg. \argremovecomment #1\comment\ArgTerm% }% } % First remove any @@comment, then any @@c comment. \def\argremovecomment#1\comment#2\ArgTerm{\argremovec #1\c\ArgTerm} \def\argremovec#1\c#2\ArgTerm{\argcheckspaces#1\^^M\ArgTerm} % Each occurence of `\^^M' or `\^^M' is replaced by a single space. % % \argremovec might leave us with trailing space, e.g., % @@end itemize @@c foo % This space token undergoes the same procedure and is eventually removed % by \finishparsearg. % \def\argcheckspaces#1\^^M{\argcheckspacesX#1\^^M \^^M} \def\argcheckspacesX#1 \^^M{\argcheckspacesY#1\^^M} \def\argcheckspacesY#1\^^M#2\^^M#3\ArgTerm{% \def\temp{#3}% \ifx\temp\empty % We cannot use \next here, as it holds the macro to run; % thus we reuse \temp. \let\temp\finishparsearg \else \let\temp\argcheckspaces \fi % Put the space token in: \temp#1 #3\ArgTerm } % If a _delimited_ argument is enclosed in braces, they get stripped; so % to get _exactly_ the rest of the line, we had to prevent such situation. % We prepended an \empty token at the very beginning and we expand it now, % just before passing the control to \next. % (Similarily, we have to think about #3 of \argcheckspacesY above: it is % either the null string, or it ends with \^^M---thus there is no danger % that a pair of braces would be stripped. % % But first, we have to remove the trailing space token. % \def\finishparsearg#1 \ArgTerm{\expandafter\next\expandafter{#1}} % \parseargdef\foo{...} % is roughly equivalent to % \def\foo{\parsearg\Xfoo} % \def\Xfoo#1{...} % % Actually, I use \csname\string\foo\endcsname, ie. \\foo, as it is my % favourite TeX trick. --kasal, 16nov03 \def\parseargdef#1{% \expandafter \doparseargdef \csname\string#1\endcsname #1% } \def\doparseargdef#1#2{% \def#2{\parsearg#1}% \def#1##1% } % Several utility definitions with active space: { \obeyspaces \gdef\obeyedspace{ } % Make each space character in the input produce a normal interword % space in the output. Don't allow a line break at this space, as this % is used only in environments like @@example, where each line of input % should produce a line of output anyway. % \gdef\sepspaces{\obeyspaces\let =\tie} % If an index command is used in an @@example environment, any spaces % therein should become regular spaces in the raw index file, not the % expansion of \tie (\leavevmode \penalty \@@M \ ). \gdef\unsepspaces{\let =\space} } \def\flushcr{\ifx\par\lisppar \def\next##1{}\else \let\next=\relax \fi \next} % Define the framework for environments in texinfo.tex. It's used like this: % % \envdef\foo{...} % \def\Efoo{...} % % It's the responsibility of \envdef to insert \begingroup before the % actual body; @@end closes the group after calling \Efoo. \envdef also % defines \thisenv, so the current environment is known; @@end checks % whether the environment name matches. The \checkenv macro can also be % used to check whether the current environment is the one expected. % % Non-false conditionals (@@iftex, @@ifset) don't fit into this, so they % are not treated as enviroments; they don't open a group. (The % implementation of @@end takes care not to call \endgroup in this % special case.) % At runtime, environments start with this: \def\startenvironment#1{\begingroup\def\thisenv{#1}} % initialize \let\thisenv\empty % ... but they get defined via ``\envdef\foo{...}'': \long\def\envdef#1#2{\def#1{\startenvironment#1#2}} \def\envparseargdef#1#2{\parseargdef#1{\startenvironment#1#2}} % Check whether we're in the right environment: \def\checkenv#1{% \def\temp{#1}% \ifx\thisenv\temp \else \badenverr \fi } % Evironment mismatch, #1 expected: \def\badenverr{% \errhelp = \EMsimple \errmessage{This command can appear only \inenvironment\temp, not \inenvironment\thisenv}% } \def\inenvironment#1{% \ifx#1\empty out of any environment% \else in environment \expandafter\string#1% \fi } % @@end foo executes the definition of \Efoo. % But first, it executes a specialized version of \checkenv % \parseargdef\end{% \if 1\csname iscond.#1\endcsname \else % The general wording of \badenverr may not be ideal, but... --kasal, 06nov03 \expandafter\checkenv\csname#1\endcsname \csname E#1\endcsname \endgroup \fi } \newhelp\EMsimple{Press RETURN to continue.} %% Simple single-character @@ commands % @@@@ prints an @@ % Kludge this until the fonts are right (grr). \def\@@{{\tt\char64}} % This is turned off because it was never documented % and you can use @@w{...} around a quote to suppress ligatures. %% Define @@` and @@' to be the same as ` and ' %% but suppressing ligatures. %\def\`{{`}} %\def\'{{'}} % Used to generate quoted braces. \def\mylbrace {{\tt\char123}} \def\myrbrace {{\tt\char125}} \let\{=\mylbrace \let\}=\myrbrace \begingroup % Definitions to produce \{ and \} commands for indices, % and @@{ and @@} for the aux file. \catcode`\{ = \other \catcode`\} = \other \catcode`\[ = 1 \catcode`\] = 2 \catcode`\! = 0 \catcode`\\ = \other !gdef!lbracecmd[\{]% !gdef!rbracecmd[\}]% !gdef!lbraceatcmd[@@{]% !gdef!rbraceatcmd[@@}]% !endgroup % @@comma{} to avoid , parsing problems. \let\comma = , % Accents: @@, @@dotaccent @@ringaccent @@ubaraccent @@udotaccent % Others are defined by plain TeX: @@` @@' @@" @@^ @@~ @@= @@u @@v @@H. \let\, = \c \let\dotaccent = \. \def\ringaccent#1{{\accent23 #1}} \let\tieaccent = \t \let\ubaraccent = \b \let\udotaccent = \d % Other special characters: @@questiondown @@exclamdown @@ordf @@ordm % Plain TeX defines: @@AA @@AE @@O @@OE @@L (plus lowercase versions) @@ss. \def\questiondown{?`} \def\exclamdown{!`} \def\ordf{\leavevmode\raise1ex\hbox{\selectfonts\lllsize \underbar{a}}} \def\ordm{\leavevmode\raise1ex\hbox{\selectfonts\lllsize \underbar{o}}} % Dotless i and dotless j, used for accents. \def\imacro{i} \def\jmacro{j} \def\dotless#1{% \def\temp{#1}% \ifx\temp\imacro \ptexi \else\ifx\temp\jmacro \j \else \errmessage{@@dotless can be used only with i or j}% \fi\fi } % The \TeX{} logo, as in plain, but resetting the spacing so that a % period following counts as ending a sentence. (Idea found in latex.) % \edef\TeX{\TeX \spacefactor=1000 } % @@LaTeX{} logo. Not quite the same results as the definition in % latex.ltx, since we use a different font for the raised A; it's most % convenient for us to use an explicitly smaller font, rather than using % the \scriptstyle font (since we don't reset \scriptstyle and % \scriptscriptstyle). % \def\LaTeX{% L\kern-.36em {\setbox0=\hbox{T}% \vbox to \ht0{\hbox{\selectfonts\lllsize A}\vss}}% \kern-.15em \TeX } % Be sure we're in horizontal mode when doing a tie, since we make space % equivalent to this in @@example-like environments. Otherwise, a space % at the beginning of a line will start with \penalty -- and % since \penalty is valid in vertical mode, we'd end up putting the % penalty on the vertical list instead of in the new paragraph. {\catcode`@@ = 11 % Avoid using \@@M directly, because that causes trouble % if the definition is written into an index file. \global\let\tiepenalty = \@@M \gdef\tie{\leavevmode\penalty\tiepenalty\ } } % @@: forces normal size whitespace following. \def\:{\spacefactor=1000 } % @@* forces a line break. \def\*{\hfil\break\hbox{}\ignorespaces} % @@/ allows a line break. \let\/=\allowbreak % @@. is an end-of-sentence period. \def\.{.\spacefactor=3000 } % @@! is an end-of-sentence bang. \def\!{!\spacefactor=3000 } % @@? is an end-of-sentence query. \def\?{?\spacefactor=3000 } % @@w prevents a word break. Without the \leavevmode, @@w at the % beginning of a paragraph, when TeX is still in vertical mode, would % produce a whole line of output instead of starting the paragraph. \def\w#1{\leavevmode\hbox{#1}} % @@group ... @@end group forces ... to be all on one page, by enclosing % it in a TeX vbox. We use \vtop instead of \vbox to construct the box % to keep its height that of a normal line. According to the rules for % \topskip (p.114 of the TeXbook), the glue inserted is % max (\topskip - \ht (first item), 0). If that height is large, % therefore, no glue is inserted, and the space between the headline and % the text is small, which looks bad. % % Another complication is that the group might be very large. This can % cause the glue on the previous page to be unduly stretched, because it % does not have much material. In this case, it's better to add an % explicit \vfill so that the extra space is at the bottom. The % threshold for doing this is if the group is more than \vfilllimit % percent of a page (\vfilllimit can be changed inside of @@tex). % \newbox\groupbox \def\vfilllimit{0.7} % \envdef\group{% \ifnum\catcode`\^^M=\active \else \errhelp = \groupinvalidhelp \errmessage{@@group invalid in context where filling is enabled}% \fi \startsavinginserts % \setbox\groupbox = \vtop\bgroup % Do @@comment since we are called inside an environment such as % @@example, where each end-of-line in the input causes an % end-of-line in the output. We don't want the end-of-line after % the `@@group' to put extra space in the output. Since @@group % should appear on a line by itself (according to the Texinfo % manual), we don't worry about eating any user text. \comment } % % The \vtop produces a box with normal height and large depth; thus, TeX puts % \baselineskip glue before it, and (when the next line of text is done) % \lineskip glue after it. Thus, space below is not quite equal to space % above. But it's pretty close. \def\Egroup{% % To get correct interline space between the last line of the group % and the first line afterwards, we have to propagate \prevdepth. \endgraf % Not \par, as it may have been set to \lisppar. \global\dimen1 = \prevdepth \egroup % End the \vtop. % \dimen0 is the vertical size of the group's box. \dimen0 = \ht\groupbox \advance\dimen0 by \dp\groupbox % \dimen2 is how much space is left on the page (more or less). \dimen2 = \pageheight \advance\dimen2 by -\pagetotal % if the group doesn't fit on the current page, and it's a big big % group, force a page break. \ifdim \dimen0 > \dimen2 \ifdim \pagetotal < \vfilllimit\pageheight \page \fi \fi \box\groupbox \prevdepth = \dimen1 \checkinserts } % % TeX puts in an \escapechar (i.e., `@@') at the beginning of the help % message, so this ends up printing `@@group can only ...'. % \newhelp\groupinvalidhelp{% group can only be used in environments such as @@example,^^J% where each line of input produces a line of output.} % @@need space-in-mils % forces a page break if there is not space-in-mils remaining. \newdimen\mil \mil=0.001in % Old definition--didn't work. %\parseargdef\need{\par % %% This method tries to make TeX break the page naturally %% if the depth of the box does not fit. %{\baselineskip=0pt% %\vtop to #1\mil{\vfil}\kern -#1\mil\nobreak %\prevdepth=-1000pt %}} \parseargdef\need{% % Ensure vertical mode, so we don't make a big box in the middle of a % paragraph. \par % % If the @@need value is less than one line space, it's useless. \dimen0 = #1\mil \dimen2 = \ht\strutbox \advance\dimen2 by \dp\strutbox \ifdim\dimen0 > \dimen2 % % Do a \strut just to make the height of this box be normal, so the % normal leading is inserted relative to the preceding line. % And a page break here is fine. \vtop to #1\mil{\strut\vfil}% % % TeX does not even consider page breaks if a penalty added to the % main vertical list is 10000 or more. But in order to see if the % empty box we just added fits on the page, we must make it consider % page breaks. On the other hand, we don't want to actually break the % page after the empty box. So we use a penalty of 9999. % % There is an extremely small chance that TeX will actually break the % page at this \penalty, if there are no other feasible breakpoints in % sight. (If the user is using lots of big @@group commands, which % almost-but-not-quite fill up a page, TeX will have a hard time doing % good page breaking, for example.) However, I could not construct an % example where a page broke at this \penalty; if it happens in a real % document, then we can reconsider our strategy. \penalty9999 % % Back up by the size of the box, whether we did a page break or not. \kern -#1\mil % % Do not allow a page break right after this kern. \nobreak \fi } % @@br forces paragraph break (and is undocumented). \let\br = \par % @@page forces the start of a new page. % \def\page{\par\vfill\supereject} % @@exdent text.... % outputs text on separate line in roman font, starting at standard page margin % This records the amount of indent in the innermost environment. % That's how much \exdent should take out. \newskip\exdentamount % This defn is used inside fill environments such as @@defun. \parseargdef\exdent{\hfil\break\hbox{\kern -\exdentamount{\rm#1}}\hfil\break} % This defn is used inside nofill environments such as @@example. \parseargdef\nofillexdent{{\advance \leftskip by -\exdentamount \leftline{\hskip\leftskip{\rm#1}}}} % @@inmargin{WHICH}{TEXT} puts TEXT in the WHICH margin next to the current % paragraph. For more general purposes, use the \margin insertion % class. WHICH is `l' or `r'. % \newskip\inmarginspacing \inmarginspacing=1cm \def\strutdepth{\dp\strutbox} % \def\doinmargin#1#2{\strut\vadjust{% \nobreak \kern-\strutdepth \vtop to \strutdepth{% \baselineskip=\strutdepth \vss % if you have multiple lines of stuff to put here, you'll need to % make the vbox yourself of the appropriate size. \ifx#1l% \llap{\ignorespaces #2\hskip\inmarginspacing}% \else \rlap{\hskip\hsize \hskip\inmarginspacing \ignorespaces #2}% \fi \null }% }} \def\inleftmargin{\doinmargin l} \def\inrightmargin{\doinmargin r} % % @@inmargin{TEXT [, RIGHT-TEXT]} % (if RIGHT-TEXT is given, use TEXT for left page, RIGHT-TEXT for right; % else use TEXT for both). % \def\inmargin#1{\parseinmargin #1,,\finish} \def\parseinmargin#1,#2,#3\finish{% not perfect, but better than nothing. \setbox0 = \hbox{\ignorespaces #2}% \ifdim\wd0 > 0pt \def\lefttext{#1}% have both texts \def\righttext{#2}% \else \def\lefttext{#1}% have only one text \def\righttext{#1}% \fi % \ifodd\pageno \def\temp{\inrightmargin\righttext}% odd page -> outside is right margin \else \def\temp{\inleftmargin\lefttext}% \fi \temp } % @@include file insert text of that file as input. % \def\include{\parseargusing\filenamecatcodes\includezzz} \def\includezzz#1{% \pushthisfilestack \def\thisfile{#1}% {% \makevalueexpandable \def\temp{\input #1 }% \expandafter }\temp \popthisfilestack } \def\filenamecatcodes{% \catcode`\\=\other \catcode`~=\other \catcode`^=\other \catcode`_=\other \catcode`|=\other \catcode`<=\other \catcode`>=\other \catcode`+=\other \catcode`-=\other } \def\pushthisfilestack{% \expandafter\pushthisfilestackX\popthisfilestack\StackTerm } \def\pushthisfilestackX{% \expandafter\pushthisfilestackY\thisfile\StackTerm } \def\pushthisfilestackY #1\StackTerm #2\StackTerm {% \gdef\popthisfilestack{\gdef\thisfile{#1}\gdef\popthisfilestack{#2}}% } \def\popthisfilestack{\errthisfilestackempty} \def\errthisfilestackempty{\errmessage{Internal error: the stack of filenames is empty.}} \def\thisfile{} % @@center line % outputs that line, centered. % \parseargdef\center{% \ifhmode \let\next\centerH \else \let\next\centerV \fi \next{\hfil \ignorespaces#1\unskip \hfil}% } \def\centerH#1{% {% \hfil\break \advance\hsize by -\leftskip \advance\hsize by -\rightskip \line{#1}% \break }% } \def\centerV#1{\line{\kern\leftskip #1\kern\rightskip}} % @@sp n outputs n lines of vertical space \parseargdef\sp{\vskip #1\baselineskip} % @@comment ...line which is ignored... % @@c is the same as @@comment % @@ignore ... @@end ignore is another way to write a comment \def\comment{\begingroup \catcode`\^^M=\other% \catcode`\@@=\other \catcode`\{=\other \catcode`\}=\other% \commentxxx} {\catcode`\^^M=\other \gdef\commentxxx#1^^M{\endgroup}} \let\c=\comment % @@paragraphindent NCHARS % We'll use ems for NCHARS, close enough. % NCHARS can also be the word `asis' or `none'. % We cannot feasibly implement @@paragraphindent asis, though. % \def\asisword{asis} % no translation, these are keywords \def\noneword{none} % \parseargdef\paragraphindent{% \def\temp{#1}% \ifx\temp\asisword \else \ifx\temp\noneword \defaultparindent = 0pt \else \defaultparindent = #1em \fi \fi \parindent = \defaultparindent } % @@exampleindent NCHARS % We'll use ems for NCHARS like @@paragraphindent. % It seems @@exampleindent asis isn't necessary, but % I preserve it to make it similar to @@paragraphindent. \parseargdef\exampleindent{% \def\temp{#1}% \ifx\temp\asisword \else \ifx\temp\noneword \lispnarrowing = 0pt \else \lispnarrowing = #1em \fi \fi } % @@firstparagraphindent WORD % If WORD is `none', then suppress indentation of the first paragraph % after a section heading. If WORD is `insert', then do indent at such % paragraphs. % % The paragraph indentation is suppressed or not by calling % \suppressfirstparagraphindent, which the sectioning commands do. % We switch the definition of this back and forth according to WORD. % By default, we suppress indentation. % \def\suppressfirstparagraphindent{\dosuppressfirstparagraphindent} \def\insertword{insert} % \parseargdef\firstparagraphindent{% \def\temp{#1}% \ifx\temp\noneword \let\suppressfirstparagraphindent = \dosuppressfirstparagraphindent \else\ifx\temp\insertword \let\suppressfirstparagraphindent = \relax \else \errhelp = \EMsimple \errmessage{Unknown @@firstparagraphindent option `\temp'}% \fi\fi } % Here is how we actually suppress indentation. Redefine \everypar to % \kern backwards by \parindent, and then reset itself to empty. % % We also make \indent itself not actually do anything until the next % paragraph. % \gdef\dosuppressfirstparagraphindent{% \gdef\indent{% \restorefirstparagraphindent \indent }% \gdef\noindent{% \restorefirstparagraphindent \noindent }% \global\everypar = {% \kern -\parindent \restorefirstparagraphindent }% } \gdef\restorefirstparagraphindent{% \global \let \indent = \ptexindent \global \let \noindent = \ptexnoindent \global \everypar = {}% } % @@asis just yields its argument. Used with @@table, for example. % \def\asis#1{#1} % @@math outputs its argument in math mode. % % One complication: _ usually means subscripts, but it could also mean % an actual _ character, as in @@math{@@var{some_variable} + 1}. So make % _ active, and distinguish by seeing if the current family is \slfam, % which is what @@var uses. { \catcode\underChar = \active \gdef\mathunderscore{% \catcode\underChar=\active \def_{\ifnum\fam=\slfam \_\else\sb\fi}% } } % Another complication: we want \\ (and @@\) to output a \ character. % FYI, plain.tex uses \\ as a temporary control sequence (why?), but % this is not advertised and we don't care. Texinfo does not % otherwise define @@\. % % The \mathchar is class=0=ordinary, family=7=ttfam, position=5C=\. \def\mathbackslash{\ifnum\fam=\ttfam \mathchar"075C \else\backslash \fi} % \def\math{% \tex \mathunderscore \let\\ = \mathbackslash \mathactive $\finishmath } \def\finishmath#1{#1$\endgroup} % Close the group opened by \tex. % Some active characters (such as <) are spaced differently in math. % We have to reset their definitions in case the @@math was an argument % to a command which sets the catcodes (such as @@item or @@section). % { \catcode`^ = \active \catcode`< = \active \catcode`> = \active \catcode`+ = \active \gdef\mathactive{% \let^ = \ptexhat \let< = \ptexless \let> = \ptexgtr \let+ = \ptexplus } } % @@bullet and @@minus need the same treatment as @@math, just above. \def\bullet{$\ptexbullet$} \def\minus{$-$} % @@dots{} outputs an ellipsis using the current font. % We do .5em per period so that it has the same spacing in a typewriter % font as three actual period characters. % \def\dots{% \leavevmode \hbox to 1.5em{% \hskip 0pt plus 0.25fil .\hfil.\hfil.% \hskip 0pt plus 0.5fil }% } % @@enddots{} is an end-of-sentence ellipsis. % \def\enddots{% \dots \spacefactor=3000 } % @@comma{} is so commas can be inserted into text without messing up % Texinfo's parsing. % \let\comma = , % @@refill is a no-op. \let\refill=\relax % If working on a large document in chapters, it is convenient to % be able to disable indexing, cross-referencing, and contents, for test runs. % This is done with @@novalidate (before @@setfilename). % \newif\iflinks \linkstrue % by default we want the aux files. \let\novalidate = \linksfalse % @@setfilename is done at the beginning of every texinfo file. % So open here the files we need to have open while reading the input. % This makes it possible to make a .fmt file for texinfo. \def\setfilename{% \fixbackslash % Turn off hack to swallow `\input texinfo'. \iflinks \tryauxfile % Open the new aux file. TeX will close it automatically at exit. \immediate\openout\auxfile=\jobname.aux \fi % \openindices needs to do some work in any case. \openindices \let\setfilename=\comment % Ignore extra @@setfilename cmds. % % If texinfo.cnf is present on the system, read it. % Useful for site-wide @@afourpaper, etc. \openin 1 texinfo.cnf \ifeof 1 \else \input texinfo.cnf \fi \closein 1 % \comment % Ignore the actual filename. } % Called from \setfilename. % \def\openindices{% \newindex{cp}% \newcodeindex{fn}% \newcodeindex{vr}% \newcodeindex{tp}% \newcodeindex{ky}% \newcodeindex{pg}% } % @@bye. \outer\def\bye{\pagealignmacro\tracingstats=1\ptexend} \message{pdf,} % adobe `portable' document format \newcount\tempnum \newcount\lnkcount \newtoks\filename \newcount\filenamelength \newcount\pgn \newtoks\toksA \newtoks\toksB \newtoks\toksC \newtoks\toksD \newbox\boxA \newcount\countA \newif\ifpdf \newif\ifpdfmakepagedest % when pdftex is run in dvi mode, \pdfoutput is defined (so \pdfoutput=1 % can be set). So we test for \relax and 0 as well as \undefined, % borrowed from ifpdf.sty. \ifx\pdfoutput\undefined \else \ifx\pdfoutput\relax \else \ifcase\pdfoutput \else \pdftrue \fi \fi \fi % \ifpdf \input pdfcolor \pdfcatalog{/PageMode /UseOutlines}% \def\dopdfimage#1#2#3{% \def\imagewidth{#2}% \def\imageheight{#3}% % without \immediate, pdftex seg faults when the same image is % included twice. (Version 3.14159-pre-1.0-unofficial-20010704.) \ifnum\pdftexversion < 14 \immediate\pdfimage \else \immediate\pdfximage \fi \ifx\empty\imagewidth\else width \imagewidth \fi \ifx\empty\imageheight\else height \imageheight \fi \ifnum\pdftexversion<13 #1.pdf% \else {#1.pdf}% \fi \ifnum\pdftexversion < 14 \else \pdfrefximage \pdflastximage \fi} \def\pdfmkdest#1{{% % We have to set dummies so commands such as @@code in a section title % aren't expanded. \atdummies \normalturnoffactive \pdfdest name{#1} xyz% }} \def\pdfmkpgn#1{#1} \let\linkcolor = \Blue % was Cyan, but that seems light? \def\endlink{\Black\pdfendlink} % Adding outlines to PDF; macros for calculating structure of outlines % come from Petr Olsak \def\expnumber#1{\expandafter\ifx\csname#1\endcsname\relax 0% \else \csname#1\endcsname \fi} \def\advancenumber#1{\tempnum=\expnumber{#1}\relax \advance\tempnum by 1 \expandafter\xdef\csname#1\endcsname{\the\tempnum}} % % #1 is the section text. #2 is the pdf expression for the number % of subentries (or empty, for subsubsections). #3 is the node % text, which might be empty if this toc entry had no % corresponding node. #4 is the page number. % \def\dopdfoutline#1#2#3#4{% % Generate a link to the node text if that exists; else, use the % page number. We could generate a destination for the section % text in the case where a section has no node, but it doesn't % seem worthwhile, since most documents are normally structured. \def\pdfoutlinedest{#3}% \ifx\pdfoutlinedest\empty \def\pdfoutlinedest{#4}\fi % \pdfoutline goto name{\pdfmkpgn{\pdfoutlinedest}}#2{#1}% } % \def\pdfmakeoutlines{% \begingroup % Thanh's hack / proper braces in bookmarks \edef\mylbrace{\iftrue \string{\else}\fi}\let\{=\mylbrace \edef\myrbrace{\iffalse{\else\string}\fi}\let\}=\myrbrace % % Read toc silently, to get counts of subentries for \pdfoutline. \def\numchapentry##1##2##3##4{% \def\thischapnum{##2}% \def\thissecnum{0}% \def\thissubsecnum{0}% }% \def\numsecentry##1##2##3##4{% \advancenumber{chap\thischapnum}% \def\thissecnum{##2}% \def\thissubsecnum{0}% }% \def\numsubsecentry##1##2##3##4{% \advancenumber{sec\thissecnum}% \def\thissubsecnum{##2}% }% \def\numsubsubsecentry##1##2##3##4{% \advancenumber{subsec\thissubsecnum}% }% \def\thischapnum{0}% \def\thissecnum{0}% \def\thissubsecnum{0}% % % use \def rather than \let here because we redefine \chapentry et % al. a second time, below. \def\appentry{\numchapentry}% \def\appsecentry{\numsecentry}% \def\appsubsecentry{\numsubsecentry}% \def\appsubsubsecentry{\numsubsubsecentry}% \def\unnchapentry{\numchapentry}% \def\unnsecentry{\numsecentry}% \def\unnsubsecentry{\numsubsecentry}% \def\unnsubsubsecentry{\numsubsubsecentry}% \input \jobname.toc % % Read toc second time, this time actually producing the outlines. % The `-' means take the \expnumber as the absolute number of % subentries, which we calculated on our first read of the .toc above. % % We use the node names as the destinations. \def\numchapentry##1##2##3##4{% \dopdfoutline{##1}{count-\expnumber{chap##2}}{##3}{##4}}% \def\numsecentry##1##2##3##4{% \dopdfoutline{##1}{count-\expnumber{sec##2}}{##3}{##4}}% \def\numsubsecentry##1##2##3##4{% \dopdfoutline{##1}{count-\expnumber{subsec##2}}{##3}{##4}}% \def\numsubsubsecentry##1##2##3##4{% count is always zero \dopdfoutline{##1}{}{##3}{##4}}% % % PDF outlines are displayed using system fonts, instead of % document fonts. Therefore we cannot use special characters, % since the encoding is unknown. For example, the eogonek from % Latin 2 (0xea) gets translated to a | character. Info from % Staszek Wawrykiewicz, 19 Jan 2004 04:09:24 +0100. % % xx to do this right, we have to translate 8-bit characters to % their "best" equivalent, based on the @@documentencoding. Right % now, I guess we'll just let the pdf reader have its way. \indexnofonts \turnoffactive \input \jobname.toc \endgroup } % \def\makelinks #1,{% \def\params{#1}\def\E{END}% \ifx\params\E \let\nextmakelinks=\relax \else \let\nextmakelinks=\makelinks \ifnum\lnkcount>0,\fi \picknum{#1}% \startlink attr{/Border [0 0 0]} goto name{\pdfmkpgn{\the\pgn}}% \linkcolor #1% \advance\lnkcount by 1% \endlink \fi \nextmakelinks } \def\picknum#1{\expandafter\pn#1} \def\pn#1{% \def\p{#1}% \ifx\p\lbrace \let\nextpn=\ppn \else \let\nextpn=\ppnn \def\first{#1} \fi \nextpn } \def\ppn#1{\pgn=#1\gobble} \def\ppnn{\pgn=\first} \def\pdfmklnk#1{\lnkcount=0\makelinks #1,END,} \def\skipspaces#1{\def\PP{#1}\def\D{|}% \ifx\PP\D\let\nextsp\relax \else\let\nextsp\skipspaces \ifx\p\space\else\addtokens{\filename}{\PP}% \advance\filenamelength by 1 \fi \fi \nextsp} \def\getfilename#1{\filenamelength=0\expandafter\skipspaces#1|\relax} \ifnum\pdftexversion < 14 \let \startlink \pdfannotlink \else \let \startlink \pdfstartlink \fi \def\pdfurl#1{% \begingroup \normalturnoffactive\def\@@{@@}% \makevalueexpandable \leavevmode\Red \startlink attr{/Border [0 0 0]}% user{/Subtype /Link /A << /S /URI /URI (#1) >>}% \endgroup} \def\pdfgettoks#1.{\setbox\boxA=\hbox{\toksA={#1.}\toksB={}\maketoks}} \def\addtokens#1#2{\edef\addtoks{\noexpand#1={\the#1#2}}\addtoks} \def\adn#1{\addtokens{\toksC}{#1}\global\countA=1\let\next=\maketoks} \def\poptoks#1#2|ENDTOKS|{\let\first=#1\toksD={#1}\toksA={#2}} \def\maketoks{% \expandafter\poptoks\the\toksA|ENDTOKS|\relax \ifx\first0\adn0 \else\ifx\first1\adn1 \else\ifx\first2\adn2 \else\ifx\first3\adn3 \else\ifx\first4\adn4 \else\ifx\first5\adn5 \else\ifx\first6\adn6 \else\ifx\first7\adn7 \else\ifx\first8\adn8 \else\ifx\first9\adn9 \else \ifnum0=\countA\else\makelink\fi \ifx\first.\let\next=\done\else \let\next=\maketoks \addtokens{\toksB}{\the\toksD} \ifx\first,\addtokens{\toksB}{\space}\fi \fi \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi \next} \def\makelink{\addtokens{\toksB}% {\noexpand\pdflink{\the\toksC}}\toksC={}\global\countA=0} \def\pdflink#1{% \startlink attr{/Border [0 0 0]} goto name{\pdfmkpgn{#1}} \linkcolor #1\endlink} \def\done{\edef\st{\global\noexpand\toksA={\the\toksB}}\st} \else \let\pdfmkdest = \gobble \let\pdfurl = \gobble \let\endlink = \relax \let\linkcolor = \relax \let\pdfmakeoutlines = \relax \fi % \ifx\pdfoutput \message{fonts,} % Change the current font style to #1, remembering it in \curfontstyle. % For now, we do not accumulate font styles: @@b{@@i{foo}} prints foo in % italics, not bold italics. % \def\setfontstyle#1{% \def\curfontstyle{#1}% not as a control sequence, because we are \edef'd. \csname ten#1\endcsname % change the current font } % Select #1 fonts with the current style. % \def\selectfonts#1{\csname #1fonts\endcsname \csname\curfontstyle\endcsname} \def\rm{\fam=0 \setfontstyle{rm}} \def\it{\fam=\itfam \setfontstyle{it}} \def\sl{\fam=\slfam \setfontstyle{sl}} \def\bf{\fam=\bffam \setfontstyle{bf}}\def\bfstylename{bf} \def\tt{\fam=\ttfam \setfontstyle{tt}} % Texinfo sort of supports the sans serif font style, which plain TeX does not. % So we set up a \sf. \newfam\sffam \def\sf{\fam=\sffam \setfontstyle{sf}} \let\li = \sf % Sometimes we call it \li, not \sf. % We don't need math for this font style. \def\ttsl{\setfontstyle{ttsl}} % Default leading. \newdimen\textleading \textleading = 13.2pt % Set the baselineskip to #1, and the lineskip and strut size % correspondingly. There is no deep meaning behind these magic numbers % used as factors; they just match (closely enough) what Knuth defined. % \def\lineskipfactor{.08333} \def\strutheightpercent{.70833} \def\strutdepthpercent {.29167} % \def\setleading#1{% \normalbaselineskip = #1\relax \normallineskip = \lineskipfactor\normalbaselineskip \normalbaselines \setbox\strutbox =\hbox{% \vrule width0pt height\strutheightpercent\baselineskip depth \strutdepthpercent \baselineskip }% } % Set the font macro #1 to the font named #2, adding on the % specified font prefix (normally `cm'). % #3 is the font's design size, #4 is a scale factor \def\setfont#1#2#3#4{\font#1=\fontprefix#2#3 scaled #4} % Use cm as the default font prefix. % To specify the font prefix, you must define \fontprefix % before you read in texinfo.tex. \ifx\fontprefix\undefined \def\fontprefix{cm} \fi % Support font families that don't use the same naming scheme as CM. \def\rmshape{r} \def\rmbshape{bx} %where the normal face is bold \def\bfshape{b} \def\bxshape{bx} \def\ttshape{tt} \def\ttbshape{tt} \def\ttslshape{sltt} \def\itshape{ti} \def\itbshape{bxti} \def\slshape{sl} \def\slbshape{bxsl} \def\sfshape{ss} \def\sfbshape{ss} \def\scshape{csc} \def\scbshape{csc} % Text fonts (11.2pt, magstep1). \def\textnominalsize{11pt} \edef\mainmagstep{\magstephalf} \setfont\textrm\rmshape{10}{\mainmagstep} \setfont\texttt\ttshape{10}{\mainmagstep} \setfont\textbf\bfshape{10}{\mainmagstep} \setfont\textit\itshape{10}{\mainmagstep} \setfont\textsl\slshape{10}{\mainmagstep} \setfont\textsf\sfshape{10}{\mainmagstep} \setfont\textsc\scshape{10}{\mainmagstep} \setfont\textttsl\ttslshape{10}{\mainmagstep} \font\texti=cmmi10 scaled \mainmagstep \font\textsy=cmsy10 scaled \mainmagstep % A few fonts for @@defun names and args. \setfont\defbf\bfshape{10}{\magstep1} \setfont\deftt\ttshape{10}{\magstep1} \setfont\defttsl\ttslshape{10}{\magstep1} \def\df{\let\tentt=\deftt \let\tenbf = \defbf \let\tenttsl=\defttsl \bf} % Fonts for indices, footnotes, small examples (9pt). \def\smallnominalsize{9pt} \setfont\smallrm\rmshape{9}{1000} \setfont\smalltt\ttshape{9}{1000} \setfont\smallbf\bfshape{10}{900} \setfont\smallit\itshape{9}{1000} \setfont\smallsl\slshape{9}{1000} \setfont\smallsf\sfshape{9}{1000} \setfont\smallsc\scshape{10}{900} \setfont\smallttsl\ttslshape{10}{900} \font\smalli=cmmi9 \font\smallsy=cmsy9 % Fonts for small examples (8pt). \def\smallernominalsize{8pt} \setfont\smallerrm\rmshape{8}{1000} \setfont\smallertt\ttshape{8}{1000} \setfont\smallerbf\bfshape{10}{800} \setfont\smallerit\itshape{8}{1000} \setfont\smallersl\slshape{8}{1000} \setfont\smallersf\sfshape{8}{1000} \setfont\smallersc\scshape{10}{800} \setfont\smallerttsl\ttslshape{10}{800} \font\smalleri=cmmi8 \font\smallersy=cmsy8 % Fonts for title page (20.4pt): \def\titlenominalsize{20pt} \setfont\titlerm\rmbshape{12}{\magstep3} \setfont\titleit\itbshape{10}{\magstep4} \setfont\titlesl\slbshape{10}{\magstep4} \setfont\titlett\ttbshape{12}{\magstep3} \setfont\titlettsl\ttslshape{10}{\magstep4} \setfont\titlesf\sfbshape{17}{\magstep1} \let\titlebf=\titlerm \setfont\titlesc\scbshape{10}{\magstep4} \font\titlei=cmmi12 scaled \magstep3 \font\titlesy=cmsy10 scaled \magstep4 \def\authorrm{\secrm} \def\authortt{\sectt} % Chapter (and unnumbered) fonts (17.28pt). \def\chapnominalsize{17pt} \setfont\chaprm\rmbshape{12}{\magstep2} \setfont\chapit\itbshape{10}{\magstep3} \setfont\chapsl\slbshape{10}{\magstep3} \setfont\chaptt\ttbshape{12}{\magstep2} \setfont\chapttsl\ttslshape{10}{\magstep3} \setfont\chapsf\sfbshape{17}{1000} \let\chapbf=\chaprm \setfont\chapsc\scbshape{10}{\magstep3} \font\chapi=cmmi12 scaled \magstep2 \font\chapsy=cmsy10 scaled \magstep3 % Section fonts (14.4pt). \def\secnominalsize{14pt} \setfont\secrm\rmbshape{12}{\magstep1} \setfont\secit\itbshape{10}{\magstep2} \setfont\secsl\slbshape{10}{\magstep2} \setfont\sectt\ttbshape{12}{\magstep1} \setfont\secttsl\ttslshape{10}{\magstep2} \setfont\secsf\sfbshape{12}{\magstep1} \let\secbf\secrm \setfont\secsc\scbshape{10}{\magstep2} \font\seci=cmmi12 scaled \magstep1 \font\secsy=cmsy10 scaled \magstep2 % Subsection fonts (13.15pt). \def\ssecnominalsize{13pt} \setfont\ssecrm\rmbshape{12}{\magstephalf} \setfont\ssecit\itbshape{10}{1315} \setfont\ssecsl\slbshape{10}{1315} \setfont\ssectt\ttbshape{12}{\magstephalf} \setfont\ssecttsl\ttslshape{10}{1315} \setfont\ssecsf\sfbshape{12}{\magstephalf} \let\ssecbf\ssecrm \setfont\ssecsc\scbshape{10}{1315} \font\sseci=cmmi12 scaled \magstephalf \font\ssecsy=cmsy10 scaled 1315 % Reduced fonts for @@acro in text (10pt). \def\reducednominalsize{10pt} \setfont\reducedrm\rmshape{10}{1000} \setfont\reducedtt\ttshape{10}{1000} \setfont\reducedbf\bfshape{10}{1000} \setfont\reducedit\itshape{10}{1000} \setfont\reducedsl\slshape{10}{1000} \setfont\reducedsf\sfshape{10}{1000} \setfont\reducedsc\scshape{10}{1000} \setfont\reducedttsl\ttslshape{10}{1000} \font\reducedi=cmmi10 \font\reducedsy=cmsy10 % In order for the font changes to affect most math symbols and letters, % we have to define the \textfont of the standard families. Since % texinfo doesn't allow for producing subscripts and superscripts except % in the main text, we don't bother to reset \scriptfont and % \scriptscriptfont (which would also require loading a lot more fonts). % \def\resetmathfonts{% \textfont0=\tenrm \textfont1=\teni \textfont2=\tensy \textfont\itfam=\tenit \textfont\slfam=\tensl \textfont\bffam=\tenbf \textfont\ttfam=\tentt \textfont\sffam=\tensf } % The font-changing commands redefine the meanings of \tenSTYLE, instead % of just \STYLE. We do this because \STYLE needs to also set the % current \fam for math mode. Our \STYLE (e.g., \rm) commands hardwire % \tenSTYLE to set the current font. % % Each font-changing command also sets the names \lsize (one size lower) % and \lllsize (three sizes lower). These relative commands are used in % the LaTeX logo and acronyms. % % This all needs generalizing, badly. % \def\textfonts{% \let\tenrm=\textrm \let\tenit=\textit \let\tensl=\textsl \let\tenbf=\textbf \let\tentt=\texttt \let\smallcaps=\textsc \let\tensf=\textsf \let\teni=\texti \let\tensy=\textsy \let\tenttsl=\textttsl \def\curfontsize{text}% \def\lsize{reduced}\def\lllsize{smaller}% \resetmathfonts \setleading{\textleading}} \def\titlefonts{% \let\tenrm=\titlerm \let\tenit=\titleit \let\tensl=\titlesl \let\tenbf=\titlebf \let\tentt=\titlett \let\smallcaps=\titlesc \let\tensf=\titlesf \let\teni=\titlei \let\tensy=\titlesy \let\tenttsl=\titlettsl \def\curfontsize{title}% \def\lsize{chap}\def\lllsize{subsec}% \resetmathfonts \setleading{25pt}} \def\titlefont#1{{\titlefonts\rm #1}} \def\chapfonts{% \let\tenrm=\chaprm \let\tenit=\chapit \let\tensl=\chapsl \let\tenbf=\chapbf \let\tentt=\chaptt \let\smallcaps=\chapsc \let\tensf=\chapsf \let\teni=\chapi \let\tensy=\chapsy \let\tenttsl=\chapttsl \def\curfontsize{chap}% \def\lsize{sec}\def\lllsize{text}% \resetmathfonts \setleading{19pt}} \def\secfonts{% \let\tenrm=\secrm \let\tenit=\secit \let\tensl=\secsl \let\tenbf=\secbf \let\tentt=\sectt \let\smallcaps=\secsc \let\tensf=\secsf \let\teni=\seci \let\tensy=\secsy \let\tenttsl=\secttsl \def\curfontsize{sec}% \def\lsize{subsec}\def\lllsize{reduced}% \resetmathfonts \setleading{16pt}} \def\subsecfonts{% \let\tenrm=\ssecrm \let\tenit=\ssecit \let\tensl=\ssecsl \let\tenbf=\ssecbf \let\tentt=\ssectt \let\smallcaps=\ssecsc \let\tensf=\ssecsf \let\teni=\sseci \let\tensy=\ssecsy \let\tenttsl=\ssecttsl \def\curfontsize{ssec}% \def\lsize{text}\def\lllsize{small}% \resetmathfonts \setleading{15pt}} \let\subsubsecfonts = \subsecfonts \def\reducedfonts{% \let\tenrm=\reducedrm \let\tenit=\reducedit \let\tensl=\reducedsl \let\tenbf=\reducedbf \let\tentt=\reducedtt \let\reducedcaps=\reducedsc \let\tensf=\reducedsf \let\teni=\reducedi \let\tensy=\reducedsy \let\tenttsl=\reducedttsl \def\curfontsize{reduced}% \def\lsize{small}\def\lllsize{smaller}% \resetmathfonts \setleading{10.5pt}} \def\smallfonts{% \let\tenrm=\smallrm \let\tenit=\smallit \let\tensl=\smallsl \let\tenbf=\smallbf \let\tentt=\smalltt \let\smallcaps=\smallsc \let\tensf=\smallsf \let\teni=\smalli \let\tensy=\smallsy \let\tenttsl=\smallttsl \def\curfontsize{small}% \def\lsize{smaller}\def\lllsize{smaller}% \resetmathfonts \setleading{10.5pt}} \def\smallerfonts{% \let\tenrm=\smallerrm \let\tenit=\smallerit \let\tensl=\smallersl \let\tenbf=\smallerbf \let\tentt=\smallertt \let\smallcaps=\smallersc \let\tensf=\smallersf \let\teni=\smalleri \let\tensy=\smallersy \let\tenttsl=\smallerttsl \def\curfontsize{smaller}% \def\lsize{smaller}\def\lllsize{smaller}% \resetmathfonts \setleading{9.5pt}} % Set the fonts to use with the @@small... environments. \let\smallexamplefonts = \smallfonts % About \smallexamplefonts. If we use \smallfonts (9pt), @@smallexample % can fit this many characters: % 8.5x11=86 smallbook=72 a4=90 a5=69 % If we use \scriptfonts (8pt), then we can fit this many characters: % 8.5x11=90+ smallbook=80 a4=90+ a5=77 % For me, subjectively, the few extra characters that fit aren't worth % the additional smallness of 8pt. So I'm making the default 9pt. % % By the way, for comparison, here's what fits with @@example (10pt): % 8.5x11=71 smallbook=60 a4=75 a5=58 % % I wish the USA used A4 paper. % --karl, 24jan03. % Set up the default fonts, so we can use them for creating boxes. % \textfonts \rm % Define these so they can be easily changed for other fonts. \def\angleleft{$\langle$} \def\angleright{$\rangle$} % Count depth in font-changes, for error checks \newcount\fontdepth \fontdepth=0 % Fonts for short table of contents. \setfont\shortcontrm\rmshape{12}{1000} \setfont\shortcontbf\bfshape{10}{\magstep1} % no cmb12 \setfont\shortcontsl\slshape{12}{1000} \setfont\shortconttt\ttshape{12}{1000} %% Add scribe-like font environments, plus @@l for inline lisp (usually sans %% serif) and @@ii for TeX italic % \smartitalic{ARG} outputs arg in italics, followed by an italic correction % unless the following character is such as not to need one. \def\smartitalicx{\ifx\next,\else\ifx\next-\else\ifx\next.\else \ptexslash\fi\fi\fi} \def\smartslanted#1{{\ifusingtt\ttsl\sl #1}\futurelet\next\smartitalicx} \def\smartitalic#1{{\ifusingtt\ttsl\it #1}\futurelet\next\smartitalicx} % like \smartslanted except unconditionally uses \ttsl. % @@var is set to this for defun arguments. \def\ttslanted#1{{\ttsl #1}\futurelet\next\smartitalicx} % like \smartslanted except unconditionally use \sl. We never want % ttsl for book titles, do we? \def\cite#1{{\sl #1}\futurelet\next\smartitalicx} \let\i=\smartitalic \let\slanted=\smartslanted \let\var=\smartslanted \let\dfn=\smartslanted \let\emph=\smartitalic % @@b, explicit bold. \def\b#1{{\bf #1}} \let\strong=\b % @@sansserif, explicit sans. \def\sansserif#1{{\sf #1}} % We can't just use \exhyphenpenalty, because that only has effect at % the end of a paragraph. Restore normal hyphenation at the end of the % group within which \nohyphenation is presumably called. % \def\nohyphenation{\hyphenchar\font = -1 \aftergroup\restorehyphenation} \def\restorehyphenation{\hyphenchar\font = `- } % Set sfcode to normal for the chars that usually have another value. % Can't use plain's \frenchspacing because it uses the `\x notation, and % sometimes \x has an active definition that messes things up. % \catcode`@@=11 \def\frenchspacing{% \sfcode\dotChar =\@@m \sfcode\questChar=\@@m \sfcode\exclamChar=\@@m \sfcode\colonChar=\@@m \sfcode\semiChar =\@@m \sfcode\commaChar =\@@m } \catcode`@@=\other \def\t#1{% {\tt \rawbackslash \frenchspacing #1}% \null } \def\samp#1{`\tclose{#1}'\null} \setfont\keyrm\rmshape{8}{1000} \font\keysy=cmsy9 \def\key#1{{\keyrm\textfont2=\keysy \leavevmode\hbox{% \raise0.4pt\hbox{\angleleft}\kern-.08em\vtop{% \vbox{\hrule\kern-0.4pt \hbox{\raise0.4pt\hbox{\vphantom{\angleleft}}#1}}% \kern-0.4pt\hrule}% \kern-.06em\raise0.4pt\hbox{\angleright}}}} % The old definition, with no lozenge: %\def\key #1{{\ttsl \nohyphenation \uppercase{#1}}\null} \def\ctrl #1{{\tt \rawbackslash \hat}#1} % @@file, @@option are the same as @@samp. \let\file=\samp \let\option=\samp % @@code is a modification of @@t, % which makes spaces the same size as normal in the surrounding text. \def\tclose#1{% {% % Change normal interword space to be same as for the current font. \spaceskip = \fontdimen2\font % % Switch to typewriter. \tt % % But `\ ' produces the large typewriter interword space. \def\ {{\spaceskip = 0pt{} }}% % % Turn off hyphenation. \nohyphenation % \rawbackslash \frenchspacing #1% }% \null } % We *must* turn on hyphenation at `-' and `_' in @@code. % Otherwise, it is too hard to avoid overfull hboxes % in the Emacs manual, the Library manual, etc. % Unfortunately, TeX uses one parameter (\hyphenchar) to control % both hyphenation at - and hyphenation within words. % We must therefore turn them both off (\tclose does that) % and arrange explicitly to hyphenate at a dash. % -- rms. { \catcode`\-=\active \catcode`\_=\active % \global\def\code{\begingroup \catcode`\-=\active \let-\codedash \catcode`\_=\active \let_\codeunder \codex } } \def\realdash{-} \def\codedash{-\discretionary{}{}{}} \def\codeunder{% % this is all so @@math{@@code{var_name}+1} can work. In math mode, _ % is "active" (mathcode"8000) and \normalunderscore (or \char95, etc.) % will therefore expand the active definition of _, which is us % (inside @@code that is), therefore an endless loop. \ifusingtt{\ifmmode \mathchar"075F % class 0=ordinary, family 7=ttfam, pos 0x5F=_. \else\normalunderscore \fi \discretionary{}{}{}}% {\_}% } \def\codex #1{\tclose{#1}\endgroup} % @@kbd is like @@code, except that if the argument is just one @@key command, % then @@kbd has no effect. % @@kbdinputstyle -- arg is `distinct' (@@kbd uses slanted tty font always), % `example' (@@kbd uses ttsl only inside of @@example and friends), % or `code' (@@kbd uses normal tty font always). \parseargdef\kbdinputstyle{% \def\arg{#1}% \ifx\arg\worddistinct \gdef\kbdexamplefont{\ttsl}\gdef\kbdfont{\ttsl}% \else\ifx\arg\wordexample \gdef\kbdexamplefont{\ttsl}\gdef\kbdfont{\tt}% \else\ifx\arg\wordcode \gdef\kbdexamplefont{\tt}\gdef\kbdfont{\tt}% \else \errhelp = \EMsimple \errmessage{Unknown @@kbdinputstyle option `\arg'}% \fi\fi\fi } \def\worddistinct{distinct} \def\wordexample{example} \def\wordcode{code} % Default is `distinct.' \kbdinputstyle distinct \def\xkey{\key} \def\kbdfoo#1#2#3\par{\def\one{#1}\def\three{#3}\def\threex{??}% \ifx\one\xkey\ifx\threex\three \key{#2}% \else{\tclose{\kbdfont\look}}\fi \else{\tclose{\kbdfont\look}}\fi} % For @@indicateurl, @@env, @@command quotes seem unnecessary, so use \code. \let\indicateurl=\code \let\env=\code \let\command=\code % @@uref (abbreviation for `urlref') takes an optional (comma-separated) % second argument specifying the text to display and an optional third % arg as text to display instead of (rather than in addition to) the url % itself. First (mandatory) arg is the url. Perhaps eventually put in % a hypertex \special here. % \def\uref#1{\douref #1,,,\finish} \def\douref#1,#2,#3,#4\finish{\begingroup \unsepspaces \pdfurl{#1}% \setbox0 = \hbox{\ignorespaces #3}% \ifdim\wd0 > 0pt \unhbox0 % third arg given, show only that \else \setbox0 = \hbox{\ignorespaces #2}% \ifdim\wd0 > 0pt \ifpdf \unhbox0 % PDF: 2nd arg given, show only it \else \unhbox0\ (\code{#1})% DVI: 2nd arg given, show both it and url \fi \else \code{#1}% only url given, so show it \fi \fi \endlink \endgroup} % @@url synonym for @@uref, since that's how everyone uses it. % \let\url=\uref % rms does not like angle brackets --karl, 17may97. % So now @@email is just like @@uref, unless we are pdf. % %\def\email#1{\angleleft{\tt #1}\angleright} \ifpdf \def\email#1{\doemail#1,,\finish} \def\doemail#1,#2,#3\finish{\begingroup \unsepspaces \pdfurl{mailto:#1}% \setbox0 = \hbox{\ignorespaces #2}% \ifdim\wd0>0pt\unhbox0\else\code{#1}\fi \endlink \endgroup} \else \let\email=\uref \fi % Check if we are currently using a typewriter font. Since all the % Computer Modern typewriter fonts have zero interword stretch (and % shrink), and it is reasonable to expect all typewriter fonts to have % this property, we can check that font parameter. % \def\ifmonospace{\ifdim\fontdimen3\font=0pt } % Typeset a dimension, e.g., `in' or `pt'. The only reason for the % argument is to make the input look right: @@dmn{pt} instead of @@dmn{}pt. % \def\dmn#1{\thinspace #1} \def\kbd#1{\def\look{#1}\expandafter\kbdfoo\look??\par} % @@l was never documented to mean ``switch to the Lisp font'', % and it is not used as such in any manual I can find. We need it for % Polish suppressed-l. --karl, 22sep96. %\def\l#1{{\li #1}\null} % Explicit font changes: @@r, @@sc, undocumented @@ii. \def\r#1{{\rm #1}} % roman font \def\sc#1{{\smallcaps#1}} % smallcaps font \def\ii#1{{\it #1}} % italic font % @@acronym for "FBI", "NATO", and the like. % We print this one point size smaller, since it's intended for % all-uppercase. % \def\acronym#1{\doacronym #1,,\finish} \def\doacronym#1,#2,#3\finish{% {\selectfonts\lsize #1}% \def\temp{#2}% \ifx\temp\empty \else \space ({\unsepspaces \ignorespaces \temp \unskip})% \fi } % @@abbr for "Comput. J." and the like. % No font change, but don't do end-of-sentence spacing. % \def\abbr#1{\doabbr #1,,\finish} \def\doabbr#1,#2,#3\finish{% {\frenchspacing #1}% \def\temp{#2}% \ifx\temp\empty \else \space ({\unsepspaces \ignorespaces \temp \unskip})% \fi } % @@pounds{} is a sterling sign, which Knuth put in the CM italic font. % \def\pounds{{\it\$}} % @@euro{} comes from a separate font, depending on the current style. % We use the free feym* fonts from the eurosym package by Henrik % Theiling, which support regular, slanted, bold and bold slanted (and % "outlined" (blackboard board, sort of) versions, which we don't need). % It is available from http://www.ctan.org/tex-archive/fonts/eurosym. % % Although only regular is the truly official Euro symbol, we ignore % that. The Euro is designed to be slightly taller than the regular % font height. % % feymr - regular % feymo - slanted % feybr - bold % feybo - bold slanted % % There is no good (free) typewriter version, to my knowledge. % A feymr10 euro is ~7.3pt wide, while a normal cmtt10 char is ~5.25pt wide. % Hmm. % % Also doesn't work in math. Do we need to do math with euro symbols? % Hope not. % % \def\euro{{\eurofont e}} \def\eurofont{% % We set the font at each command, rather than predefining it in % \textfonts and the other font-switching commands, so that % installations which never need the symbold don't have to have the % font installed. % % There is only one designed size (nominal 10pt), so we always scale % that to the current nominal size. % % By the way, simply using "at 1em" works for cmr10 and the like, but % does not work for cmbx10 and other extended/shrunken fonts. % \def\eurosize{\csname\curfontsize nominalsize\endcsname}% % \ifx\curfontstyle\bfstylename % bold: \font\thiseurofont = \ifusingit{feybo10}{feybr10} at \eurosize \else % regular: \font\thiseurofont = \ifusingit{feymo10}{feymr10} at \eurosize \fi \thiseurofont } % @@registeredsymbol - R in a circle. The font for the R should really % be smaller yet, but lllsize is the best we can do for now. % Adapted from the plain.tex definition of \copyright. % \def\registeredsymbol{% $^{{\ooalign{\hfil\raise.07ex\hbox{\selectfonts\lllsize R}% \hfil\crcr\Orb}}% }$% } % Laurent Siebenmann reports \Orb undefined with: % Textures 1.7.7 (preloaded format=plain 93.10.14) (68K) 16 APR 2004 02:38 % so we'll define it if necessary. % \ifx\Orb\undefined \def\Orb{\mathhexbox20D} \fi \message{page headings,} \newskip\titlepagetopglue \titlepagetopglue = 1.5in \newskip\titlepagebottomglue \titlepagebottomglue = 2pc % First the title page. Must do @@settitle before @@titlepage. \newif\ifseenauthor \newif\iffinishedtitlepage % Do an implicit @@contents or @@shortcontents after @@end titlepage if the % user says @@setcontentsaftertitlepage or @@setshortcontentsaftertitlepage. % \newif\ifsetcontentsaftertitlepage \let\setcontentsaftertitlepage = \setcontentsaftertitlepagetrue \newif\ifsetshortcontentsaftertitlepage \let\setshortcontentsaftertitlepage = \setshortcontentsaftertitlepagetrue \parseargdef\shorttitlepage{\begingroup\hbox{}\vskip 1.5in \chaprm \centerline{#1}% \endgroup\page\hbox{}\page} \envdef\titlepage{% % Open one extra group, as we want to close it in the middle of \Etitlepage. \begingroup \parindent=0pt \textfonts % Leave some space at the very top of the page. \vglue\titlepagetopglue % No rule at page bottom unless we print one at the top with @@title. \finishedtitlepagetrue % % Most title ``pages'' are actually two pages long, with space % at the top of the second. We don't want the ragged left on the second. \let\oldpage = \page \def\page{% \iffinishedtitlepage\else \finishtitlepage \fi \let\page = \oldpage \page \null }% } \def\Etitlepage{% \iffinishedtitlepage\else \finishtitlepage \fi % It is important to do the page break before ending the group, % because the headline and footline are only empty inside the group. % If we use the new definition of \page, we always get a blank page % after the title page, which we certainly don't want. \oldpage \endgroup % % Need this before the \...aftertitlepage checks so that if they are % in effect the toc pages will come out with page numbers. \HEADINGSon % % If they want short, they certainly want long too. \ifsetshortcontentsaftertitlepage \shortcontents \contents \global\let\shortcontents = \relax \global\let\contents = \relax \fi % \ifsetcontentsaftertitlepage \contents \global\let\contents = \relax \global\let\shortcontents = \relax \fi } \def\finishtitlepage{% \vskip4pt \hrule height 2pt width \hsize \vskip\titlepagebottomglue \finishedtitlepagetrue } %%% Macros to be used within @@titlepage: \let\subtitlerm=\tenrm \def\subtitlefont{\subtitlerm \normalbaselineskip = 13pt \normalbaselines} \def\authorfont{\authorrm \normalbaselineskip = 16pt \normalbaselines \let\tt=\authortt} \parseargdef\title{% \checkenv\titlepage \leftline{\titlefonts\rm #1} % print a rule at the page bottom also. \finishedtitlepagefalse \vskip4pt \hrule height 4pt width \hsize \vskip4pt } \parseargdef\subtitle{% \checkenv\titlepage {\subtitlefont \rightline{#1}}% } % @@author should come last, but may come many times. % It can also be used inside @@quotation. % \parseargdef\author{% \def\temp{\quotation}% \ifx\thisenv\temp \def\quotationauthor{#1}% printed in \Equotation. \else \checkenv\titlepage \ifseenauthor\else \vskip 0pt plus 1filll \seenauthortrue \fi {\authorfont \leftline{#1}}% \fi } %%% Set up page headings and footings. \let\thispage=\folio \newtoks\evenheadline % headline on even pages \newtoks\oddheadline % headline on odd pages \newtoks\evenfootline % footline on even pages \newtoks\oddfootline % footline on odd pages % Now make TeX use those variables \headline={{\textfonts\rm \ifodd\pageno \the\oddheadline \else \the\evenheadline \fi}} \footline={{\textfonts\rm \ifodd\pageno \the\oddfootline \else \the\evenfootline \fi}\HEADINGShook} \let\HEADINGShook=\relax % Commands to set those variables. % For example, this is what @@headings on does % @@evenheading @@thistitle|@@thispage|@@thischapter % @@oddheading @@thischapter|@@thispage|@@thistitle % @@evenfooting @@thisfile|| % @@oddfooting ||@@thisfile \def\evenheading{\parsearg\evenheadingxxx} \def\evenheadingxxx #1{\evenheadingyyy #1\|\|\|\|\finish} \def\evenheadingyyy #1\|#2\|#3\|#4\finish{% \global\evenheadline={\rlap{\centerline{#2}}\line{#1\hfil#3}}} \def\oddheading{\parsearg\oddheadingxxx} \def\oddheadingxxx #1{\oddheadingyyy #1\|\|\|\|\finish} \def\oddheadingyyy #1\|#2\|#3\|#4\finish{% \global\oddheadline={\rlap{\centerline{#2}}\line{#1\hfil#3}}} \parseargdef\everyheading{\oddheadingxxx{#1}\evenheadingxxx{#1}}% \def\evenfooting{\parsearg\evenfootingxxx} \def\evenfootingxxx #1{\evenfootingyyy #1\|\|\|\|\finish} \def\evenfootingyyy #1\|#2\|#3\|#4\finish{% \global\evenfootline={\rlap{\centerline{#2}}\line{#1\hfil#3}}} \def\oddfooting{\parsearg\oddfootingxxx} \def\oddfootingxxx #1{\oddfootingyyy #1\|\|\|\|\finish} \def\oddfootingyyy #1\|#2\|#3\|#4\finish{% \global\oddfootline = {\rlap{\centerline{#2}}\line{#1\hfil#3}}% % % Leave some space for the footline. Hopefully ok to assume % @@evenfooting will not be used by itself. \global\advance\pageheight by -\baselineskip \global\advance\vsize by -\baselineskip } \parseargdef\everyfooting{\oddfootingxxx{#1}\evenfootingxxx{#1}} % @@headings double turns headings on for double-sided printing. % @@headings single turns headings on for single-sided printing. % @@headings off turns them off. % @@headings on same as @@headings double, retained for compatibility. % @@headings after turns on double-sided headings after this page. % @@headings doubleafter turns on double-sided headings after this page. % @@headings singleafter turns on single-sided headings after this page. % By default, they are off at the start of a document, % and turned `on' after @@end titlepage. \def\headings #1 {\csname HEADINGS#1\endcsname} \def\HEADINGSoff{% \global\evenheadline={\hfil} \global\evenfootline={\hfil} \global\oddheadline={\hfil} \global\oddfootline={\hfil}} \HEADINGSoff % When we turn headings on, set the page number to 1. % For double-sided printing, put current file name in lower left corner, % chapter name on inside top of right hand pages, document % title on inside top of left hand pages, and page numbers on outside top % edge of all pages. \def\HEADINGSdouble{% \global\pageno=1 \global\evenfootline={\hfil} \global\oddfootline={\hfil} \global\evenheadline={\line{\folio\hfil\thistitle}} \global\oddheadline={\line{\thischapter\hfil\folio}} \global\let\contentsalignmacro = \chapoddpage } \let\contentsalignmacro = \chappager % For single-sided printing, chapter title goes across top left of page, % page number on top right. \def\HEADINGSsingle{% \global\pageno=1 \global\evenfootline={\hfil} \global\oddfootline={\hfil} \global\evenheadline={\line{\thischapter\hfil\folio}} \global\oddheadline={\line{\thischapter\hfil\folio}} \global\let\contentsalignmacro = \chappager } \def\HEADINGSon{\HEADINGSdouble} \def\HEADINGSafter{\let\HEADINGShook=\HEADINGSdoublex} \let\HEADINGSdoubleafter=\HEADINGSafter \def\HEADINGSdoublex{% \global\evenfootline={\hfil} \global\oddfootline={\hfil} \global\evenheadline={\line{\folio\hfil\thistitle}} \global\oddheadline={\line{\thischapter\hfil\folio}} \global\let\contentsalignmacro = \chapoddpage } \def\HEADINGSsingleafter{\let\HEADINGShook=\HEADINGSsinglex} \def\HEADINGSsinglex{% \global\evenfootline={\hfil} \global\oddfootline={\hfil} \global\evenheadline={\line{\thischapter\hfil\folio}} \global\oddheadline={\line{\thischapter\hfil\folio}} \global\let\contentsalignmacro = \chappager } % Subroutines used in generating headings % This produces Day Month Year style of output. % Only define if not already defined, in case a txi-??.tex file has set % up a different format (e.g., txi-cs.tex does this). \ifx\today\undefined \def\today{% \number\day\space \ifcase\month \or\putwordMJan\or\putwordMFeb\or\putwordMMar\or\putwordMApr \or\putwordMMay\or\putwordMJun\or\putwordMJul\or\putwordMAug \or\putwordMSep\or\putwordMOct\or\putwordMNov\or\putwordMDec \fi \space\number\year} \fi % @@settitle line... specifies the title of the document, for headings. % It generates no output of its own. \def\thistitle{\putwordNoTitle} \def\settitle{\parsearg{\gdef\thistitle}} \message{tables,} % Tables -- @@table, @@ftable, @@vtable, @@item(x). % default indentation of table text \newdimen\tableindent \tableindent=.8in % default indentation of @@itemize and @@enumerate text \newdimen\itemindent \itemindent=.3in % margin between end of table item and start of table text. \newdimen\itemmargin \itemmargin=.1in % used internally for \itemindent minus \itemmargin \newdimen\itemmax % Note @@table, @@ftable, and @@vtable define @@item, @@itemx, etc., with % these defs. % They also define \itemindex % to index the item name in whatever manner is desired (perhaps none). \newif\ifitemxneedsnegativevskip \def\itemxpar{\par\ifitemxneedsnegativevskip\nobreak\vskip-\parskip\nobreak\fi} \def\internalBitem{\smallbreak \parsearg\itemzzz} \def\internalBitemx{\itemxpar \parsearg\itemzzz} \def\itemzzz #1{\begingroup % \advance\hsize by -\rightskip \advance\hsize by -\tableindent \setbox0=\hbox{\itemindicate{#1}}% \itemindex{#1}% \nobreak % This prevents a break before @@itemx. % % If the item text does not fit in the space we have, put it on a line % by itself, and do not allow a page break either before or after that % line. We do not start a paragraph here because then if the next % command is, e.g., @@kindex, the whatsit would get put into the % horizontal list on a line by itself, resulting in extra blank space. \ifdim \wd0>\itemmax % % Make this a paragraph so we get the \parskip glue and wrapping, % but leave it ragged-right. \begingroup \advance\leftskip by-\tableindent \advance\hsize by\tableindent \advance\rightskip by0pt plus1fil \leavevmode\unhbox0\par \endgroup % % We're going to be starting a paragraph, but we don't want the % \parskip glue -- logically it's part of the @@item we just started. \nobreak \vskip-\parskip % % Stop a page break at the \parskip glue coming up. However, if % what follows is an environment such as @@example, there will be no % \parskip glue; then the negative vskip we just inserted would % cause the example and the item to crash together. So we use this % bizarre value of 10001 as a signal to \aboveenvbreak to insert % \parskip glue after all. Section titles are handled this way also. % \penalty 10001 \endgroup \itemxneedsnegativevskipfalse \else % The item text fits into the space. Start a paragraph, so that the % following text (if any) will end up on the same line. \noindent % Do this with kerns and \unhbox so that if there is a footnote in % the item text, it can migrate to the main vertical list and % eventually be printed. \nobreak\kern-\tableindent \dimen0 = \itemmax \advance\dimen0 by \itemmargin \advance\dimen0 by -\wd0 \unhbox0 \nobreak\kern\dimen0 \endgroup \itemxneedsnegativevskiptrue \fi } \def\item{\errmessage{@@item while not in a list environment}} \def\itemx{\errmessage{@@itemx while not in a list environment}} % @@table, @@ftable, @@vtable. \envdef\table{% \let\itemindex\gobble \tablecheck{table}% } \envdef\ftable{% \def\itemindex ##1{\doind {fn}{\code{##1}}}% \tablecheck{ftable}% } \envdef\vtable{% \def\itemindex ##1{\doind {vr}{\code{##1}}}% \tablecheck{vtable}% } \def\tablecheck#1{% \ifnum \the\catcode`\^^M=\active \endgroup \errmessage{This command won't work in this context; perhaps the problem is that we are \inenvironment\thisenv}% \def\next{\doignore{#1}}% \else \let\next\tablex \fi \next } \def\tablex#1{% \def\itemindicate{#1}% \parsearg\tabley } \def\tabley#1{% {% \makevalueexpandable \edef\temp{\noexpand\tablez #1\space\space\space}% \expandafter }\temp \endtablez } \def\tablez #1 #2 #3 #4\endtablez{% \aboveenvbreak \ifnum 0#1>0 \advance \leftskip by #1\mil \fi \ifnum 0#2>0 \tableindent=#2\mil \fi \ifnum 0#3>0 \advance \rightskip by #3\mil \fi \itemmax=\tableindent \advance \itemmax by -\itemmargin \advance \leftskip by \tableindent \exdentamount=\tableindent \parindent = 0pt \parskip = \smallskipamount \ifdim \parskip=0pt \parskip=2pt \fi \let\item = \internalBitem \let\itemx = \internalBitemx } \def\Etable{\endgraf\afterenvbreak} \let\Eftable\Etable \let\Evtable\Etable \let\Eitemize\Etable \let\Eenumerate\Etable % This is the counter used by @@enumerate, which is really @@itemize \newcount \itemno \envdef\itemize{\parsearg\doitemize} \def\doitemize#1{% \aboveenvbreak \itemmax=\itemindent \advance\itemmax by -\itemmargin \advance\leftskip by \itemindent \exdentamount=\itemindent \parindent=0pt \parskip=\smallskipamount \ifdim\parskip=0pt \parskip=2pt \fi \def\itemcontents{#1}% % @@itemize with no arg is equivalent to @@itemize @@bullet. \ifx\itemcontents\empty\def\itemcontents{\bullet}\fi \let\item=\itemizeitem } % Definition of @@item while inside @@itemize and @@enumerate. % \def\itemizeitem{% \advance\itemno by 1 % for enumerations {\let\par=\endgraf \smallbreak}% reasonable place to break {% % If the document has an @@itemize directly after a section title, a % \nobreak will be last on the list, and \sectionheading will have % done a \vskip-\parskip. In that case, we don't want to zero % parskip, or the item text will crash with the heading. On the % other hand, when there is normal text preceding the item (as there % usually is), we do want to zero parskip, or there would be too much % space. In that case, we won't have a \nobreak before. At least % that's the theory. \ifnum\lastpenalty<10000 \parskip=0in \fi \noindent \hbox to 0pt{\hss \itemcontents \kern\itemmargin}% \vadjust{\penalty 1200}}% not good to break after first line of item. \flushcr } % \splitoff TOKENS\endmark defines \first to be the first token in % TOKENS, and \rest to be the remainder. % \def\splitoff#1#2\endmark{\def\first{#1}\def\rest{#2}}% % Allow an optional argument of an uppercase letter, lowercase letter, % or number, to specify the first label in the enumerated list. No % argument is the same as `1'. % \envparseargdef\enumerate{\enumeratey #1 \endenumeratey} \def\enumeratey #1 #2\endenumeratey{% % If we were given no argument, pretend we were given `1'. \def\thearg{#1}% \ifx\thearg\empty \def\thearg{1}\fi % % Detect if the argument is a single token. If so, it might be a % letter. Otherwise, the only valid thing it can be is a number. % (We will always have one token, because of the test we just made. % This is a good thing, since \splitoff doesn't work given nothing at % all -- the first parameter is undelimited.) \expandafter\splitoff\thearg\endmark \ifx\rest\empty % Only one token in the argument. It could still be anything. % A ``lowercase letter'' is one whose \lccode is nonzero. % An ``uppercase letter'' is one whose \lccode is both nonzero, and % not equal to itself. % Otherwise, we assume it's a number. % % We need the \relax at the end of the \ifnum lines to stop TeX from % continuing to look for a . % \ifnum\lccode\expandafter`\thearg=0\relax \numericenumerate % a number (we hope) \else % It's a letter. \ifnum\lccode\expandafter`\thearg=\expandafter`\thearg\relax \lowercaseenumerate % lowercase letter \else \uppercaseenumerate % uppercase letter \fi \fi \else % Multiple tokens in the argument. We hope it's a number. \numericenumerate \fi } % An @@enumerate whose labels are integers. The starting integer is % given in \thearg. % \def\numericenumerate{% \itemno = \thearg \startenumeration{\the\itemno}% } % The starting (lowercase) letter is in \thearg. \def\lowercaseenumerate{% \itemno = \expandafter`\thearg \startenumeration{% % Be sure we're not beyond the end of the alphabet. \ifnum\itemno=0 \errmessage{No more lowercase letters in @@enumerate; get a bigger alphabet}% \fi \char\lccode\itemno }% } % The starting (uppercase) letter is in \thearg. \def\uppercaseenumerate{% \itemno = \expandafter`\thearg \startenumeration{% % Be sure we're not beyond the end of the alphabet. \ifnum\itemno=0 \errmessage{No more uppercase letters in @@enumerate; get a bigger alphabet} \fi \char\uccode\itemno }% } % Call \doitemize, adding a period to the first argument and supplying the % common last two arguments. Also subtract one from the initial value in % \itemno, since @@item increments \itemno. % \def\startenumeration#1{% \advance\itemno by -1 \doitemize{#1.}\flushcr } % @@alphaenumerate and @@capsenumerate are abbreviations for giving an arg % to @@enumerate. % \def\alphaenumerate{\enumerate{a}} \def\capsenumerate{\enumerate{A}} \def\Ealphaenumerate{\Eenumerate} \def\Ecapsenumerate{\Eenumerate} % @@multitable macros % Amy Hendrickson, 8/18/94, 3/6/96 % % @@multitable ... @@end multitable will make as many columns as desired. % Contents of each column will wrap at width given in preamble. Width % can be specified either with sample text given in a template line, % or in percent of \hsize, the current width of text on page. % Table can continue over pages but will only break between lines. % To make preamble: % % Either define widths of columns in terms of percent of \hsize: % @@multitable @@columnfractions .25 .3 .45 % @@item ... % % Numbers following @@columnfractions are the percent of the total % current hsize to be used for each column. You may use as many % columns as desired. % Or use a template: % @@multitable {Column 1 template} {Column 2 template} {Column 3 template} % @@item ... % using the widest term desired in each column. % Each new table line starts with @@item, each subsequent new column % starts with @@tab. Empty columns may be produced by supplying @@tab's % with nothing between them for as many times as empty columns are needed, % ie, @@tab@@tab@@tab will produce two empty columns. % @@item, @@tab do not need to be on their own lines, but it will not hurt % if they are. % Sample multitable: % @@multitable {Column 1 template} {Column 2 template} {Column 3 template} % @@item first col stuff @@tab second col stuff @@tab third col % @@item % first col stuff % @@tab % second col stuff % @@tab % third col % @@item first col stuff @@tab second col stuff % @@tab Many paragraphs of text may be used in any column. % % They will wrap at the width determined by the template. % @@item@@tab@@tab This will be in third column. % @@end multitable % Default dimensions may be reset by user. % @@multitableparskip is vertical space between paragraphs in table. % @@multitableparindent is paragraph indent in table. % @@multitablecolmargin is horizontal space to be left between columns. % @@multitablelinespace is space to leave between table items, baseline % to baseline. % 0pt means it depends on current normal line spacing. % \newskip\multitableparskip \newskip\multitableparindent \newdimen\multitablecolspace \newskip\multitablelinespace \multitableparskip=0pt \multitableparindent=6pt \multitablecolspace=12pt \multitablelinespace=0pt % Macros used to set up halign preamble: % \let\endsetuptable\relax \def\xendsetuptable{\endsetuptable} \let\columnfractions\relax \def\xcolumnfractions{\columnfractions} \newif\ifsetpercent % #1 is the @@columnfraction, usually a decimal number like .5, but might % be just 1. We just use it, whatever it is. % \def\pickupwholefraction#1 {% \global\advance\colcount by 1 \expandafter\xdef\csname col\the\colcount\endcsname{#1\hsize}% \setuptable } \newcount\colcount \def\setuptable#1{% \def\firstarg{#1}% \ifx\firstarg\xendsetuptable \let\go = \relax \else \ifx\firstarg\xcolumnfractions \global\setpercenttrue \else \ifsetpercent \let\go\pickupwholefraction \else \global\advance\colcount by 1 \setbox0=\hbox{#1\unskip\space}% Add a normal word space as a % separator; typically that is always in the input, anyway. \expandafter\xdef\csname col\the\colcount\endcsname{\the\wd0}% \fi \fi \ifx\go\pickupwholefraction % Put the argument back for the \pickupwholefraction call, so % we'll always have a period there to be parsed. \def\go{\pickupwholefraction#1}% \else \let\go = \setuptable \fi% \fi \go } % multitable-only commands. % % @@headitem starts a heading row, which we typeset in bold. % Assignments have to be global since we are inside the implicit group % of an alignment entry. Note that \everycr resets \everytab. \def\headitem{\checkenv\multitable \crcr \global\everytab={\bf}\the\everytab}% % % A \tab used to include \hskip1sp. But then the space in a template % line is not enough. That is bad. So let's go back to just `&' until % we encounter the problem it was intended to solve again. % --karl, nathan@@acm.org, 20apr99. \def\tab{\checkenv\multitable &\the\everytab}% % @@multitable ... @@end multitable definitions: % \newtoks\everytab % insert after every tab. % \envdef\multitable{% \vskip\parskip \startsavinginserts % % @@item within a multitable starts a normal row. % We use \def instead of \let so that if one of the multitable entries % contains an @@itemize, we don't choke on the \item (seen as \crcr aka % \endtemplate) expanding \doitemize. \def\item{\crcr}% % \tolerance=9500 \hbadness=9500 \setmultitablespacing \parskip=\multitableparskip \parindent=\multitableparindent \overfullrule=0pt \global\colcount=0 % \everycr = {% \noalign{% \global\everytab={}% \global\colcount=0 % Reset the column counter. % Check for saved footnotes, etc. \checkinserts % Keeps underfull box messages off when table breaks over pages. %\filbreak % Maybe so, but it also creates really weird page breaks when the % table breaks over pages. Wouldn't \vfil be better? Wait until the % problem manifests itself, so it can be fixed for real --karl. }% }% % \parsearg\domultitable } \def\domultitable#1{% % To parse everything between @@multitable and @@item: \setuptable#1 \endsetuptable % % This preamble sets up a generic column definition, which will % be used as many times as user calls for columns. % \vtop will set a single line and will also let text wrap and % continue for many paragraphs if desired. \halign\bgroup &% \global\advance\colcount by 1 \multistrut \vtop{% % Use the current \colcount to find the correct column width: \hsize=\expandafter\csname col\the\colcount\endcsname % % In order to keep entries from bumping into each other % we will add a \leftskip of \multitablecolspace to all columns after % the first one. % % If a template has been used, we will add \multitablecolspace % to the width of each template entry. % % If the user has set preamble in terms of percent of \hsize we will % use that dimension as the width of the column, and the \leftskip % will keep entries from bumping into each other. Table will start at % left margin and final column will justify at right margin. % % Make sure we don't inherit \rightskip from the outer environment. \rightskip=0pt \ifnum\colcount=1 % The first column will be indented with the surrounding text. \advance\hsize by\leftskip \else \ifsetpercent \else % If user has not set preamble in terms of percent of \hsize % we will advance \hsize by \multitablecolspace. \advance\hsize by \multitablecolspace \fi % In either case we will make \leftskip=\multitablecolspace: \leftskip=\multitablecolspace \fi % Ignoring space at the beginning and end avoids an occasional spurious % blank line, when TeX decides to break the line at the space before the % box from the multistrut, so the strut ends up on a line by itself. % For example: % @@multitable @@columnfractions .11 .89 % @@item @@code{#} % @@tab Legal holiday which is valid in major parts of the whole country. % Is automatically provided with highlighting sequences respectively % marking characters. \noindent\ignorespaces##\unskip\multistrut }\cr } \def\Emultitable{% \crcr \egroup % end the \halign \global\setpercentfalse } \def\setmultitablespacing{% \def\multistrut{\strut}% just use the standard line spacing % % Compute \multitablelinespace (if not defined by user) for use in % \multitableparskip calculation. We used define \multistrut based on % this, but (ironically) that caused the spacing to be off. % See bug-texinfo report from Werner Lemberg, 31 Oct 2004 12:52:20 +0100. \ifdim\multitablelinespace=0pt \setbox0=\vbox{X}\global\multitablelinespace=\the\baselineskip \global\advance\multitablelinespace by-\ht0 \fi %% Test to see if parskip is larger than space between lines of %% table. If not, do nothing. %% If so, set to same dimension as multitablelinespace. \ifdim\multitableparskip>\multitablelinespace \global\multitableparskip=\multitablelinespace \global\advance\multitableparskip-7pt %% to keep parskip somewhat smaller %% than skip between lines in the table. \fi% \ifdim\multitableparskip=0pt \global\multitableparskip=\multitablelinespace \global\advance\multitableparskip-7pt %% to keep parskip somewhat smaller %% than skip between lines in the table. \fi} \message{conditionals,} % @@iftex, @@ifnotdocbook, @@ifnothtml, @@ifnotinfo, @@ifnotplaintext, % @@ifnotxml always succeed. They currently do nothing; we don't % attempt to check whether the conditionals are properly nested. But we % have to remember that they are conditionals, so that @@end doesn't % attempt to close an environment group. % \def\makecond#1{% \expandafter\let\csname #1\endcsname = \relax \expandafter\let\csname iscond.#1\endcsname = 1 } \makecond{iftex} \makecond{ifnotdocbook} \makecond{ifnothtml} \makecond{ifnotinfo} \makecond{ifnotplaintext} \makecond{ifnotxml} % Ignore @@ignore, @@ifhtml, @@ifinfo, and the like. % \def\direntry{\doignore{direntry}} \def\documentdescription{\doignore{documentdescription}} \def\docbook{\doignore{docbook}} \def\html{\doignore{html}} \def\ifdocbook{\doignore{ifdocbook}} \def\ifhtml{\doignore{ifhtml}} \def\ifinfo{\doignore{ifinfo}} \def\ifnottex{\doignore{ifnottex}} \def\ifplaintext{\doignore{ifplaintext}} \def\ifxml{\doignore{ifxml}} \def\ignore{\doignore{ignore}} \def\menu{\doignore{menu}} \def\xml{\doignore{xml}} % Ignore text until a line `@@end #1', keeping track of nested conditionals. % % A count to remember the depth of nesting. \newcount\doignorecount \def\doignore#1{\begingroup % Scan in ``verbatim'' mode: \catcode`\@@ = \other \catcode`\{ = \other \catcode`\} = \other % % Make sure that spaces turn into tokens that match what \doignoretext wants. \spaceisspace % % Count number of #1's that we've seen. \doignorecount = 0 % % Swallow text until we reach the matching `@@end #1'. \dodoignore{#1}% } { \catcode`_=11 % We want to use \_STOP_ which cannot appear in texinfo source. \obeylines % % \gdef\dodoignore#1{% % #1 contains the command name as a string, e.g., `ifinfo'. % % Define a command to find the next `@@end #1', which must be on a line % by itself. \long\def\doignoretext##1^^M@@end #1{\doignoretextyyy##1^^M@@#1\_STOP_}% % And this command to find another #1 command, at the beginning of a % line. (Otherwise, we would consider a line `@@c @@ifset', for % example, to count as an @@ifset for nesting.) \long\def\doignoretextyyy##1^^M@@#1##2\_STOP_{\doignoreyyy{##2}\_STOP_}% % % And now expand that command. \obeylines % \doignoretext ^^M% }% } \def\doignoreyyy#1{% \def\temp{#1}% \ifx\temp\empty % Nothing found. \let\next\doignoretextzzz \else % Found a nested condition, ... \advance\doignorecount by 1 \let\next\doignoretextyyy % ..., look for another. % If we're here, #1 ends with ^^M\ifinfo (for example). \fi \next #1% the token \_STOP_ is present just after this macro. } % We have to swallow the remaining "\_STOP_". % \def\doignoretextzzz#1{% \ifnum\doignorecount = 0 % We have just found the outermost @@end. \let\next\enddoignore \else % Still inside a nested condition. \advance\doignorecount by -1 \let\next\doignoretext % Look for the next @@end. \fi \next } % Finish off ignored text. \def\enddoignore{\endgroup\ignorespaces} % @@set VAR sets the variable VAR to an empty value. % @@set VAR REST-OF-LINE sets VAR to the value REST-OF-LINE. % % Since we want to separate VAR from REST-OF-LINE (which might be % empty), we can't just use \parsearg; we have to insert a space of our % own to delimit the rest of the line, and then take it out again if we % didn't need it. % We rely on the fact that \parsearg sets \catcode`\ =10. % \parseargdef\set{\setyyy#1 \endsetyyy} \def\setyyy#1 #2\endsetyyy{% {% \makevalueexpandable \def\temp{#2}% \edef\next{\gdef\makecsname{SET#1}}% \ifx\temp\empty \next{}% \else \setzzz#2\endsetzzz \fi }% } % Remove the trailing space \setxxx inserted. \def\setzzz#1 \endsetzzz{\next{#1}} % @@clear VAR clears (i.e., unsets) the variable VAR. % \parseargdef\clear{% {% \makevalueexpandable \global\expandafter\let\csname SET#1\endcsname=\relax }% } % @@value{foo} gets the text saved in variable foo. \def\value{\begingroup\makevalueexpandable\valuexxx} \def\valuexxx#1{\expandablevalue{#1}\endgroup} { \catcode`\- = \active \catcode`\_ = \active % \gdef\makevalueexpandable{% \let\value = \expandablevalue % We don't want these characters active, ... \catcode`\-=\other \catcode`\_=\other % ..., but we might end up with active ones in the argument if % we're called from @@code, as @@code{@@value{foo-bar_}}, though. % So \let them to their normal equivalents. \let-\realdash \let_\normalunderscore } } % We have this subroutine so that we can handle at least some @@value's % properly in indexes (we call \makevalueexpandable in \indexdummies). % The command has to be fully expandable (if the variable is set), since % the result winds up in the index file. This means that if the % variable's value contains other Texinfo commands, it's almost certain % it will fail (although perhaps we could fix that with sufficient work % to do a one-level expansion on the result, instead of complete). % \def\expandablevalue#1{% \expandafter\ifx\csname SET#1\endcsname\relax {[No value for ``#1'']}% \message{Variable `#1', used in @@value, is not set.}% \else \csname SET#1\endcsname \fi } % @@ifset VAR ... @@end ifset reads the `...' iff VAR has been defined % with @@set. % % To get special treatment of `@@end ifset,' call \makeond and the redefine. % \makecond{ifset} \def\ifset{\parsearg{\doifset{\let\next=\ifsetfail}}} \def\doifset#1#2{% {% \makevalueexpandable \let\next=\empty \expandafter\ifx\csname SET#2\endcsname\relax #1% If not set, redefine \next. \fi \expandafter }\next } \def\ifsetfail{\doignore{ifset}} % @@ifclear VAR ... @@end ifclear reads the `...' iff VAR has never been % defined with @@set, or has been undefined with @@clear. % % The `\else' inside the `\doifset' parameter is a trick to reuse the % above code: if the variable is not set, do nothing, if it is set, % then redefine \next to \ifclearfail. % \makecond{ifclear} \def\ifclear{\parsearg{\doifset{\else \let\next=\ifclearfail}}} \def\ifclearfail{\doignore{ifclear}} % @@dircategory CATEGORY -- specify a category of the dir file % which this file should belong to. Ignore this in TeX. \let\dircategory=\comment % @@defininfoenclose. \let\definfoenclose=\comment \message{indexing,} % Index generation facilities % Define \newwrite to be identical to plain tex's \newwrite % except not \outer, so it can be used within macros and \if's. \edef\newwrite{\makecsname{ptexnewwrite}} % \newindex {foo} defines an index named foo. % It automatically defines \fooindex such that % \fooindex ...rest of line... puts an entry in the index foo. % It also defines \fooindfile to be the number of the output channel for % the file that accumulates this index. The file's extension is foo. % The name of an index should be no more than 2 characters long % for the sake of vms. % \def\newindex#1{% \iflinks \expandafter\newwrite \csname#1indfile\endcsname \openout \csname#1indfile\endcsname \jobname.#1 % Open the file \fi \expandafter\xdef\csname#1index\endcsname{% % Define @@#1index \noexpand\doindex{#1}} } % @@defindex foo == \newindex{foo} % \def\defindex{\parsearg\newindex} % Define @@defcodeindex, like @@defindex except put all entries in @@code. % \def\defcodeindex{\parsearg\newcodeindex} % \def\newcodeindex#1{% \iflinks \expandafter\newwrite \csname#1indfile\endcsname \openout \csname#1indfile\endcsname \jobname.#1 \fi \expandafter\xdef\csname#1index\endcsname{% \noexpand\docodeindex{#1}}% } % @@synindex foo bar makes index foo feed into index bar. % Do this instead of @@defindex foo if you don't want it as a separate index. % % @@syncodeindex foo bar similar, but put all entries made for index foo % inside @@code. % \def\synindex#1 #2 {\dosynindex\doindex{#1}{#2}} \def\syncodeindex#1 #2 {\dosynindex\docodeindex{#1}{#2}} % #1 is \doindex or \docodeindex, #2 the index getting redefined (foo), % #3 the target index (bar). \def\dosynindex#1#2#3{% % Only do \closeout if we haven't already done it, else we'll end up % closing the target index. \expandafter \ifx\csname donesynindex#2\endcsname \undefined % The \closeout helps reduce unnecessary open files; the limit on the % Acorn RISC OS is a mere 16 files. \expandafter\closeout\csname#2indfile\endcsname \expandafter\let\csname\donesynindex#2\endcsname = 1 \fi % redefine \fooindfile: \expandafter\let\expandafter\temp\expandafter=\csname#3indfile\endcsname \expandafter\let\csname#2indfile\endcsname=\temp % redefine \fooindex: \expandafter\xdef\csname#2index\endcsname{\noexpand#1{#3}}% } % Define \doindex, the driver for all \fooindex macros. % Argument #1 is generated by the calling \fooindex macro, % and it is "foo", the name of the index. % \doindex just uses \parsearg; it calls \doind for the actual work. % This is because \doind is more useful to call from other macros. % There is also \dosubind {index}{topic}{subtopic} % which makes an entry in a two-level index such as the operation index. \def\doindex#1{\edef\indexname{#1}\parsearg\singleindexer} \def\singleindexer #1{\doind{\indexname}{#1}} % like the previous two, but they put @@code around the argument. \def\docodeindex#1{\edef\indexname{#1}\parsearg\singlecodeindexer} \def\singlecodeindexer #1{\doind{\indexname}{\code{#1}}} % Take care of Texinfo commands that can appear in an index entry. % Since there are some commands we want to expand, and others we don't, % we have to laboriously prevent expansion for those that we don't. % \def\indexdummies{% \def\@@{@@}% change to @@@@ when we switch to @@ as escape char in index files. \def\ {\realbackslash\space }% % Need these in case \tex is in effect and \{ is a \delimiter again. % But can't use \lbracecmd and \rbracecmd because texindex assumes % braces and backslashes are used only as delimiters. \let\{ = \mylbrace \let\} = \myrbrace % % \definedummyword defines \#1 as \realbackslash #1\space, thus % effectively preventing its expansion. This is used only for control % words, not control letters, because the \space would be incorrect % for control characters, but is needed to separate the control word % from whatever follows. % % For control letters, we have \definedummyletter, which omits the % space. % % These can be used both for control words that take an argument and % those that do not. If it is followed by {arg} in the input, then % that will dutifully get written to the index (or wherever). % \def\definedummyword##1{% \expandafter\def\csname ##1\endcsname{\realbackslash ##1\space}% }% \def\definedummyletter##1{% \expandafter\def\csname ##1\endcsname{\realbackslash ##1}% }% \let\definedummyaccent\definedummyletter % % Do the redefinitions. \commondummies } % For the aux file, @@ is the escape character. So we want to redefine % everything using @@ instead of \realbackslash. When everything uses % @@, this will be simpler. % \def\atdummies{% \def\@@{@@@@}% \def\ {@@ }% \let\{ = \lbraceatcmd \let\} = \rbraceatcmd % % (See comments in \indexdummies.) \def\definedummyword##1{% \expandafter\def\csname ##1\endcsname{@@##1\space}% }% \def\definedummyletter##1{% \expandafter\def\csname ##1\endcsname{@@##1}% }% \let\definedummyaccent\definedummyletter % % Do the redefinitions. \commondummies } % Called from \indexdummies and \atdummies. \definedummyword and % \definedummyletter must be defined first. % \def\commondummies{% % \normalturnoffactive % \commondummiesnofonts % \definedummyletter{_}% % % Non-English letters. \definedummyword{AA}% \definedummyword{AE}% \definedummyword{L}% \definedummyword{OE}% \definedummyword{O}% \definedummyword{aa}% \definedummyword{ae}% \definedummyword{l}% \definedummyword{oe}% \definedummyword{o}% \definedummyword{ss}% \definedummyword{exclamdown}% \definedummyword{questiondown}% \definedummyword{ordf}% \definedummyword{ordm}% % % Although these internal commands shouldn't show up, sometimes they do. \definedummyword{bf}% \definedummyword{gtr}% \definedummyword{hat}% \definedummyword{less}% \definedummyword{sf}% \definedummyword{sl}% \definedummyword{tclose}% \definedummyword{tt}% % \definedummyword{LaTeX}% \definedummyword{TeX}% % % Assorted special characters. \definedummyword{bullet}% \definedummyword{comma}% \definedummyword{copyright}% \definedummyword{registeredsymbol}% \definedummyword{dots}% \definedummyword{enddots}% \definedummyword{equiv}% \definedummyword{error}% \definedummyword{euro}% \definedummyword{expansion}% \definedummyword{minus}% \definedummyword{pounds}% \definedummyword{point}% \definedummyword{print}% \definedummyword{result}% % % Handle some cases of @@value -- where it does not contain any % (non-fully-expandable) commands. \makevalueexpandable % % Normal spaces, not active ones. \unsepspaces % % No macro expansion. \turnoffmacros } % \commondummiesnofonts: common to \commondummies and \indexnofonts. % % Better have this without active chars. { \catcode`\~=\other \gdef\commondummiesnofonts{% % Control letters and accents. \definedummyletter{!}% \definedummyaccent{"}% \definedummyaccent{'}% \definedummyletter{*}% \definedummyaccent{,}% \definedummyletter{.}% \definedummyletter{/}% \definedummyletter{:}% \definedummyaccent{=}% \definedummyletter{?}% \definedummyaccent{^}% \definedummyaccent{`}% \definedummyaccent{~}% \definedummyword{u}% \definedummyword{v}% \definedummyword{H}% \definedummyword{dotaccent}% \definedummyword{ringaccent}% \definedummyword{tieaccent}% \definedummyword{ubaraccent}% \definedummyword{udotaccent}% \definedummyword{dotless}% % % Texinfo font commands. \definedummyword{b}% \definedummyword{i}% \definedummyword{r}% \definedummyword{sc}% \definedummyword{t}% % % Commands that take arguments. \definedummyword{acronym}% \definedummyword{cite}% \definedummyword{code}% \definedummyword{command}% \definedummyword{dfn}% \definedummyword{emph}% \definedummyword{env}% \definedummyword{file}% \definedummyword{kbd}% \definedummyword{key}% \definedummyword{math}% \definedummyword{option}% \definedummyword{samp}% \definedummyword{strong}% \definedummyword{tie}% \definedummyword{uref}% \definedummyword{url}% \definedummyword{var}% \definedummyword{verb}% \definedummyword{w}% } } % \indexnofonts is used when outputting the strings to sort the index % by, and when constructing control sequence names. It eliminates all % control sequences and just writes whatever the best ASCII sort string % would be for a given command (usually its argument). % \def\indexnofonts{% % Accent commands should become @@asis. \def\definedummyaccent##1{% \expandafter\let\csname ##1\endcsname\asis }% % We can just ignore other control letters. \def\definedummyletter##1{% \expandafter\def\csname ##1\endcsname{}% }% % Hopefully, all control words can become @@asis. \let\definedummyword\definedummyaccent % \commondummiesnofonts % % Don't no-op \tt, since it isn't a user-level command % and is used in the definitions of the active chars like <, >, |, etc. % Likewise with the other plain tex font commands. %\let\tt=\asis % \def\ { }% \def\@@{@@}% % how to handle braces? \def\_{\normalunderscore}% % % Non-English letters. \def\AA{AA}% \def\AE{AE}% \def\L{L}% \def\OE{OE}% \def\O{O}% \def\aa{aa}% \def\ae{ae}% \def\l{l}% \def\oe{oe}% \def\o{o}% \def\ss{ss}% \def\exclamdown{!}% \def\questiondown{?}% \def\ordf{a}% \def\ordm{o}% % \def\LaTeX{LaTeX}% \def\TeX{TeX}% % % Assorted special characters. % (The following {} will end up in the sort string, but that's ok.) \def\bullet{bullet}% \def\comma{,}% \def\copyright{copyright}% \def\registeredsymbol{R}% \def\dots{...}% \def\enddots{...}% \def\equiv{==}% \def\error{error}% \def\euro{euro}% \def\expansion{==>}% \def\minus{-}% \def\pounds{pounds}% \def\point{.}% \def\print{-|}% \def\result{=>}% % % Don't write macro names. \emptyusermacros } \let\indexbackslash=0 %overridden during \printindex. \let\SETmarginindex=\relax % put index entries in margin (undocumented)? % Most index entries go through here, but \dosubind is the general case. % #1 is the index name, #2 is the entry text. \def\doind#1#2{\dosubind{#1}{#2}{}} % Workhorse for all \fooindexes. % #1 is name of index, #2 is stuff to put there, #3 is subentry -- % empty if called from \doind, as we usually are (the main exception % is with most defuns, which call us directly). % \def\dosubind#1#2#3{% \iflinks {% % Store the main index entry text (including the third arg). \toks0 = {#2}% % If third arg is present, precede it with a space. \def\thirdarg{#3}% \ifx\thirdarg\empty \else \toks0 = \expandafter{\the\toks0 \space #3}% \fi % \edef\writeto{\csname#1indfile\endcsname}% % \ifvmode \dosubindsanitize \else \dosubindwrite \fi }% \fi } % Write the entry in \toks0 to the index file: % \def\dosubindwrite{% % Put the index entry in the margin if desired. \ifx\SETmarginindex\relax\else \insert\margin{\hbox{\vrule height8pt depth3pt width0pt \the\toks0}}% \fi % % Remember, we are within a group. \indexdummies % Must do this here, since \bf, etc expand at this stage \escapechar=`\\ \def\backslashcurfont{\indexbackslash}% \indexbackslash isn't defined now % so it will be output as is; and it will print as backslash. % % Process the index entry with all font commands turned off, to % get the string to sort by. {\indexnofonts \edef\temp{\the\toks0}% need full expansion \xdef\indexsorttmp{\temp}% }% % % Set up the complete index entry, with both the sort key and % the original text, including any font commands. We write % three arguments to \entry to the .?? file (four in the % subentry case), texindex reduces to two when writing the .??s % sorted result. \edef\temp{% \write\writeto{% \string\entry{\indexsorttmp}{\noexpand\folio}{\the\toks0}}% }% \temp } % Take care of unwanted page breaks: % % If a skip is the last thing on the list now, preserve it % by backing up by \lastskip, doing the \write, then inserting % the skip again. Otherwise, the whatsit generated by the % \write will make \lastskip zero. The result is that sequences % like this: % @@end defun % @@tindex whatever % @@defun ... % will have extra space inserted, because the \medbreak in the % start of the @@defun won't see the skip inserted by the @@end of % the previous defun. % % But don't do any of this if we're not in vertical mode. We % don't want to do a \vskip and prematurely end a paragraph. % % Avoid page breaks due to these extra skips, too. % % But wait, there is a catch there: % We'll have to check whether \lastskip is zero skip. \ifdim is not % sufficient for this purpose, as it ignores stretch and shrink parts % of the skip. The only way seems to be to check the textual % representation of the skip. % % The following is almost like \def\zeroskipmacro{0.0pt} except that % the ``p'' and ``t'' characters have catcode \other, not 11 (letter). % \edef\zeroskipmacro{\expandafter\the\csname z@@skip\endcsname} % % ..., ready, GO: % \def\dosubindsanitize{% % \lastskip and \lastpenalty cannot both be nonzero simultaneously. \skip0 = \lastskip \edef\lastskipmacro{\the\lastskip}% \count255 = \lastpenalty % % If \lastskip is nonzero, that means the last item was a % skip. And since a skip is discardable, that means this % -\skip0 glue we're inserting is preceded by a % non-discardable item, therefore it is not a potential % breakpoint, therefore no \nobreak needed. \ifx\lastskipmacro\zeroskipmacro \else \vskip-\skip0 \fi % \dosubindwrite % \ifx\lastskipmacro\zeroskipmacro % If \lastskip was zero, perhaps the last item was a penalty, and % perhaps it was >=10000, e.g., a \nobreak. In that case, we want % to re-insert the same penalty (values >10000 are used for various % signals); since we just inserted a non-discardable item, any % following glue (such as a \parskip) would be a breakpoint. For example: % % @@deffn deffn-whatever % @@vindex index-whatever % Description. % would allow a break between the index-whatever whatsit % and the "Description." paragraph. \ifnum\count255>9999 \penalty\count255 \fi \else % On the other hand, if we had a nonzero \lastskip, % this make-up glue would be preceded by a non-discardable item % (the whatsit from the \write), so we must insert a \nobreak. \nobreak\vskip\skip0 \fi } % The index entry written in the file actually looks like % \entry {sortstring}{page}{topic} % or % \entry {sortstring}{page}{topic}{subtopic} % The texindex program reads in these files and writes files % containing these kinds of lines: % \initial {c} % before the first topic whose initial is c % \entry {topic}{pagelist} % for a topic that is used without subtopics % \primary {topic} % for the beginning of a topic that is used with subtopics % \secondary {subtopic}{pagelist} % for each subtopic. % Define the user-accessible indexing commands % @@findex, @@vindex, @@kindex, @@cindex. \def\findex {\fnindex} \def\kindex {\kyindex} \def\cindex {\cpindex} \def\vindex {\vrindex} \def\tindex {\tpindex} \def\pindex {\pgindex} \def\cindexsub {\begingroup\obeylines\cindexsub} {\obeylines % \gdef\cindexsub "#1" #2^^M{\endgroup % \dosubind{cp}{#2}{#1}}} % Define the macros used in formatting output of the sorted index material. % @@printindex causes a particular index (the ??s file) to get printed. % It does not print any chapter heading (usually an @@unnumbered). % \parseargdef\printindex{\begingroup \dobreak \chapheadingskip{10000}% % \smallfonts \rm \tolerance = 9500 \everypar = {}% don't want the \kern\-parindent from indentation suppression. % % See if the index file exists and is nonempty. % Change catcode of @@ here so that if the index file contains % \initial {@@} % as its first line, TeX doesn't complain about mismatched braces % (because it thinks @@} is a control sequence). \catcode`\@@ = 11 \openin 1 \jobname.#1s \ifeof 1 % \enddoublecolumns gets confused if there is no text in the index, % and it loses the chapter title and the aux file entries for the % index. The easiest way to prevent this problem is to make sure % there is some text. \putwordIndexNonexistent \else % % If the index file exists but is empty, then \openin leaves \ifeof % false. We have to make TeX try to read something from the file, so % it can discover if there is anything in it. \read 1 to \temp \ifeof 1 \putwordIndexIsEmpty \else % Index files are almost Texinfo source, but we use \ as the escape % character. It would be better to use @@, but that's too big a change % to make right now. \def\indexbackslash{\backslashcurfont}% \catcode`\\ = 0 \escapechar = `\\ \begindoublecolumns \input \jobname.#1s \enddoublecolumns \fi \fi \closein 1 \endgroup} % These macros are used by the sorted index file itself. % Change them to control the appearance of the index. \def\initial#1{{% % Some minor font changes for the special characters. \let\tentt=\sectt \let\tt=\sectt \let\sf=\sectt % % Remove any glue we may have, we'll be inserting our own. \removelastskip % % We like breaks before the index initials, so insert a bonus. \nobreak \vskip 0pt plus 3\baselineskip \penalty 0 \vskip 0pt plus -3\baselineskip % % Typeset the initial. Making this add up to a whole number of % baselineskips increases the chance of the dots lining up from column % to column. It still won't often be perfect, because of the stretch % we need before each entry, but it's better. % % No shrink because it confuses \balancecolumns. \vskip 1.67\baselineskip plus .5\baselineskip \leftline{\secbf #1}% % Do our best not to break after the initial. \nobreak \vskip .33\baselineskip plus .1\baselineskip }} % \entry typesets a paragraph consisting of the text (#1), dot leaders, and % then page number (#2) flushed to the right margin. It is used for index % and table of contents entries. The paragraph is indented by \leftskip. % % A straightforward implementation would start like this: % \def\entry#1#2{... % But this frozes the catcodes in the argument, and can cause problems to % @@code, which sets - active. This problem was fixed by a kludge--- % ``-'' was active throughout whole index, but this isn't really right. % % The right solution is to prevent \entry from swallowing the whole text. % --kasal, 21nov03 \def\entry{% \begingroup % % Start a new paragraph if necessary, so our assignments below can't % affect previous text. \par % % Do not fill out the last line with white space. \parfillskip = 0in % % No extra space above this paragraph. \parskip = 0in % % Do not prefer a separate line ending with a hyphen to fewer lines. \finalhyphendemerits = 0 % % \hangindent is only relevant when the entry text and page number % don't both fit on one line. In that case, bob suggests starting the % dots pretty far over on the line. Unfortunately, a large % indentation looks wrong when the entry text itself is broken across % lines. So we use a small indentation and put up with long leaders. % % \hangafter is reset to 1 (which is the value we want) at the start % of each paragraph, so we need not do anything with that. \hangindent = 2em % % When the entry text needs to be broken, just fill out the first line % with blank space. \rightskip = 0pt plus1fil % % A bit of stretch before each entry for the benefit of balancing % columns. \vskip 0pt plus1pt % % Swallow the left brace of the text (first parameter): \afterassignment\doentry \let\temp = } \def\doentry{% \bgroup % Instead of the swallowed brace. \noindent \aftergroup\finishentry % And now comes the text of the entry. } \def\finishentry#1{% % #1 is the page number. % % The following is kludged to not output a line of dots in the index if % there are no page numbers. The next person who breaks this will be % cursed by a Unix daemon. \def\tempa{{\rm }}% \def\tempb{#1}% \edef\tempc{\tempa}% \edef\tempd{\tempb}% \ifx\tempc\tempd \ % \else % % If we must, put the page number on a line of its own, and fill out % this line with blank space. (The \hfil is overwhelmed with the % fill leaders glue in \indexdotfill if the page number does fit.) \hfil\penalty50 \null\nobreak\indexdotfill % Have leaders before the page number. % % The `\ ' here is removed by the implicit \unskip that TeX does as % part of (the primitive) \par. Without it, a spurious underfull % \hbox ensues. \ifpdf \pdfgettoks#1.% \ \the\toksA \else \ #1% \fi \fi \par \endgroup } % Like \dotfill except takes at least 1 em. \def\indexdotfill{\cleaders \hbox{$\mathsurround=0pt \mkern1.5mu ${\it .}$ \mkern1.5mu$}\hskip 1em plus 1fill} \def\primary #1{\line{#1\hfil}} \newskip\secondaryindent \secondaryindent=0.5cm \def\secondary#1#2{{% \parfillskip=0in \parskip=0in \hangindent=1in \hangafter=1 \noindent\hskip\secondaryindent\hbox{#1}\indexdotfill \ifpdf \pdfgettoks#2.\ \the\toksA % The page number ends the paragraph. \else #2 \fi \par }} % Define two-column mode, which we use to typeset indexes. % Adapted from the TeXbook, page 416, which is to say, % the manmac.tex format used to print the TeXbook itself. \catcode`\@@=11 \newbox\partialpage \newdimen\doublecolumnhsize \def\begindoublecolumns{\begingroup % ended by \enddoublecolumns % Grab any single-column material above us. \output = {% % % Here is a possibility not foreseen in manmac: if we accumulate a % whole lot of material, we might end up calling this \output % routine twice in a row (see the doublecol-lose test, which is % essentially a couple of indexes with @@setchapternewpage off). In % that case we just ship out what is in \partialpage with the normal % output routine. Generally, \partialpage will be empty when this % runs and this will be a no-op. See the indexspread.tex test case. \ifvoid\partialpage \else \onepageout{\pagecontents\partialpage}% \fi % \global\setbox\partialpage = \vbox{% % Unvbox the main output page. \unvbox\PAGE \kern-\topskip \kern\baselineskip }% }% \eject % run that output routine to set \partialpage % % Use the double-column output routine for subsequent pages. \output = {\doublecolumnout}% % % Change the page size parameters. We could do this once outside this % routine, in each of @@smallbook, @@afourpaper, and the default 8.5x11 % format, but then we repeat the same computation. Repeating a couple % of assignments once per index is clearly meaningless for the % execution time, so we may as well do it in one place. % % First we halve the line length, less a little for the gutter between % the columns. We compute the gutter based on the line length, so it % changes automatically with the paper format. The magic constant % below is chosen so that the gutter has the same value (well, +-<1pt) % as it did when we hard-coded it. % % We put the result in a separate register, \doublecolumhsize, so we % can restore it in \pagesofar, after \hsize itself has (potentially) % been clobbered. % \doublecolumnhsize = \hsize \advance\doublecolumnhsize by -.04154\hsize \divide\doublecolumnhsize by 2 \hsize = \doublecolumnhsize % % Double the \vsize as well. (We don't need a separate register here, % since nobody clobbers \vsize.) \vsize = 2\vsize } % The double-column output routine for all double-column pages except % the last. % \def\doublecolumnout{% \splittopskip=\topskip \splitmaxdepth=\maxdepth % Get the available space for the double columns -- the normal % (undoubled) page height minus any material left over from the % previous page. \dimen@@ = \vsize \divide\dimen@@ by 2 \advance\dimen@@ by -\ht\partialpage % % box0 will be the left-hand column, box2 the right. \setbox0=\vsplit255 to\dimen@@ \setbox2=\vsplit255 to\dimen@@ \onepageout\pagesofar \unvbox255 \penalty\outputpenalty } % % Re-output the contents of the output page -- any previous material, % followed by the two boxes we just split, in box0 and box2. \def\pagesofar{% \unvbox\partialpage % \hsize = \doublecolumnhsize \wd0=\hsize \wd2=\hsize \hbox to\pagewidth{\box0\hfil\box2}% } % % All done with double columns. \def\enddoublecolumns{% \output = {% % Split the last of the double-column material. Leave it on the % current page, no automatic page break. \balancecolumns % % If we end up splitting too much material for the current page, % though, there will be another page break right after this \output % invocation ends. Having called \balancecolumns once, we do not % want to call it again. Therefore, reset \output to its normal % definition right away. (We hope \balancecolumns will never be % called on to balance too much material, but if it is, this makes % the output somewhat more palatable.) \global\output = {\onepageout{\pagecontents\PAGE}}% }% \eject \endgroup % started in \begindoublecolumns % % \pagegoal was set to the doubled \vsize above, since we restarted % the current page. We're now back to normal single-column % typesetting, so reset \pagegoal to the normal \vsize (after the % \endgroup where \vsize got restored). \pagegoal = \vsize } % % Called at the end of the double column material. \def\balancecolumns{% \setbox0 = \vbox{\unvbox255}% like \box255 but more efficient, see p.120. \dimen@@ = \ht0 \advance\dimen@@ by \topskip \advance\dimen@@ by-\baselineskip \divide\dimen@@ by 2 % target to split to %debug\message{final 2-column material height=\the\ht0, target=\the\dimen@@.}% \splittopskip = \topskip % Loop until we get a decent breakpoint. {% \vbadness = 10000 \loop \global\setbox3 = \copy0 \global\setbox1 = \vsplit3 to \dimen@@ \ifdim\ht3>\dimen@@ \global\advance\dimen@@ by 1pt \repeat }% %debug\message{split to \the\dimen@@, column heights: \the\ht1, \the\ht3.}% \setbox0=\vbox to\dimen@@{\unvbox1}% \setbox2=\vbox to\dimen@@{\unvbox3}% % \pagesofar } \catcode`\@@ = \other \message{sectioning,} % Chapters, sections, etc. % \unnumberedno is an oxymoron, of course. But we count the unnumbered % sections so that we can refer to them unambiguously in the pdf % outlines by their "section number". We avoid collisions with chapter % numbers by starting them at 10000. (If a document ever has 10000 % chapters, we're in trouble anyway, I'm sure.) \newcount\unnumberedno \unnumberedno = 10000 \newcount\chapno \newcount\secno \secno=0 \newcount\subsecno \subsecno=0 \newcount\subsubsecno \subsubsecno=0 % This counter is funny since it counts through charcodes of letters A, B, ... \newcount\appendixno \appendixno = `\@@ % % \def\appendixletter{\char\the\appendixno} % We do the following ugly conditional instead of the above simple % construct for the sake of pdftex, which needs the actual % letter in the expansion, not just typeset. % \def\appendixletter{% \ifnum\appendixno=`A A% \else\ifnum\appendixno=`B B% \else\ifnum\appendixno=`C C% \else\ifnum\appendixno=`D D% \else\ifnum\appendixno=`E E% \else\ifnum\appendixno=`F F% \else\ifnum\appendixno=`G G% \else\ifnum\appendixno=`H H% \else\ifnum\appendixno=`I I% \else\ifnum\appendixno=`J J% \else\ifnum\appendixno=`K K% \else\ifnum\appendixno=`L L% \else\ifnum\appendixno=`M M% \else\ifnum\appendixno=`N N% \else\ifnum\appendixno=`O O% \else\ifnum\appendixno=`P P% \else\ifnum\appendixno=`Q Q% \else\ifnum\appendixno=`R R% \else\ifnum\appendixno=`S S% \else\ifnum\appendixno=`T T% \else\ifnum\appendixno=`U U% \else\ifnum\appendixno=`V V% \else\ifnum\appendixno=`W W% \else\ifnum\appendixno=`X X% \else\ifnum\appendixno=`Y Y% \else\ifnum\appendixno=`Z Z% % The \the is necessary, despite appearances, because \appendixletter is % expanded while writing the .toc file. \char\appendixno is not % expandable, thus it is written literally, thus all appendixes come out % with the same letter (or @@) in the toc without it. \else\char\the\appendixno \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi} % Each @@chapter defines this as the name of the chapter. % page headings and footings can use it. @@section does likewise. % However, they are not reliable, because we don't use marks. \def\thischapter{} \def\thissection{} \newcount\absseclevel % used to calculate proper heading level \newcount\secbase\secbase=0 % @@raisesections/@@lowersections modify this count % @@raisesections: treat @@section as chapter, @@subsection as section, etc. \def\raisesections{\global\advance\secbase by -1} \let\up=\raisesections % original BFox name % @@lowersections: treat @@chapter as section, @@section as subsection, etc. \def\lowersections{\global\advance\secbase by 1} \let\down=\lowersections % original BFox name % we only have subsub. \chardef\maxseclevel = 3 % % A numbered section within an unnumbered changes to unnumbered too. % To achive this, remember the "biggest" unnum. sec. we are currently in: \chardef\unmlevel = \maxseclevel % % Trace whether the current chapter is an appendix or not: % \chapheadtype is "N" or "A", unnumbered chapters are ignored. \def\chapheadtype{N} % Choose a heading macro % #1 is heading type % #2 is heading level % #3 is text for heading \def\genhead#1#2#3{% % Compute the abs. sec. level: \absseclevel=#2 \advance\absseclevel by \secbase % Make sure \absseclevel doesn't fall outside the range: \ifnum \absseclevel < 0 \absseclevel = 0 \else \ifnum \absseclevel > 3 \absseclevel = 3 \fi \fi % The heading type: \def\headtype{#1}% \if \headtype U% \ifnum \absseclevel < \unmlevel \chardef\unmlevel = \absseclevel \fi \else % Check for appendix sections: \ifnum \absseclevel = 0 \edef\chapheadtype{\headtype}% \else \if \headtype A\if \chapheadtype N% \errmessage{@@appendix... within a non-appendix chapter}% \fi\fi \fi % Check for numbered within unnumbered: \ifnum \absseclevel > \unmlevel \def\headtype{U}% \else \chardef\unmlevel = 3 \fi \fi % Now print the heading: \if \headtype U% \ifcase\absseclevel \unnumberedzzz{#3}% \or \unnumberedseczzz{#3}% \or \unnumberedsubseczzz{#3}% \or \unnumberedsubsubseczzz{#3}% \fi \else \if \headtype A% \ifcase\absseclevel \appendixzzz{#3}% \or \appendixsectionzzz{#3}% \or \appendixsubseczzz{#3}% \or \appendixsubsubseczzz{#3}% \fi \else \ifcase\absseclevel \chapterzzz{#3}% \or \seczzz{#3}% \or \numberedsubseczzz{#3}% \or \numberedsubsubseczzz{#3}% \fi \fi \fi \suppressfirstparagraphindent } % an interface: \def\numhead{\genhead N} \def\apphead{\genhead A} \def\unnmhead{\genhead U} % @@chapter, @@appendix, @@unnumbered. Increment top-level counter, reset % all lower-level sectioning counters to zero. % % Also set \chaplevelprefix, which we prepend to @@float sequence numbers % (e.g., figures), q.v. By default (before any chapter), that is empty. \let\chaplevelprefix = \empty % \outer\parseargdef\chapter{\numhead0{#1}} % normally numhead0 calls chapterzzz \def\chapterzzz#1{% % section resetting is \global in case the chapter is in a group, such % as an @@include file. \global\secno=0 \global\subsecno=0 \global\subsubsecno=0 \global\advance\chapno by 1 % % Used for \float. \gdef\chaplevelprefix{\the\chapno.}% \resetallfloatnos % \message{\putwordChapter\space \the\chapno}% % % Write the actual heading. \chapmacro{#1}{Ynumbered}{\the\chapno}% % % So @@section and the like are numbered underneath this chapter. \global\let\section = \numberedsec \global\let\subsection = \numberedsubsec \global\let\subsubsection = \numberedsubsubsec } \outer\parseargdef\appendix{\apphead0{#1}} % normally apphead0 calls appendixzzz \def\appendixzzz#1{% \global\secno=0 \global\subsecno=0 \global\subsubsecno=0 \global\advance\appendixno by 1 \gdef\chaplevelprefix{\appendixletter.}% \resetallfloatnos % \def\appendixnum{\putwordAppendix\space \appendixletter}% \message{\appendixnum}% % \chapmacro{#1}{Yappendix}{\appendixletter}% % \global\let\section = \appendixsec \global\let\subsection = \appendixsubsec \global\let\subsubsection = \appendixsubsubsec } \outer\parseargdef\unnumbered{\unnmhead0{#1}} % normally unnmhead0 calls unnumberedzzz \def\unnumberedzzz#1{% \global\secno=0 \global\subsecno=0 \global\subsubsecno=0 \global\advance\unnumberedno by 1 % % Since an unnumbered has no number, no prefix for figures. \global\let\chaplevelprefix = \empty \resetallfloatnos % % This used to be simply \message{#1}, but TeX fully expands the % argument to \message. Therefore, if #1 contained @@-commands, TeX % expanded them. For example, in `@@unnumbered The @@cite{Book}', TeX % expanded @@cite (which turns out to cause errors because \cite is meant % to be executed, not expanded). % % Anyway, we don't want the fully-expanded definition of @@cite to appear % as a result of the \message, we just want `@@cite' itself. We use % \the to achieve this: TeX expands \the only once, % simply yielding the contents of . (We also do this for % the toc entries.) \toks0 = {#1}% \message{(\the\toks0)}% % \chapmacro{#1}{Ynothing}{\the\unnumberedno}% % \global\let\section = \unnumberedsec \global\let\subsection = \unnumberedsubsec \global\let\subsubsection = \unnumberedsubsubsec } % @@centerchap is like @@unnumbered, but the heading is centered. \outer\parseargdef\centerchap{% % Well, we could do the following in a group, but that would break % an assumption that \chapmacro is called at the outermost level. % Thus we are safer this way: --kasal, 24feb04 \let\centerparametersmaybe = \centerparameters \unnmhead0{#1}% \let\centerparametersmaybe = \relax } % @@top is like @@unnumbered. \let\top\unnumbered % Sections. \outer\parseargdef\numberedsec{\numhead1{#1}} % normally calls seczzz \def\seczzz#1{% \global\subsecno=0 \global\subsubsecno=0 \global\advance\secno by 1 \sectionheading{#1}{sec}{Ynumbered}{\the\chapno.\the\secno}% } \outer\parseargdef\appendixsection{\apphead1{#1}} % normally calls appendixsectionzzz \def\appendixsectionzzz#1{% \global\subsecno=0 \global\subsubsecno=0 \global\advance\secno by 1 \sectionheading{#1}{sec}{Yappendix}{\appendixletter.\the\secno}% } \let\appendixsec\appendixsection \outer\parseargdef\unnumberedsec{\unnmhead1{#1}} % normally calls unnumberedseczzz \def\unnumberedseczzz#1{% \global\subsecno=0 \global\subsubsecno=0 \global\advance\secno by 1 \sectionheading{#1}{sec}{Ynothing}{\the\unnumberedno.\the\secno}% } % Subsections. \outer\parseargdef\numberedsubsec{\numhead2{#1}} % normally calls numberedsubseczzz \def\numberedsubseczzz#1{% \global\subsubsecno=0 \global\advance\subsecno by 1 \sectionheading{#1}{subsec}{Ynumbered}{\the\chapno.\the\secno.\the\subsecno}% } \outer\parseargdef\appendixsubsec{\apphead2{#1}} % normally calls appendixsubseczzz \def\appendixsubseczzz#1{% \global\subsubsecno=0 \global\advance\subsecno by 1 \sectionheading{#1}{subsec}{Yappendix}% {\appendixletter.\the\secno.\the\subsecno}% } \outer\parseargdef\unnumberedsubsec{\unnmhead2{#1}} %normally calls unnumberedsubseczzz \def\unnumberedsubseczzz#1{% \global\subsubsecno=0 \global\advance\subsecno by 1 \sectionheading{#1}{subsec}{Ynothing}% {\the\unnumberedno.\the\secno.\the\subsecno}% } % Subsubsections. \outer\parseargdef\numberedsubsubsec{\numhead3{#1}} % normally numberedsubsubseczzz \def\numberedsubsubseczzz#1{% \global\advance\subsubsecno by 1 \sectionheading{#1}{subsubsec}{Ynumbered}% {\the\chapno.\the\secno.\the\subsecno.\the\subsubsecno}% } \outer\parseargdef\appendixsubsubsec{\apphead3{#1}} % normally appendixsubsubseczzz \def\appendixsubsubseczzz#1{% \global\advance\subsubsecno by 1 \sectionheading{#1}{subsubsec}{Yappendix}% {\appendixletter.\the\secno.\the\subsecno.\the\subsubsecno}% } \outer\parseargdef\unnumberedsubsubsec{\unnmhead3{#1}} %normally unnumberedsubsubseczzz \def\unnumberedsubsubseczzz#1{% \global\advance\subsubsecno by 1 \sectionheading{#1}{subsubsec}{Ynothing}% {\the\unnumberedno.\the\secno.\the\subsecno.\the\subsubsecno}% } % These macros control what the section commands do, according % to what kind of chapter we are in (ordinary, appendix, or unnumbered). % Define them by default for a numbered chapter. \let\section = \numberedsec \let\subsection = \numberedsubsec \let\subsubsection = \numberedsubsubsec % Define @@majorheading, @@heading and @@subheading % NOTE on use of \vbox for chapter headings, section headings, and such: % 1) We use \vbox rather than the earlier \line to permit % overlong headings to fold. % 2) \hyphenpenalty is set to 10000 because hyphenation in a % heading is obnoxious; this forbids it. % 3) Likewise, headings look best if no \parindent is used, and % if justification is not attempted. Hence \raggedright. \def\majorheading{% {\advance\chapheadingskip by 10pt \chapbreak }% \parsearg\chapheadingzzz } \def\chapheading{\chapbreak \parsearg\chapheadingzzz} \def\chapheadingzzz#1{% {\chapfonts \vbox{\hyphenpenalty=10000\tolerance=5000 \parindent=0pt\raggedright \rm #1\hfill}}% \bigskip \par\penalty 200\relax \suppressfirstparagraphindent } % @@heading, @@subheading, @@subsubheading. \parseargdef\heading{\sectionheading{#1}{sec}{Yomitfromtoc}{} \suppressfirstparagraphindent} \parseargdef\subheading{\sectionheading{#1}{subsec}{Yomitfromtoc}{} \suppressfirstparagraphindent} \parseargdef\subsubheading{\sectionheading{#1}{subsubsec}{Yomitfromtoc}{} \suppressfirstparagraphindent} % These macros generate a chapter, section, etc. heading only % (including whitespace, linebreaking, etc. around it), % given all the information in convenient, parsed form. %%% Args are the skip and penalty (usually negative) \def\dobreak#1#2{\par\ifdim\lastskip<#1\removelastskip\penalty#2\vskip#1\fi} %%% Define plain chapter starts, and page on/off switching for it % Parameter controlling skip before chapter headings (if needed) \newskip\chapheadingskip \def\chapbreak{\dobreak \chapheadingskip {-4000}} \def\chappager{\par\vfill\supereject} \def\chapoddpage{\chappager \ifodd\pageno \else \hbox to 0pt{} \chappager\fi} \def\setchapternewpage #1 {\csname CHAPPAG#1\endcsname} \def\CHAPPAGoff{% \global\let\contentsalignmacro = \chappager \global\let\pchapsepmacro=\chapbreak \global\let\pagealignmacro=\chappager} \def\CHAPPAGon{% \global\let\contentsalignmacro = \chappager \global\let\pchapsepmacro=\chappager \global\let\pagealignmacro=\chappager \global\def\HEADINGSon{\HEADINGSsingle}} \def\CHAPPAGodd{% \global\let\contentsalignmacro = \chapoddpage \global\let\pchapsepmacro=\chapoddpage \global\let\pagealignmacro=\chapoddpage \global\def\HEADINGSon{\HEADINGSdouble}} \CHAPPAGon % Chapter opening. % % #1 is the text, #2 is the section type (Ynumbered, Ynothing, % Yappendix, Yomitfromtoc), #3 the chapter number. % % To test against our argument. \def\Ynothingkeyword{Ynothing} \def\Yomitfromtockeyword{Yomitfromtoc} \def\Yappendixkeyword{Yappendix} % \def\chapmacro#1#2#3{% \pchapsepmacro {% \chapfonts \rm % % Have to define \thissection before calling \donoderef, because the % xref code eventually uses it. On the other hand, it has to be called % after \pchapsepmacro, or the headline will change too soon. \gdef\thissection{#1}% \gdef\thischaptername{#1}% % % Only insert the separating space if we have a chapter/appendix % number, and don't print the unnumbered ``number''. \def\temptype{#2}% \ifx\temptype\Ynothingkeyword \setbox0 = \hbox{}% \def\toctype{unnchap}% \def\thischapter{#1}% \else\ifx\temptype\Yomitfromtockeyword \setbox0 = \hbox{}% contents like unnumbered, but no toc entry \def\toctype{omit}% \xdef\thischapter{}% \else\ifx\temptype\Yappendixkeyword \setbox0 = \hbox{\putwordAppendix{} #3\enspace}% \def\toctype{app}% % We don't substitute the actual chapter name into \thischapter % because we don't want its macros evaluated now. And we don't % use \thissection because that changes with each section. % \xdef\thischapter{\putwordAppendix{} \appendixletter: \noexpand\thischaptername}% \else \setbox0 = \hbox{#3\enspace}% \def\toctype{numchap}% \xdef\thischapter{\putwordChapter{} \the\chapno: \noexpand\thischaptername}% \fi\fi\fi % % Write the toc entry for this chapter. Must come before the % \donoderef, because we include the current node name in the toc % entry, and \donoderef resets it to empty. \writetocentry{\toctype}{#1}{#3}% % % For pdftex, we have to write out the node definition (aka, make % the pdfdest) after any page break, but before the actual text has % been typeset. If the destination for the pdf outline is after the % text, then jumping from the outline may wind up with the text not % being visible, for instance under high magnification. \donoderef{#2}% % % Typeset the actual heading. \vbox{\hyphenpenalty=10000 \tolerance=5000 \parindent=0pt \raggedright \hangindent=\wd0 \centerparametersmaybe \unhbox0 #1\par}% }% \nobreak\bigskip % no page break after a chapter title \nobreak } % @@centerchap -- centered and unnumbered. \let\centerparametersmaybe = \relax \def\centerparameters{% \advance\rightskip by 3\rightskip \leftskip = \rightskip \parfillskip = 0pt } % I don't think this chapter style is supported any more, so I'm not % updating it with the new noderef stuff. We'll see. --karl, 11aug03. % \def\setchapterstyle #1 {\csname CHAPF#1\endcsname} % \def\unnchfopen #1{% \chapoddpage {\chapfonts \vbox{\hyphenpenalty=10000\tolerance=5000 \parindent=0pt\raggedright \rm #1\hfill}}\bigskip \par\nobreak } \def\chfopen #1#2{\chapoddpage {\chapfonts \vbox to 3in{\vfil \hbox to\hsize{\hfil #2} \hbox to\hsize{\hfil #1} \vfil}}% \par\penalty 5000 % } \def\centerchfopen #1{% \chapoddpage {\chapfonts \vbox{\hyphenpenalty=10000\tolerance=5000 \parindent=0pt \hfill {\rm #1}\hfill}}\bigskip \par\nobreak } \def\CHAPFopen{% \global\let\chapmacro=\chfopen \global\let\centerchapmacro=\centerchfopen} % Section titles. These macros combine the section number parts and % call the generic \sectionheading to do the printing. % \newskip\secheadingskip \def\secheadingbreak{\dobreak \secheadingskip{-1000}} % Subsection titles. \newskip\subsecheadingskip \def\subsecheadingbreak{\dobreak \subsecheadingskip{-500}} % Subsubsection titles. \def\subsubsecheadingskip{\subsecheadingskip} \def\subsubsecheadingbreak{\subsecheadingbreak} % Print any size, any type, section title. % % #1 is the text, #2 is the section level (sec/subsec/subsubsec), #3 is % the section type for xrefs (Ynumbered, Ynothing, Yappendix), #4 is the % section number. % \def\sectionheading#1#2#3#4{% {% % Switch to the right set of fonts. \csname #2fonts\endcsname \rm % % Insert space above the heading. \csname #2headingbreak\endcsname % % Only insert the space after the number if we have a section number. \def\sectionlevel{#2}% \def\temptype{#3}% % \ifx\temptype\Ynothingkeyword \setbox0 = \hbox{}% \def\toctype{unn}% \gdef\thissection{#1}% \else\ifx\temptype\Yomitfromtockeyword % for @@headings -- no section number, don't include in toc, % and don't redefine \thissection. \setbox0 = \hbox{}% \def\toctype{omit}% \let\sectionlevel=\empty \else\ifx\temptype\Yappendixkeyword \setbox0 = \hbox{#4\enspace}% \def\toctype{app}% \gdef\thissection{#1}% \else \setbox0 = \hbox{#4\enspace}% \def\toctype{num}% \gdef\thissection{#1}% \fi\fi\fi % % Write the toc entry (before \donoderef). See comments in \chfplain. \writetocentry{\toctype\sectionlevel}{#1}{#4}% % % Write the node reference (= pdf destination for pdftex). % Again, see comments in \chfplain. \donoderef{#3}% % % Output the actual section heading. \vbox{\hyphenpenalty=10000 \tolerance=5000 \parindent=0pt \raggedright \hangindent=\wd0 % zero if no section number \unhbox0 #1}% }% % Add extra space after the heading -- half of whatever came above it. % Don't allow stretch, though. \kern .5 \csname #2headingskip\endcsname % % Do not let the kern be a potential breakpoint, as it would be if it % was followed by glue. \nobreak % % We'll almost certainly start a paragraph next, so don't let that % glue accumulate. (Not a breakpoint because it's preceded by a % discardable item.) \vskip-\parskip % % This is purely so the last item on the list is a known \penalty > % 10000. This is so \startdefun can avoid allowing breakpoints after % section headings. Otherwise, it would insert a valid breakpoint between: % % @@section sec-whatever % @@deffn def-whatever \penalty 10001 } \message{toc,} % Table of contents. \newwrite\tocfile % Write an entry to the toc file, opening it if necessary. % Called from @@chapter, etc. % % Example usage: \writetocentry{sec}{Section Name}{\the\chapno.\the\secno} % We append the current node name (if any) and page number as additional % arguments for the \{chap,sec,...}entry macros which will eventually % read this. The node name is used in the pdf outlines as the % destination to jump to. % % We open the .toc file for writing here instead of at @@setfilename (or % any other fixed time) so that @@contents can be anywhere in the document. % But if #1 is `omit', then we don't do anything. This is used for the % table of contents chapter openings themselves. % \newif\iftocfileopened \def\omitkeyword{omit}% % \def\writetocentry#1#2#3{% \edef\writetoctype{#1}% \ifx\writetoctype\omitkeyword \else \iftocfileopened\else \immediate\openout\tocfile = \jobname.toc \global\tocfileopenedtrue \fi % \iflinks \toks0 = {#2}% \toks2 = \expandafter{\lastnode}% \edef\temp{\write\tocfile{\realbackslash #1entry{\the\toks0}{#3}% {\the\toks2}{\noexpand\folio}}}% \temp \fi \fi % % Tell \shipout to create a pdf destination on each page, if we're % writing pdf. These are used in the table of contents. We can't % just write one on every page because the title pages are numbered % 1 and 2 (the page numbers aren't printed), and so are the first % two pages of the document. Thus, we'd have two destinations named % `1', and two named `2'. \ifpdf \global\pdfmakepagedesttrue \fi } \newskip\contentsrightmargin \contentsrightmargin=1in \newcount\savepageno \newcount\lastnegativepageno \lastnegativepageno = -1 % Prepare to read what we've written to \tocfile. % \def\startcontents#1{% % If @@setchapternewpage on, and @@headings double, the contents should % start on an odd page, unlike chapters. Thus, we maintain % \contentsalignmacro in parallel with \pagealignmacro. % From: Torbjorn Granlund \contentsalignmacro \immediate\closeout\tocfile % % Don't need to put `Contents' or `Short Contents' in the headline. % It is abundantly clear what they are. \def\thischapter{}% \chapmacro{#1}{Yomitfromtoc}{}% % \savepageno = \pageno \begingroup % Set up to handle contents files properly. \catcode`\\=0 \catcode`\{=1 \catcode`\}=2 \catcode`\@@=11 % We can't do this, because then an actual ^ in a section % title fails, e.g., @@chapter ^ -- exponentiation. --karl, 9jul97. %\catcode`\^=7 % to see ^^e4 as \"a etc. juha@@piuha.ydi.vtt.fi \raggedbottom % Worry more about breakpoints than the bottom. \advance\hsize by -\contentsrightmargin % Don't use the full line length. % % Roman numerals for page numbers. \ifnum \pageno>0 \global\pageno = \lastnegativepageno \fi } % Normal (long) toc. \def\contents{% \startcontents{\putwordTOC}% \openin 1 \jobname.toc \ifeof 1 \else \input \jobname.toc \fi \vfill \eject \contentsalignmacro % in case @@setchapternewpage odd is in effect \ifeof 1 \else \pdfmakeoutlines \fi \closein 1 \endgroup \lastnegativepageno = \pageno \global\pageno = \savepageno } % And just the chapters. \def\summarycontents{% \startcontents{\putwordShortTOC}% % \let\numchapentry = \shortchapentry \let\appentry = \shortchapentry \let\unnchapentry = \shortunnchapentry % We want a true roman here for the page numbers. \secfonts \let\rm=\shortcontrm \let\bf=\shortcontbf \let\sl=\shortcontsl \let\tt=\shortconttt \rm \hyphenpenalty = 10000 \advance\baselineskip by 1pt % Open it up a little. \def\numsecentry##1##2##3##4{} \let\appsecentry = \numsecentry \let\unnsecentry = \numsecentry \let\numsubsecentry = \numsecentry \let\appsubsecentry = \numsecentry \let\unnsubsecentry = \numsecentry \let\numsubsubsecentry = \numsecentry \let\appsubsubsecentry = \numsecentry \let\unnsubsubsecentry = \numsecentry \openin 1 \jobname.toc \ifeof 1 \else \input \jobname.toc \fi \closein 1 \vfill \eject \contentsalignmacro % in case @@setchapternewpage odd is in effect \endgroup \lastnegativepageno = \pageno \global\pageno = \savepageno } \let\shortcontents = \summarycontents % Typeset the label for a chapter or appendix for the short contents. % The arg is, e.g., `A' for an appendix, or `3' for a chapter. % \def\shortchaplabel#1{% % This space should be enough, since a single number is .5em, and the % widest letter (M) is 1em, at least in the Computer Modern fonts. % But use \hss just in case. % (This space doesn't include the extra space that gets added after % the label; that gets put in by \shortchapentry above.) % % We'd like to right-justify chapter numbers, but that looks strange % with appendix letters. And right-justifying numbers and % left-justifying letters looks strange when there is less than 10 % chapters. Have to read the whole toc once to know how many chapters % there are before deciding ... \hbox to 1em{#1\hss}% } % These macros generate individual entries in the table of contents. % The first argument is the chapter or section name. % The last argument is the page number. % The arguments in between are the chapter number, section number, ... % Chapters, in the main contents. \def\numchapentry#1#2#3#4{\dochapentry{#2\labelspace#1}{#4}} % % Chapters, in the short toc. % See comments in \dochapentry re vbox and related settings. \def\shortchapentry#1#2#3#4{% \tocentry{\shortchaplabel{#2}\labelspace #1}{\doshortpageno\bgroup#4\egroup}% } % Appendices, in the main contents. % Need the word Appendix, and a fixed-size box. % \def\appendixbox#1{% % We use M since it's probably the widest letter. \setbox0 = \hbox{\putwordAppendix{} M}% \hbox to \wd0{\putwordAppendix{} #1\hss}} % \def\appentry#1#2#3#4{\dochapentry{\appendixbox{#2}\labelspace#1}{#4}} % Unnumbered chapters. \def\unnchapentry#1#2#3#4{\dochapentry{#1}{#4}} \def\shortunnchapentry#1#2#3#4{\tocentry{#1}{\doshortpageno\bgroup#4\egroup}} % Sections. \def\numsecentry#1#2#3#4{\dosecentry{#2\labelspace#1}{#4}} \let\appsecentry=\numsecentry \def\unnsecentry#1#2#3#4{\dosecentry{#1}{#4}} % Subsections. \def\numsubsecentry#1#2#3#4{\dosubsecentry{#2\labelspace#1}{#4}} \let\appsubsecentry=\numsubsecentry \def\unnsubsecentry#1#2#3#4{\dosubsecentry{#1}{#4}} % And subsubsections. \def\numsubsubsecentry#1#2#3#4{\dosubsubsecentry{#2\labelspace#1}{#4}} \let\appsubsubsecentry=\numsubsubsecentry \def\unnsubsubsecentry#1#2#3#4{\dosubsubsecentry{#1}{#4}} % This parameter controls the indentation of the various levels. % Same as \defaultparindent. \newdimen\tocindent \tocindent = 15pt % Now for the actual typesetting. In all these, #1 is the text and #2 is the % page number. % % If the toc has to be broken over pages, we want it to be at chapters % if at all possible; hence the \penalty. \def\dochapentry#1#2{% \penalty-300 \vskip1\baselineskip plus.33\baselineskip minus.25\baselineskip \begingroup \chapentryfonts \tocentry{#1}{\dopageno\bgroup#2\egroup}% \endgroup \nobreak\vskip .25\baselineskip plus.1\baselineskip } \def\dosecentry#1#2{\begingroup \secentryfonts \leftskip=\tocindent \tocentry{#1}{\dopageno\bgroup#2\egroup}% \endgroup} \def\dosubsecentry#1#2{\begingroup \subsecentryfonts \leftskip=2\tocindent \tocentry{#1}{\dopageno\bgroup#2\egroup}% \endgroup} \def\dosubsubsecentry#1#2{\begingroup \subsubsecentryfonts \leftskip=3\tocindent \tocentry{#1}{\dopageno\bgroup#2\egroup}% \endgroup} % We use the same \entry macro as for the index entries. \let\tocentry = \entry % Space between chapter (or whatever) number and the title. \def\labelspace{\hskip1em \relax} \def\dopageno#1{{\rm #1}} \def\doshortpageno#1{{\rm #1}} \def\chapentryfonts{\secfonts \rm} \def\secentryfonts{\textfonts} \def\subsecentryfonts{\textfonts} \def\subsubsecentryfonts{\textfonts} \message{environments,} % @@foo ... @@end foo. % @@point{}, @@result{}, @@expansion{}, @@print{}, @@equiv{}. % % Since these characters are used in examples, it should be an even number of % \tt widths. Each \tt character is 1en, so two makes it 1em. % \def\point{$\star$} \def\result{\leavevmode\raise.15ex\hbox to 1em{\hfil$\Rightarrow$\hfil}} \def\expansion{\leavevmode\raise.1ex\hbox to 1em{\hfil$\mapsto$\hfil}} \def\print{\leavevmode\lower.1ex\hbox to 1em{\hfil$\dashv$\hfil}} \def\equiv{\leavevmode\lower.1ex\hbox to 1em{\hfil$\ptexequiv$\hfil}} % The @@error{} command. % Adapted from the TeXbook's \boxit. % \newbox\errorbox % {\tentt \global\dimen0 = 3em}% Width of the box. \dimen2 = .55pt % Thickness of rules % The text. (`r' is open on the right, `e' somewhat less so on the left.) \setbox0 = \hbox{\kern-.75pt \tensf error\kern-1.5pt} % \setbox\errorbox=\hbox to \dimen0{\hfil \hsize = \dimen0 \advance\hsize by -5.8pt % Space to left+right. \advance\hsize by -2\dimen2 % Rules. \vbox{% \hrule height\dimen2 \hbox{\vrule width\dimen2 \kern3pt % Space to left of text. \vtop{\kern2.4pt \box0 \kern2.4pt}% Space above/below. \kern3pt\vrule width\dimen2}% Space to right. \hrule height\dimen2} \hfil} % \def\error{\leavevmode\lower.7ex\copy\errorbox} % @@tex ... @@end tex escapes into raw Tex temporarily. % One exception: @@ is still an escape character, so that @@end tex works. % But \@@ or @@@@ will get a plain tex @@ character. \envdef\tex{% \catcode `\\=0 \catcode `\{=1 \catcode `\}=2 \catcode `\$=3 \catcode `\&=4 \catcode `\#=6 \catcode `\^=7 \catcode `\_=8 \catcode `\~=\active \let~=\tie \catcode `\%=14 \catcode `\+=\other \catcode `\"=\other \catcode `\|=\other \catcode `\<=\other \catcode `\>=\other \escapechar=`\\ % \let\b=\ptexb \let\bullet=\ptexbullet \let\c=\ptexc \let\,=\ptexcomma \let\.=\ptexdot \let\dots=\ptexdots \let\equiv=\ptexequiv \let\!=\ptexexclam \let\i=\ptexi \let\indent=\ptexindent \let\noindent=\ptexnoindent \let\{=\ptexlbrace \let\+=\tabalign \let\}=\ptexrbrace \let\/=\ptexslash \let\*=\ptexstar \let\t=\ptext % \def\endldots{\mathinner{\ldots\ldots\ldots\ldots}}% \def\enddots{\relax\ifmmode\endldots\else$\mathsurround=0pt \endldots\,$\fi}% \def\@@{@@}% } % There is no need to define \Etex. % Define @@lisp ... @@end lisp. % @@lisp environment forms a group so it can rebind things, % including the definition of @@end lisp (which normally is erroneous). % Amount to narrow the margins by for @@lisp. \newskip\lispnarrowing \lispnarrowing=0.4in % This is the definition that ^^M gets inside @@lisp, @@example, and other % such environments. \null is better than a space, since it doesn't % have any width. \def\lisppar{\null\endgraf} % This space is always present above and below environments. \newskip\envskipamount \envskipamount = 0pt % Make spacing and below environment symmetrical. We use \parskip here % to help in doing that, since in @@example-like environments \parskip % is reset to zero; thus the \afterenvbreak inserts no space -- but the % start of the next paragraph will insert \parskip. % \def\aboveenvbreak{{% % =10000 instead of <10000 because of a special case in \itemzzz and % \sectionheading, q.v. \ifnum \lastpenalty=10000 \else \advance\envskipamount by \parskip \endgraf \ifdim\lastskip<\envskipamount \removelastskip % it's not a good place to break if the last penalty was \nobreak % or better ... \ifnum\lastpenalty<10000 \penalty-50 \fi \vskip\envskipamount \fi \fi }} \let\afterenvbreak = \aboveenvbreak % \nonarrowing is a flag. If "set", @@lisp etc don't narrow margins. \let\nonarrowing=\relax % @@cartouche ... @@end cartouche: draw rectangle w/rounded corners around % environment contents. \font\circle=lcircle10 \newdimen\circthick \newdimen\cartouter\newdimen\cartinner \newskip\normbskip\newskip\normpskip\newskip\normlskip \circthick=\fontdimen8\circle % \def\ctl{{\circle\char'013\hskip -6pt}}% 6pt from pl file: 1/2charwidth \def\ctr{{\hskip 6pt\circle\char'010}} \def\cbl{{\circle\char'012\hskip -6pt}} \def\cbr{{\hskip 6pt\circle\char'011}} \def\carttop{\hbox to \cartouter{\hskip\lskip \ctl\leaders\hrule height\circthick\hfil\ctr \hskip\rskip}} \def\cartbot{\hbox to \cartouter{\hskip\lskip \cbl\leaders\hrule height\circthick\hfil\cbr \hskip\rskip}} % \newskip\lskip\newskip\rskip \envdef\cartouche{% \ifhmode\par\fi % can't be in the midst of a paragraph. \startsavinginserts \lskip=\leftskip \rskip=\rightskip \leftskip=0pt\rightskip=0pt % we want these *outside*. \cartinner=\hsize \advance\cartinner by-\lskip \advance\cartinner by-\rskip \cartouter=\hsize \advance\cartouter by 18.4pt % allow for 3pt kerns on either % side, and for 6pt waste from % each corner char, and rule thickness \normbskip=\baselineskip \normpskip=\parskip \normlskip=\lineskip % Flag to tell @@lisp, etc., not to narrow margin. \let\nonarrowing=\comment \vbox\bgroup \baselineskip=0pt\parskip=0pt\lineskip=0pt \carttop \hbox\bgroup \hskip\lskip \vrule\kern3pt \vbox\bgroup \kern3pt \hsize=\cartinner \baselineskip=\normbskip \lineskip=\normlskip \parskip=\normpskip \vskip -\parskip \comment % For explanation, see the end of \def\group. } \def\Ecartouche{% \ifhmode\par\fi \kern3pt \egroup \kern3pt\vrule \hskip\rskip \egroup \cartbot \egroup \checkinserts } % This macro is called at the beginning of all the @@example variants, % inside a group. \def\nonfillstart{% \aboveenvbreak \hfuzz = 12pt % Don't be fussy \sepspaces % Make spaces be word-separators rather than space tokens. \let\par = \lisppar % don't ignore blank lines \obeylines % each line of input is a line of output \parskip = 0pt \parindent = 0pt \emergencystretch = 0pt % don't try to avoid overfull boxes % @@cartouche defines \nonarrowing to inhibit narrowing % at next level down. \ifx\nonarrowing\relax \advance \leftskip by \lispnarrowing \exdentamount=\lispnarrowing \fi \let\exdent=\nofillexdent } % If you want all examples etc. small: @@set dispenvsize small. % If you want even small examples the full size: @@set dispenvsize nosmall. % This affects the following displayed environments: % @@example, @@display, @@format, @@lisp % \def\smallword{small} \def\nosmallword{nosmall} \let\SETdispenvsize\relax \def\setnormaldispenv{% \ifx\SETdispenvsize\smallword \smallexamplefonts \rm \fi } \def\setsmalldispenv{% \ifx\SETdispenvsize\nosmallword \else \smallexamplefonts \rm \fi } % We often define two environments, @@foo and @@smallfoo. % Let's do it by one command: \def\makedispenv #1#2{ \expandafter\envdef\csname#1\endcsname {\setnormaldispenv #2} \expandafter\envdef\csname small#1\endcsname {\setsmalldispenv #2} \expandafter\let\csname E#1\endcsname \afterenvbreak \expandafter\let\csname Esmall#1\endcsname \afterenvbreak } % Define two synonyms: \def\maketwodispenvs #1#2#3{ \makedispenv{#1}{#3} \makedispenv{#2}{#3} } % @@lisp: indented, narrowed, typewriter font; @@example: same as @@lisp. % % @@smallexample and @@smalllisp: use smaller fonts. % Originally contributed by Pavel@@xerox. % \maketwodispenvs {lisp}{example}{% \nonfillstart \tt \let\kbdfont = \kbdexamplefont % Allow @@kbd to do something special. \gobble % eat return } % @@display/@@smalldisplay: same as @@lisp except keep current font. % \makedispenv {display}{% \nonfillstart \gobble } % @@format/@@smallformat: same as @@display except don't narrow margins. % \makedispenv{format}{% \let\nonarrowing = t% \nonfillstart \gobble } % @@flushleft: same as @@format, but doesn't obey \SETdispenvsize. \envdef\flushleft{% \let\nonarrowing = t% \nonfillstart \gobble } \let\Eflushleft = \afterenvbreak % @@flushright. % \envdef\flushright{% \let\nonarrowing = t% \nonfillstart \advance\leftskip by 0pt plus 1fill \gobble } \let\Eflushright = \afterenvbreak % @@quotation does normal linebreaking (hence we can't use \nonfillstart) % and narrows the margins. We keep \parskip nonzero in general, since % we're doing normal filling. So, when using \aboveenvbreak and % \afterenvbreak, temporarily make \parskip 0. % \envdef\quotation{% {\parskip=0pt \aboveenvbreak}% because \aboveenvbreak inserts \parskip \parindent=0pt % % @@cartouche defines \nonarrowing to inhibit narrowing at next level down. \ifx\nonarrowing\relax \advance\leftskip by \lispnarrowing \advance\rightskip by \lispnarrowing \exdentamount = \lispnarrowing \let\nonarrowing = \relax \fi \parsearg\quotationlabel } % We have retained a nonzero parskip for the environment, since we're % doing normal filling. % \def\Equotation{% \par \ifx\quotationauthor\undefined\else % indent a bit. \leftline{\kern 2\leftskip \sl ---\quotationauthor}% \fi {\parskip=0pt \afterenvbreak}% } % If we're given an argument, typeset it in bold with a colon after. \def\quotationlabel#1{% \def\temp{#1}% \ifx\temp\empty \else {\bf #1: }% \fi } % LaTeX-like @@verbatim...@@end verbatim and @@verb{...} % If we want to allow any as delimiter, % we need the curly braces so that makeinfo sees the @@verb command, eg: % `@@verbx...x' would look like the '@@verbx' command. --janneke@@gnu.org % % [Knuth]: Donald Ervin Knuth, 1996. The TeXbook. % % [Knuth] p.344; only we need to do the other characters Texinfo sets % active too. Otherwise, they get lost as the first character on a % verbatim line. \def\dospecials{% \do\ \do\\\do\{\do\}\do\$\do\&% \do\#\do\^\do\^^K\do\_\do\^^A\do\%\do\~% \do\<\do\>\do\|\do\@@\do+\do\"% } % % [Knuth] p. 380 \def\uncatcodespecials{% \def\do##1{\catcode`##1=\other}\dospecials} % % [Knuth] pp. 380,381,391 % Disable Spanish ligatures ?` and !` of \tt font \begingroup \catcode`\`=\active\gdef`{\relax\lq} \endgroup % % Setup for the @@verb command. % % Eight spaces for a tab \begingroup \catcode`\^^I=\active \gdef\tabeightspaces{\catcode`\^^I=\active\def^^I{\ \ \ \ \ \ \ \ }} \endgroup % \def\setupverb{% \tt % easiest (and conventionally used) font for verbatim \def\par{\leavevmode\endgraf}% \catcode`\`=\active \tabeightspaces % Respect line breaks, % print special symbols as themselves, and % make each space count % must do in this order: \obeylines \uncatcodespecials \sepspaces } % Setup for the @@verbatim environment % % Real tab expansion \newdimen\tabw \setbox0=\hbox{\tt\space} \tabw=8\wd0 % tab amount % \def\starttabbox{\setbox0=\hbox\bgroup} \begingroup \catcode`\^^I=\active \gdef\tabexpand{% \catcode`\^^I=\active \def^^I{\leavevmode\egroup \dimen0=\wd0 % the width so far, or since the previous tab \divide\dimen0 by\tabw \multiply\dimen0 by\tabw % compute previous multiple of \tabw \advance\dimen0 by\tabw % advance to next multiple of \tabw \wd0=\dimen0 \box0 \starttabbox }% } \endgroup \def\setupverbatim{% \nonfillstart \advance\leftskip by -\defbodyindent % Easiest (and conventionally used) font for verbatim \tt \def\par{\leavevmode\egroup\box0\endgraf}% \catcode`\`=\active \tabexpand % Respect line breaks, % print special symbols as themselves, and % make each space count % must do in this order: \obeylines \uncatcodespecials \sepspaces \everypar{\starttabbox}% } % Do the @@verb magic: verbatim text is quoted by unique % delimiter characters. Before first delimiter expect a % right brace, after last delimiter expect closing brace: % % \def\doverb'{'#1'}'{#1} % % [Knuth] p. 382; only eat outer {} \begingroup \catcode`[=1\catcode`]=2\catcode`\{=\other\catcode`\}=\other \gdef\doverb{#1[\def\next##1#1}[##1\endgroup]\next] \endgroup % \def\verb{\begingroup\setupverb\doverb} % % % Do the @@verbatim magic: define the macro \doverbatim so that % the (first) argument ends when '@@end verbatim' is reached, ie: % % \def\doverbatim#1@@end verbatim{#1} % % For Texinfo it's a lot easier than for LaTeX, % because texinfo's \verbatim doesn't stop at '\end{verbatim}': % we need not redefine '\', '{' and '}'. % % Inspired by LaTeX's verbatim command set [latex.ltx] % \begingroup \catcode`\ =\active \obeylines % % ignore everything up to the first ^^M, that's the newline at the end % of the @@verbatim input line itself. Otherwise we get an extra blank % line in the output. \xdef\doverbatim#1^^M#2@@end verbatim{#2\noexpand\end\gobble verbatim}% % We really want {...\end verbatim} in the body of the macro, but % without the active space; thus we have to use \xdef and \gobble. \endgroup % \envdef\verbatim{% \setupverbatim\doverbatim } \let\Everbatim = \afterenvbreak % @@verbatiminclude FILE - insert text of file in verbatim environment. % \def\verbatiminclude{\parseargusing\filenamecatcodes\doverbatiminclude} % \def\doverbatiminclude#1{% {% \makevalueexpandable \setupverbatim \input #1 \afterenvbreak }% } % @@copying ... @@end copying. % Save the text away for @@insertcopying later. % % We save the uninterpreted tokens, rather than creating a box. % Saving the text in a box would be much easier, but then all the % typesetting commands (@@smallbook, font changes, etc.) have to be done % beforehand -- and a) we want @@copying to be done first in the source % file; b) letting users define the frontmatter in as flexible order as % possible is very desirable. % \def\copying{\checkenv{}\begingroup\scanargctxt\docopying} \def\docopying#1@@end copying{\endgroup\def\copyingtext{#1}} % \def\insertcopying{% \begingroup \parindent = 0pt % paragraph indentation looks wrong on title page \scanexp\copyingtext \endgroup } \message{defuns,} % @@defun etc. \newskip\defbodyindent \defbodyindent=.4in \newskip\defargsindent \defargsindent=50pt \newskip\deflastargmargin \deflastargmargin=18pt % Start the processing of @@deffn: \def\startdefun{% \ifnum\lastpenalty<10000 \medbreak \else % If there are two @@def commands in a row, we'll have a \nobreak, % which is there to keep the function description together with its % header. But if there's nothing but headers, we need to allow a % break somewhere. Check specifically for penalty 10002, inserted % by \defargscommonending, instead of 10000, since the sectioning % commands also insert a nobreak penalty, and we don't want to allow % a break between a section heading and a defun. % \ifnum\lastpenalty=10002 \penalty2000 \fi % % Similarly, after a section heading, do not allow a break. % But do insert the glue. \medskip % preceded by discardable penalty, so not a breakpoint \fi % \parindent=0in \advance\leftskip by \defbodyindent \exdentamount=\defbodyindent } \def\dodefunx#1{% % First, check whether we are in the right environment: \checkenv#1% % % As above, allow line break if we have multiple x headers in a row. % It's not a great place, though. \ifnum\lastpenalty=10002 \penalty3000 \fi % % And now, it's time to reuse the body of the original defun: \expandafter\gobbledefun#1% } \def\gobbledefun#1\startdefun{} % \printdefunline \deffnheader{text} % \def\printdefunline#1#2{% \begingroup % call \deffnheader: #1#2 \endheader % common ending: \interlinepenalty = 10000 \advance\rightskip by 0pt plus 1fil \endgraf \nobreak\vskip -\parskip \penalty 10002 % signal to \startdefun and \dodefunx % Some of the @@defun-type tags do not enable magic parentheses, % rendering the following check redundant. But we don't optimize. \checkparencounts \endgroup } \def\Edefun{\endgraf\medbreak} % \makedefun{deffn} creates \deffn, \deffnx and \Edeffn; % the only thing remainnig is to define \deffnheader. % \def\makedefun#1{% \expandafter\let\csname E#1\endcsname = \Edefun \edef\temp{\noexpand\domakedefun \makecsname{#1}\makecsname{#1x}\makecsname{#1header}}% \temp } % \domakedefun \deffn \deffnx \deffnheader % % Define \deffn and \deffnx, without parameters. % \deffnheader has to be defined explicitly. % \def\domakedefun#1#2#3{% \envdef#1{% \startdefun \parseargusing\activeparens{\printdefunline#3}% }% \def#2{\dodefunx#1}% \def#3% } %%% Untyped functions: % @@deffn category name args \makedefun{deffn}{\deffngeneral{}} % @@deffn category class name args \makedefun{defop}#1 {\defopon{#1\ \putwordon}} % \defopon {category on}class name args \def\defopon#1#2 {\deffngeneral{\putwordon\ \code{#2}}{#1\ \code{#2}} } % \deffngeneral {subind}category name args % \def\deffngeneral#1#2 #3 #4\endheader{% % Remember that \dosubind{fn}{foo}{} is equivalent to \doind{fn}{foo}. \dosubind{fn}{\code{#3}}{#1}% \defname{#2}{}{#3}\magicamp\defunargs{#4\unskip}% } %%% Typed functions: % @@deftypefn category type name args \makedefun{deftypefn}{\deftypefngeneral{}} % @@deftypeop category class type name args \makedefun{deftypeop}#1 {\deftypeopon{#1\ \putwordon}} % \deftypeopon {category on}class type name args \def\deftypeopon#1#2 {\deftypefngeneral{\putwordon\ \code{#2}}{#1\ \code{#2}} } % \deftypefngeneral {subind}category type name args % \def\deftypefngeneral#1#2 #3 #4 #5\endheader{% \dosubind{fn}{\code{#4}}{#1}% \defname{#2}{#3}{#4}\defunargs{#5\unskip}% } %%% Typed variables: % @@deftypevr category type var args \makedefun{deftypevr}{\deftypecvgeneral{}} % @@deftypecv category class type var args \makedefun{deftypecv}#1 {\deftypecvof{#1\ \putwordof}} % \deftypecvof {category of}class type var args \def\deftypecvof#1#2 {\deftypecvgeneral{\putwordof\ \code{#2}}{#1\ \code{#2}} } % \deftypecvgeneral {subind}category type var args % \def\deftypecvgeneral#1#2 #3 #4 #5\endheader{% \dosubind{vr}{\code{#4}}{#1}% \defname{#2}{#3}{#4}\defunargs{#5\unskip}% } %%% Untyped variables: % @@defvr category var args \makedefun{defvr}#1 {\deftypevrheader{#1} {} } % @@defcv category class var args \makedefun{defcv}#1 {\defcvof{#1\ \putwordof}} % \defcvof {category of}class var args \def\defcvof#1#2 {\deftypecvof{#1}#2 {} } %%% Type: % @@deftp category name args \makedefun{deftp}#1 #2 #3\endheader{% \doind{tp}{\code{#2}}% \defname{#1}{}{#2}\defunargs{#3\unskip}% } % Remaining @@defun-like shortcuts: \makedefun{defun}{\deffnheader{\putwordDeffunc} } \makedefun{defmac}{\deffnheader{\putwordDefmac} } \makedefun{defspec}{\deffnheader{\putwordDefspec} } \makedefun{deftypefun}{\deftypefnheader{\putwordDeffunc} } \makedefun{defvar}{\defvrheader{\putwordDefvar} } \makedefun{defopt}{\defvrheader{\putwordDefopt} } \makedefun{deftypevar}{\deftypevrheader{\putwordDefvar} } \makedefun{defmethod}{\defopon\putwordMethodon} \makedefun{deftypemethod}{\deftypeopon\putwordMethodon} \makedefun{defivar}{\defcvof\putwordInstanceVariableof} \makedefun{deftypeivar}{\deftypecvof\putwordInstanceVariableof} % \defname, which formats the name of the @@def (not the args). % #1 is the category, such as "Function". % #2 is the return type, if any. % #3 is the function name. % % We are followed by (but not passed) the arguments, if any. % \def\defname#1#2#3{% % Get the values of \leftskip and \rightskip as they were outside the @@def... \advance\leftskip by -\defbodyindent % % How we'll format the type name. Putting it in brackets helps % distinguish it from the body text that may end up on the next line % just below it. \def\temp{#1}% \setbox0=\hbox{\kern\deflastargmargin \ifx\temp\empty\else [\rm\temp]\fi} % % Figure out line sizes for the paragraph shape. % The first line needs space for \box0; but if \rightskip is nonzero, % we need only space for the part of \box0 which exceeds it: \dimen0=\hsize \advance\dimen0 by -\wd0 \advance\dimen0 by \rightskip % The continuations: \dimen2=\hsize \advance\dimen2 by -\defargsindent % (plain.tex says that \dimen1 should be used only as global.) \parshape 2 0in \dimen0 \defargsindent \dimen2 % % Put the type name to the right margin. \noindent \hbox to 0pt{% \hfil\box0 \kern-\hsize % \hsize has to be shortened this way: \kern\leftskip % Intentionally do not respect \rightskip, since we need the space. }% % % Allow all lines to be underfull without complaint: \tolerance=10000 \hbadness=10000 \exdentamount=\defbodyindent {% % defun fonts. We use typewriter by default (used to be bold) because: % . we're printing identifiers, they should be in tt in principle. % . in languages with many accents, such as Czech or French, it's % common to leave accents off identifiers. The result looks ok in % tt, but exceedingly strange in rm. % . we don't want -- and --- to be treated as ligatures. % . this still does not fix the ?` and !` ligatures, but so far no % one has made identifiers using them :). \df \tt \def\temp{#2}% return value type \ifx\temp\empty\else \tclose{\temp} \fi #3% output function name }% {\rm\enskip}% hskip 0.5 em of \tenrm % \boldbrax % arguments will be output next, if any. } % Print arguments in slanted roman (not ttsl), inconsistently with using % tt for the name. This is because literal text is sometimes needed in % the argument list (groff manual), and ttsl and tt are not very % distinguishable. Prevent hyphenation at `-' chars. % \def\defunargs#1{% % use sl by default (not ttsl), % tt for the names. \df \sl \hyphenchar\font=0 % % On the other hand, if an argument has two dashes (for instance), we % want a way to get ttsl. Let's try @@var for that. \let\var=\ttslanted #1% \sl\hyphenchar\font=45 } % We want ()&[] to print specially on the defun line. % \def\activeparens{% \catcode`\(=\active \catcode`\)=\active \catcode`\[=\active \catcode`\]=\active \catcode`\&=\active } % Make control sequences which act like normal parenthesis chars. \let\lparen = ( \let\rparen = ) % Be sure that we always have a definition for `(', etc. For example, % if the fn name has parens in it, \boldbrax will not be in effect yet, % so TeX would otherwise complain about undefined control sequence. { \activeparens \global\let(=\lparen \global\let)=\rparen \global\let[=\lbrack \global\let]=\rbrack \global\let& = \& \gdef\boldbrax{\let(=\opnr\let)=\clnr\let[=\lbrb\let]=\rbrb} \gdef\magicamp{\let&=\amprm} } \newcount\parencount % If we encounter &foo, then turn on ()-hacking afterwards \newif\ifampseen \def\amprm#1 {\ampseentrue{\bf\ }} \def\parenfont{% \ifampseen % At the first level, print parens in roman, % otherwise use the default font. \ifnum \parencount=1 \rm \fi \else % The \sf parens (in \boldbrax) actually are a little bolder than % the contained text. This is especially needed for [ and ] . \sf \fi } \def\infirstlevel#1{% \ifampseen \ifnum\parencount=1 #1% \fi \fi } \def\bfafterword#1 {#1 \bf} \def\opnr{% \global\advance\parencount by 1 {\parenfont(}% \infirstlevel \bfafterword } \def\clnr{% {\parenfont)}% \infirstlevel \sl \global\advance\parencount by -1 } \newcount\brackcount \def\lbrb{% \global\advance\brackcount by 1 {\bf[}% } \def\rbrb{% {\bf]}% \global\advance\brackcount by -1 } \def\checkparencounts{% \ifnum\parencount=0 \else \badparencount \fi \ifnum\brackcount=0 \else \badbrackcount \fi } \def\badparencount{% \errmessage{Unbalanced parentheses in @@def}% \global\parencount=0 } \def\badbrackcount{% \errmessage{Unbalanced square braces in @@def}% \global\brackcount=0 } \message{macros,} % @@macro. % To do this right we need a feature of e-TeX, \scantokens, % which we arrange to emulate with a temporary file in ordinary TeX. \ifx\eTeXversion\undefined \newwrite\macscribble \def\scantokens#1{% \toks0={#1}% \immediate\openout\macscribble=\jobname.tmp \immediate\write\macscribble{\the\toks0}% \immediate\closeout\macscribble \input \jobname.tmp } \fi \def\scanmacro#1{% \begingroup \newlinechar`\^^M \let\xeatspaces\eatspaces % Undo catcode changes of \startcontents and \doprintindex % When called from @@insertcopying or (short)caption, we need active % backslash to get it printed correctly. Previously, we had % \catcode`\\=\other instead. We'll see whether a problem appears % with macro expansion. --kasal, 19aug04 \catcode`\@@=0 \catcode`\\=\active \escapechar=`\@@ % ... and \example \spaceisspace % % Append \endinput to make sure that TeX does not see the ending newline. % % I've verified that it is necessary both for e-TeX and for ordinary TeX % --kasal, 29nov03 \scantokens{#1\endinput}% \endgroup } \def\scanexp#1{% \edef\temp{\noexpand\scanmacro{#1}}% \temp } \newcount\paramno % Count of parameters \newtoks\macname % Macro name \newif\ifrecursive % Is it recursive? \def\macrolist{} % List of all defined macros in the form % \do\macro1\do\macro2... % Utility routines. % This does \let #1 = #2, with \csnames; that is, % \let \csname#1\endcsname = \csname#2\endcsname % (except of course we have to play expansion games). % \def\cslet#1#2{% \expandafter\let \csname#1\expandafter\endcsname \csname#2\endcsname } % Trim leading and trailing spaces off a string. % Concepts from aro-bend problem 15 (see CTAN). {\catcode`\@@=11 \gdef\eatspaces #1{\expandafter\trim@@\expandafter{#1 }} \gdef\trim@@ #1{\trim@@@@ @@#1 @@ #1 @@ @@@@} \gdef\trim@@@@ #1@@ #2@@ #3@@@@{\trim@@@@@@\empty #2 @@} \def\unbrace#1{#1} \unbrace{\gdef\trim@@@@@@ #1 } #2@@{#1} } % Trim a single trailing ^^M off a string. {\catcode`\^^M=\other \catcode`\Q=3% \gdef\eatcr #1{\eatcra #1Q^^MQ}% \gdef\eatcra#1^^MQ{\eatcrb#1Q}% \gdef\eatcrb#1Q#2Q{#1}% } % Macro bodies are absorbed as an argument in a context where % all characters are catcode 10, 11 or 12, except \ which is active % (as in normal texinfo). It is necessary to change the definition of \. % It's necessary to have hard CRs when the macro is executed. This is % done by making ^^M (\endlinechar) catcode 12 when reading the macro % body, and then making it the \newlinechar in \scanmacro. \def\scanctxt{% \catcode`\"=\other \catcode`\+=\other \catcode`\<=\other \catcode`\>=\other \catcode`\@@=\other \catcode`\^=\other \catcode`\_=\other \catcode`\|=\other \catcode`\~=\other } \def\scanargctxt{% \scanctxt \catcode`\\=\other \catcode`\^^M=\other } \def\macrobodyctxt{% \scanctxt \catcode`\{=\other \catcode`\}=\other \catcode`\^^M=\other \usembodybackslash } \def\macroargctxt{% \scanctxt \catcode`\\=\other } % \mbodybackslash is the definition of \ in @@macro bodies. % It maps \foo\ => \csname macarg.foo\endcsname => #N % where N is the macro parameter number. % We define \csname macarg.\endcsname to be \realbackslash, so % \\ in macro replacement text gets you a backslash. {\catcode`@@=0 @@catcode`@@\=@@active @@gdef@@usembodybackslash{@@let\=@@mbodybackslash} @@gdef@@mbodybackslash#1\{@@csname macarg.#1@@endcsname} } \expandafter\def\csname macarg.\endcsname{\realbackslash} \def\macro{\recursivefalse\parsearg\macroxxx} \def\rmacro{\recursivetrue\parsearg\macroxxx} \def\macroxxx#1{% \getargs{#1}% now \macname is the macname and \argl the arglist \ifx\argl\empty % no arguments \paramno=0% \else \expandafter\parsemargdef \argl;% \fi \if1\csname ismacro.\the\macname\endcsname \message{Warning: redefining \the\macname}% \else \expandafter\ifx\csname \the\macname\endcsname \relax \else \errmessage{Macro name \the\macname\space already defined}\fi \global\cslet{macsave.\the\macname}{\the\macname}% \global\expandafter\let\csname ismacro.\the\macname\endcsname=1% % Add the macroname to \macrolist \toks0 = \expandafter{\macrolist\do}% \xdef\macrolist{\the\toks0 \expandafter\noexpand\csname\the\macname\endcsname}% \fi \begingroup \macrobodyctxt \ifrecursive \expandafter\parsermacbody \else \expandafter\parsemacbody \fi} \parseargdef\unmacro{% \if1\csname ismacro.#1\endcsname \global\cslet{#1}{macsave.#1}% \global\expandafter\let \csname ismacro.#1\endcsname=0% % Remove the macro name from \macrolist: \begingroup \expandafter\let\csname#1\endcsname \relax \let\do\unmacrodo \xdef\macrolist{\macrolist}% \endgroup \else \errmessage{Macro #1 not defined}% \fi } % Called by \do from \dounmacro on each macro. The idea is to omit any % macro definitions that have been changed to \relax. % \def\unmacrodo#1{% \ifx#1\relax % remove this \else \noexpand\do \noexpand #1% \fi } % This makes use of the obscure feature that if the last token of a % is #, then the preceding argument is delimited by % an opening brace, and that opening brace is not consumed. \def\getargs#1{\getargsxxx#1{}} \def\getargsxxx#1#{\getmacname #1 \relax\getmacargs} \def\getmacname #1 #2\relax{\macname={#1}} \def\getmacargs#1{\def\argl{#1}} % Parse the optional {params} list. Set up \paramno and \paramlist % so \defmacro knows what to do. Define \macarg.blah for each blah % in the params list, to be ##N where N is the position in that list. % That gets used by \mbodybackslash (above). % We need to get `macro parameter char #' into several definitions. % The technique used is stolen from LaTeX: let \hash be something % unexpandable, insert that wherever you need a #, and then redefine % it to # just before using the token list produced. % % The same technique is used to protect \eatspaces till just before % the macro is used. \def\parsemargdef#1;{\paramno=0\def\paramlist{}% \let\hash\relax\let\xeatspaces\relax\parsemargdefxxx#1,;,} \def\parsemargdefxxx#1,{% \if#1;\let\next=\relax \else \let\next=\parsemargdefxxx \advance\paramno by 1% \expandafter\edef\csname macarg.\eatspaces{#1}\endcsname {\xeatspaces{\hash\the\paramno}}% \edef\paramlist{\paramlist\hash\the\paramno,}% \fi\next} % These two commands read recursive and nonrecursive macro bodies. % (They're different since rec and nonrec macros end differently.) \long\def\parsemacbody#1@@end macro% {\xdef\temp{\eatcr{#1}}\endgroup\defmacro}% \long\def\parsermacbody#1@@end rmacro% {\xdef\temp{\eatcr{#1}}\endgroup\defmacro}% % This defines the macro itself. There are six cases: recursive and % nonrecursive macros of zero, one, and many arguments. % Much magic with \expandafter here. % \xdef is used so that macro definitions will survive the file % they're defined in; @@include reads the file inside a group. \def\defmacro{% \let\hash=##% convert placeholders to macro parameter chars \ifrecursive \ifcase\paramno % 0 \expandafter\xdef\csname\the\macname\endcsname{% \noexpand\scanmacro{\temp}}% \or % 1 \expandafter\xdef\csname\the\macname\endcsname{% \bgroup\noexpand\macroargctxt \noexpand\braceorline \expandafter\noexpand\csname\the\macname xxx\endcsname}% \expandafter\xdef\csname\the\macname xxx\endcsname##1{% \egroup\noexpand\scanmacro{\temp}}% \else % many \expandafter\xdef\csname\the\macname\endcsname{% \bgroup\noexpand\macroargctxt \noexpand\csname\the\macname xx\endcsname}% \expandafter\xdef\csname\the\macname xx\endcsname##1{% \expandafter\noexpand\csname\the\macname xxx\endcsname ##1,}% \expandafter\expandafter \expandafter\xdef \expandafter\expandafter \csname\the\macname xxx\endcsname \paramlist{\egroup\noexpand\scanmacro{\temp}}% \fi \else \ifcase\paramno % 0 \expandafter\xdef\csname\the\macname\endcsname{% \noexpand\norecurse{\the\macname}% \noexpand\scanmacro{\temp}\egroup}% \or % 1 \expandafter\xdef\csname\the\macname\endcsname{% \bgroup\noexpand\macroargctxt \noexpand\braceorline \expandafter\noexpand\csname\the\macname xxx\endcsname}% \expandafter\xdef\csname\the\macname xxx\endcsname##1{% \egroup \noexpand\norecurse{\the\macname}% \noexpand\scanmacro{\temp}\egroup}% \else % many \expandafter\xdef\csname\the\macname\endcsname{% \bgroup\noexpand\macroargctxt \expandafter\noexpand\csname\the\macname xx\endcsname}% \expandafter\xdef\csname\the\macname xx\endcsname##1{% \expandafter\noexpand\csname\the\macname xxx\endcsname ##1,}% \expandafter\expandafter \expandafter\xdef \expandafter\expandafter \csname\the\macname xxx\endcsname \paramlist{% \egroup \noexpand\norecurse{\the\macname}% \noexpand\scanmacro{\temp}\egroup}% \fi \fi} \def\norecurse#1{\bgroup\cslet{#1}{macsave.#1}} % \braceorline decides whether the next nonwhitespace character is a % {. If so it reads up to the closing }, if not, it reads the whole % line. Whatever was read is then fed to the next control sequence % as an argument (by \parsebrace or \parsearg) \def\braceorline#1{\let\next=#1\futurelet\nchar\braceorlinexxx} \def\braceorlinexxx{% \ifx\nchar\bgroup\else \expandafter\parsearg \fi \next} % We want to disable all macros during \shipout so that they are not % expanded by \write. \def\turnoffmacros{\begingroup \def\do##1{\let\noexpand##1=\relax}% \edef\next{\macrolist}\expandafter\endgroup\next} % For \indexnofonts, we need to get rid of all macros, leaving only the % arguments (if present). Of course this is not nearly correct, but it % is the best we can do for now. makeinfo does not expand macros in the % argument to @@deffn, which ends up writing an index entry, and texindex % isn't prepared for an index sort entry that starts with \. % % Since macro invocations are followed by braces, we can just redefine them % to take a single TeX argument. The case of a macro invocation that % goes to end-of-line is not handled. % \def\emptyusermacros{\begingroup \def\do##1{\let\noexpand##1=\noexpand\asis}% \edef\next{\macrolist}\expandafter\endgroup\next} % @@alias. % We need some trickery to remove the optional spaces around the equal % sign. Just make them active and then expand them all to nothing. \def\alias{\parseargusing\obeyspaces\aliasxxx} \def\aliasxxx #1{\aliasyyy#1\relax} \def\aliasyyy #1=#2\relax{% {% \expandafter\let\obeyedspace=\empty \xdef\next{\global\let\makecsname{#1}=\makecsname{#2}}% }% \next } \message{cross references,} \newwrite\auxfile \newif\ifhavexrefs % True if xref values are known. \newif\ifwarnedxrefs % True if we warned once that they aren't known. % @@inforef is relatively simple. \def\inforef #1{\inforefzzz #1,,,,**} \def\inforefzzz #1,#2,#3,#4**{\putwordSee{} \putwordInfo{} \putwordfile{} \file{\ignorespaces #3{}}, node \samp{\ignorespaces#1{}}} % @@node's only job in TeX is to define \lastnode, which is used in % cross-references. The @@node line might or might not have commas, and % might or might not have spaces before the first comma, like: % @@node foo , bar , ... % We don't want such trailing spaces in the node name. % \parseargdef\node{\checkenv{}\donode #1 ,\finishnodeparse} % % also remove a trailing comma, in case of something like this: % @@node Help-Cross, , , Cross-refs \def\donode#1 ,#2\finishnodeparse{\dodonode #1,\finishnodeparse} \def\dodonode#1,#2\finishnodeparse{\gdef\lastnode{#1}} \let\nwnode=\node \let\lastnode=\empty % Write a cross-reference definition for the current node. #1 is the % type (Ynumbered, Yappendix, Ynothing). % \def\donoderef#1{% \ifx\lastnode\empty\else \setref{\lastnode}{#1}% \global\let\lastnode=\empty \fi } % @@anchor{NAME} -- define xref target at arbitrary point. % \newcount\savesfregister % \def\savesf{\relax \ifhmode \savesfregister=\spacefactor \fi} \def\restoresf{\relax \ifhmode \spacefactor=\savesfregister \fi} \def\anchor#1{\savesf \setref{#1}{Ynothing}\restoresf \ignorespaces} % \setref{NAME}{SNT} defines a cross-reference point NAME (a node or an % anchor), which consists of three parts: % 1) NAME-title - the current sectioning name taken from \thissection, % or the anchor name. % 2) NAME-snt - section number and type, passed as the SNT arg, or % empty for anchors. % 3) NAME-pg - the page number. % % This is called from \donoderef, \anchor, and \dofloat. In the case of % floats, there is an additional part, which is not written here: % 4) NAME-lof - the text as it should appear in a @@listoffloats. % \def\setref#1#2{% \pdfmkdest{#1}% \iflinks {% \atdummies % preserve commands, but don't expand them \turnoffactive \otherbackslash \edef\writexrdef##1##2{% \write\auxfile{@@xrdef{#1-% #1 of \setref, expanded by the \edef ##1}{##2}}% these are parameters of \writexrdef }% \toks0 = \expandafter{\thissection}% \immediate \writexrdef{title}{\the\toks0 }% \immediate \writexrdef{snt}{\csname #2\endcsname}% \Ynumbered etc. \writexrdef{pg}{\folio}% will be written later, during \shipout }% \fi } % @@xref, @@pxref, and @@ref generate cross-references. For \xrefX, #1 is % the node name, #2 the name of the Info cross-reference, #3 the printed % node name, #4 the name of the Info file, #5 the name of the printed % manual. All but the node name can be omitted. % \def\pxref#1{\putwordsee{} \xrefX[#1,,,,,,,]} \def\xref#1{\putwordSee{} \xrefX[#1,,,,,,,]} \def\ref#1{\xrefX[#1,,,,,,,]} \def\xrefX[#1,#2,#3,#4,#5,#6]{\begingroup \unsepspaces \def\printedmanual{\ignorespaces #5}% \def\printedrefname{\ignorespaces #3}% \setbox1=\hbox{\printedmanual\unskip}% \setbox0=\hbox{\printedrefname\unskip}% \ifdim \wd0 = 0pt % No printed node name was explicitly given. \expandafter\ifx\csname SETxref-automatic-section-title\endcsname\relax % Use the node name inside the square brackets. \def\printedrefname{\ignorespaces #1}% \else % Use the actual chapter/section title appear inside % the square brackets. Use the real section title if we have it. \ifdim \wd1 > 0pt % It is in another manual, so we don't have it. \def\printedrefname{\ignorespaces #1}% \else \ifhavexrefs % We know the real title if we have the xref values. \def\printedrefname{\refx{#1-title}{}}% \else % Otherwise just copy the Info node name. \def\printedrefname{\ignorespaces #1}% \fi% \fi \fi \fi % % Make link in pdf output. \ifpdf \leavevmode \getfilename{#4}% {\turnoffactive \otherbackslash \ifnum\filenamelength>0 \startlink attr{/Border [0 0 0]}% goto file{\the\filename.pdf} name{#1}% \else \startlink attr{/Border [0 0 0]}% goto name{\pdfmkpgn{#1}}% \fi }% \linkcolor \fi % % Float references are printed completely differently: "Figure 1.2" % instead of "[somenode], p.3". We distinguish them by the % LABEL-title being set to a magic string. {% % Have to otherify everything special to allow the \csname to % include an _ in the xref name, etc. \indexnofonts \turnoffactive \otherbackslash \expandafter\global\expandafter\let\expandafter\Xthisreftitle \csname XR#1-title\endcsname }% \iffloat\Xthisreftitle % If the user specified the print name (third arg) to the ref, % print it instead of our usual "Figure 1.2". \ifdim\wd0 = 0pt \refx{#1-snt}% \else \printedrefname \fi % % if the user also gave the printed manual name (fifth arg), append % "in MANUALNAME". \ifdim \wd1 > 0pt \space \putwordin{} \cite{\printedmanual}% \fi \else % node/anchor (non-float) references. % % If we use \unhbox0 and \unhbox1 to print the node names, TeX does not % insert empty discretionaries after hyphens, which means that it will % not find a line break at a hyphen in a node names. Since some manuals % are best written with fairly long node names, containing hyphens, this % is a loss. Therefore, we give the text of the node name again, so it % is as if TeX is seeing it for the first time. \ifdim \wd1 > 0pt \putwordsection{} ``\printedrefname'' \putwordin{} \cite{\printedmanual}% \else % _ (for example) has to be the character _ for the purposes of the % control sequence corresponding to the node, but it has to expand % into the usual \leavevmode...\vrule stuff for purposes of % printing. So we \turnoffactive for the \refx-snt, back on for the % printing, back off for the \refx-pg. {\turnoffactive \otherbackslash % Only output a following space if the -snt ref is nonempty; for % @@unnumbered and @@anchor, it won't be. \setbox2 = \hbox{\ignorespaces \refx{#1-snt}{}}% \ifdim \wd2 > 0pt \refx{#1-snt}\space\fi }% % output the `[mynode]' via a macro so it can be overridden. \xrefprintnodename\printedrefname % % But we always want a comma and a space: ,\space % % output the `page 3'. \turnoffactive \otherbackslash \putwordpage\tie\refx{#1-pg}{}% \fi \fi \endlink \endgroup} % This macro is called from \xrefX for the `[nodename]' part of xref % output. It's a separate macro only so it can be changed more easily, % since square brackets don't work well in some documents. Particularly % one that Bob is working on :). % \def\xrefprintnodename#1{[#1]} % Things referred to by \setref. % \def\Ynothing{} \def\Yomitfromtoc{} \def\Ynumbered{% \ifnum\secno=0 \putwordChapter@@tie \the\chapno \else \ifnum\subsecno=0 \putwordSection@@tie \the\chapno.\the\secno \else \ifnum\subsubsecno=0 \putwordSection@@tie \the\chapno.\the\secno.\the\subsecno \else \putwordSection@@tie \the\chapno.\the\secno.\the\subsecno.\the\subsubsecno \fi\fi\fi } \def\Yappendix{% \ifnum\secno=0 \putwordAppendix@@tie @@char\the\appendixno{}% \else \ifnum\subsecno=0 \putwordSection@@tie @@char\the\appendixno.\the\secno \else \ifnum\subsubsecno=0 \putwordSection@@tie @@char\the\appendixno.\the\secno.\the\subsecno \else \putwordSection@@tie @@char\the\appendixno.\the\secno.\the\subsecno.\the\subsubsecno \fi\fi\fi } % Define \refx{NAME}{SUFFIX} to reference a cross-reference string named NAME. % If its value is nonempty, SUFFIX is output afterward. % \def\refx#1#2{% {% \indexnofonts \otherbackslash \expandafter\global\expandafter\let\expandafter\thisrefX \csname XR#1\endcsname }% \ifx\thisrefX\relax % If not defined, say something at least. \angleleft un\-de\-fined\angleright \iflinks \ifhavexrefs \message{\linenumber Undefined cross reference `#1'.}% \else \ifwarnedxrefs\else \global\warnedxrefstrue \message{Cross reference values unknown; you must run TeX again.}% \fi \fi \fi \else % It's defined, so just use it. \thisrefX \fi #2% Output the suffix in any case. } % This is the macro invoked by entries in the aux file. Usually it's % just a \def (we prepend XR to the control sequence name to avoid % collisions). But if this is a float type, we have more work to do. % \def\xrdef#1#2{% \expandafter\gdef\csname XR#1\endcsname{#2}% remember this xref value. % % Was that xref control sequence that we just defined for a float? \expandafter\iffloat\csname XR#1\endcsname % it was a float, and we have the (safe) float type in \iffloattype. \expandafter\let\expandafter\floatlist \csname floatlist\iffloattype\endcsname % % Is this the first time we've seen this float type? \expandafter\ifx\floatlist\relax \toks0 = {\do}% yes, so just \do \else % had it before, so preserve previous elements in list. \toks0 = \expandafter{\floatlist\do}% \fi % % Remember this xref in the control sequence \floatlistFLOATTYPE, % for later use in \listoffloats. \expandafter\xdef\csname floatlist\iffloattype\endcsname{\the\toks0{#1}}% \fi } % Read the last existing aux file, if any. No error if none exists. % \def\tryauxfile{% \openin 1 \jobname.aux \ifeof 1 \else \readauxfile \global\havexrefstrue \fi \closein 1 } \def\readauxfile{\begingroup \catcode`\^^@@=\other \catcode`\^^A=\other \catcode`\^^B=\other \catcode`\^^C=\other \catcode`\^^D=\other \catcode`\^^E=\other \catcode`\^^F=\other \catcode`\^^G=\other \catcode`\^^H=\other \catcode`\^^K=\other \catcode`\^^L=\other \catcode`\^^N=\other \catcode`\^^P=\other \catcode`\^^Q=\other \catcode`\^^R=\other \catcode`\^^S=\other \catcode`\^^T=\other \catcode`\^^U=\other \catcode`\^^V=\other \catcode`\^^W=\other \catcode`\^^X=\other \catcode`\^^Z=\other \catcode`\^^[=\other \catcode`\^^\=\other \catcode`\^^]=\other \catcode`\^^^=\other \catcode`\^^_=\other % It was suggested to set the catcode of ^ to 7, which would allow ^^e4 etc. % in xref tags, i.e., node names. But since ^^e4 notation isn't % supported in the main text, it doesn't seem desirable. Furthermore, % that is not enough: for node names that actually contain a ^ % character, we would end up writing a line like this: 'xrdef {'hat % b-title}{'hat b} and \xrdef does a \csname...\endcsname on the first % argument, and \hat is not an expandable control sequence. It could % all be worked out, but why? Either we support ^^ or we don't. % % The other change necessary for this was to define \auxhat: % \def\auxhat{\def^{'hat }}% extra space so ok if followed by letter % and then to call \auxhat in \setq. % \catcode`\^=\other % % Special characters. Should be turned off anyway, but... \catcode`\~=\other \catcode`\[=\other \catcode`\]=\other \catcode`\"=\other \catcode`\_=\other \catcode`\|=\other \catcode`\<=\other \catcode`\>=\other \catcode`\$=\other \catcode`\#=\other \catcode`\&=\other \catcode`\%=\other \catcode`+=\other % avoid \+ for paranoia even though we've turned it off % % This is to support \ in node names and titles, since the \ % characters end up in a \csname. It's easier than % leaving it active and making its active definition an actual \ % character. What I don't understand is why it works in the *value* % of the xrdef. Seems like it should be a catcode12 \, and that % should not typeset properly. But it works, so I'm moving on for % now. --karl, 15jan04. \catcode`\\=\other % % Make the characters 128-255 be printing characters. {% \count 1=128 \def\loop{% \catcode\count 1=\other \advance\count 1 by 1 \ifnum \count 1<256 \loop \fi }% }% % % @@ is our escape character in .aux files, and we need braces. \catcode`\{=1 \catcode`\}=2 \catcode`\@@=0 % \input \jobname.aux \endgroup} \message{insertions,} % including footnotes. \newcount \footnoteno % The trailing space in the following definition for supereject is % vital for proper filling; pages come out unaligned when you do a % pagealignmacro call if that space before the closing brace is % removed. (Generally, numeric constants should always be followed by a % space to prevent strange expansion errors.) \def\supereject{\par\penalty -20000\footnoteno =0 } % @@footnotestyle is meaningful for info output only. \let\footnotestyle=\comment {\catcode `\@@=11 % % Auto-number footnotes. Otherwise like plain. \gdef\footnote{% \let\indent=\ptexindent \let\noindent=\ptexnoindent \global\advance\footnoteno by \@@ne \edef\thisfootno{$^{\the\footnoteno}$}% % % In case the footnote comes at the end of a sentence, preserve the % extra spacing after we do the footnote number. \let\@@sf\empty \ifhmode\edef\@@sf{\spacefactor\the\spacefactor}\ptexslash\fi % % Remove inadvertent blank space before typesetting the footnote number. \unskip \thisfootno\@@sf \dofootnote }% % Don't bother with the trickery in plain.tex to not require the % footnote text as a parameter. Our footnotes don't need to be so general. % % Oh yes, they do; otherwise, @@ifset (and anything else that uses % \parseargline) fails inside footnotes because the tokens are fixed when % the footnote is read. --karl, 16nov96. % \gdef\dofootnote{% \insert\footins\bgroup % We want to typeset this text as a normal paragraph, even if the % footnote reference occurs in (for example) a display environment. % So reset some parameters. \hsize=\pagewidth \interlinepenalty\interfootnotelinepenalty \splittopskip\ht\strutbox % top baseline for broken footnotes \splitmaxdepth\dp\strutbox \floatingpenalty\@@MM \leftskip\z@@skip \rightskip\z@@skip \spaceskip\z@@skip \xspaceskip\z@@skip \parindent\defaultparindent % \smallfonts \rm % % Because we use hanging indentation in footnotes, a @@noindent appears % to exdent this text, so make it be a no-op. makeinfo does not use % hanging indentation so @@noindent can still be needed within footnote % text after an @@example or the like (not that this is good style). \let\noindent = \relax % % Hang the footnote text off the number. Use \everypar in case the % footnote extends for more than one paragraph. \everypar = {\hang}% \textindent{\thisfootno}% % % Don't crash into the line above the footnote text. Since this % expands into a box, it must come within the paragraph, lest it % provide a place where TeX can split the footnote. \footstrut \futurelet\next\fo@@t } }%end \catcode `\@@=11 % In case a @@footnote appears in a vbox, save the footnote text and create % the real \insert just after the vbox finished. Otherwise, the insertion % would be lost. % Similarily, if a @@footnote appears inside an alignment, save the footnote % text to a box and make the \insert when a row of the table is finished. % And the same can be done for other insert classes. --kasal, 16nov03. % Replace the \insert primitive by a cheating macro. % Deeper inside, just make sure that the saved insertions are not spilled % out prematurely. % \def\startsavinginserts{% \ifx \insert\ptexinsert \let\insert\saveinsert \else \let\checkinserts\relax \fi } % This \insert replacement works for both \insert\footins{foo} and % \insert\footins\bgroup foo\egroup, but it doesn't work for \insert27{foo}. % \def\saveinsert#1{% \edef\next{\noexpand\savetobox \makeSAVEname#1}% \afterassignment\next % swallow the left brace \let\temp = } \def\makeSAVEname#1{\makecsname{SAVE\expandafter\gobble\string#1}} \def\savetobox#1{\global\setbox#1 = \vbox\bgroup \unvbox#1} \def\checksaveins#1{\ifvoid#1\else \placesaveins#1\fi} \def\placesaveins#1{% \ptexinsert \csname\expandafter\gobblesave\string#1\endcsname {\box#1}% } % eat @@SAVE -- beware, all of them have catcode \other: { \def\dospecials{\do S\do A\do V\do E} \uncatcodespecials % ;-) \gdef\gobblesave @@SAVE{} } % initialization: \def\newsaveins #1{% \edef\next{\noexpand\newsaveinsX \makeSAVEname#1}% \next } \def\newsaveinsX #1{% \csname newbox\endcsname #1% \expandafter\def\expandafter\checkinserts\expandafter{\checkinserts \checksaveins #1}% } % initialize: \let\checkinserts\empty \newsaveins\footins \newsaveins\margin % @@image. We use the macros from epsf.tex to support this. % If epsf.tex is not installed and @@image is used, we complain. % % Check for and read epsf.tex up front. If we read it only at @@image % time, we might be inside a group, and then its definitions would get % undone and the next image would fail. \openin 1 = epsf.tex \ifeof 1 \else % Do not bother showing banner with epsf.tex v2.7k (available in % doc/epsf.tex and on ctan). \def\epsfannounce{\toks0 = }% \input epsf.tex \fi \closein 1 % % We will only complain once about lack of epsf.tex. \newif\ifwarnednoepsf \newhelp\noepsfhelp{epsf.tex must be installed for images to work. It is also included in the Texinfo distribution, or you can get it from ftp://tug.org/tex/epsf.tex.} % \def\image#1{% \ifx\epsfbox\undefined \ifwarnednoepsf \else \errhelp = \noepsfhelp \errmessage{epsf.tex not found, images will be ignored}% \global\warnednoepsftrue \fi \else \imagexxx #1,,,,,\finish \fi } % % Arguments to @@image: % #1 is (mandatory) image filename; we tack on .eps extension. % #2 is (optional) width, #3 is (optional) height. % #4 is (ignored optional) html alt text. % #5 is (ignored optional) extension. % #6 is just the usual extra ignored arg for parsing this stuff. \newif\ifimagevmode \def\imagexxx#1,#2,#3,#4,#5,#6\finish{\begingroup \catcode`\^^M = 5 % in case we're inside an example \normalturnoffactive % allow _ et al. in names % If the image is by itself, center it. \ifvmode \imagevmodetrue \nobreak\bigskip % Usually we'll have text after the image which will insert % \parskip glue, so insert it here too to equalize the space % above and below. \nobreak\vskip\parskip \nobreak \line\bgroup\hss \fi % % Output the image. \ifpdf \dopdfimage{#1}{#2}{#3}% \else % \epsfbox itself resets \epsf?size at each figure. \setbox0 = \hbox{\ignorespaces #2}\ifdim\wd0 > 0pt \epsfxsize=#2\relax \fi \setbox0 = \hbox{\ignorespaces #3}\ifdim\wd0 > 0pt \epsfysize=#3\relax \fi \epsfbox{#1.eps}% \fi % \ifimagevmode \hss \egroup \bigbreak \fi % space after the image \endgroup} % @@float FLOATTYPE,LABEL,LOC ... @@end float for displayed figures, tables, % etc. We don't actually implement floating yet, we always include the % float "here". But it seemed the best name for the future. % \envparseargdef\float{\eatcommaspace\eatcommaspace\dofloat#1, , ,\finish} % There may be a space before second and/or third parameter; delete it. \def\eatcommaspace#1, {#1,} % #1 is the optional FLOATTYPE, the text label for this float, typically % "Figure", "Table", "Example", etc. Can't contain commas. If omitted, % this float will not be numbered and cannot be referred to. % % #2 is the optional xref label. Also must be present for the float to % be referable. % % #3 is the optional positioning argument; for now, it is ignored. It % will somehow specify the positions allowed to float to (here, top, bottom). % % We keep a separate counter for each FLOATTYPE, which we reset at each % chapter-level command. \let\resetallfloatnos=\empty % \def\dofloat#1,#2,#3,#4\finish{% \let\thiscaption=\empty \let\thisshortcaption=\empty % % don't lose footnotes inside @@float. % % BEWARE: when the floats start float, we have to issue warning whenever an % insert appears inside a float which could possibly float. --kasal, 26may04 % \startsavinginserts % % We can't be used inside a paragraph. \par % \vtop\bgroup \def\floattype{#1}% \def\floatlabel{#2}% \def\floatloc{#3}% we do nothing with this yet. % \ifx\floattype\empty \let\safefloattype=\empty \else {% % the floattype might have accents or other special characters, % but we need to use it in a control sequence name. \indexnofonts \turnoffactive \xdef\safefloattype{\floattype}% }% \fi % % If label is given but no type, we handle that as the empty type. \ifx\floatlabel\empty \else % We want each FLOATTYPE to be numbered separately (Figure 1, % Table 1, Figure 2, ...). (And if no label, no number.) % \expandafter\getfloatno\csname\safefloattype floatno\endcsname \global\advance\floatno by 1 % {% % This magic value for \thissection is output by \setref as the % XREFLABEL-title value. \xrefX uses it to distinguish float % labels (which have a completely different output format) from % node and anchor labels. And \xrdef uses it to construct the % lists of floats. % \edef\thissection{\floatmagic=\safefloattype}% \setref{\floatlabel}{Yfloat}% }% \fi % % start with \parskip glue, I guess. \vskip\parskip % % Don't suppress indentation if a float happens to start a section. \restorefirstparagraphindent } % we have these possibilities: % @@float Foo,lbl & @@caption{Cap}: Foo 1.1: Cap % @@float Foo,lbl & no caption: Foo 1.1 % @@float Foo & @@caption{Cap}: Foo: Cap % @@float Foo & no caption: Foo % @@float ,lbl & Caption{Cap}: 1.1: Cap % @@float ,lbl & no caption: 1.1 % @@float & @@caption{Cap}: Cap % @@float & no caption: % \def\Efloat{% \let\floatident = \empty % % In all cases, if we have a float type, it comes first. \ifx\floattype\empty \else \def\floatident{\floattype}\fi % % If we have an xref label, the number comes next. \ifx\floatlabel\empty \else \ifx\floattype\empty \else % if also had float type, need tie first. \appendtomacro\floatident{\tie}% \fi % the number. \appendtomacro\floatident{\chaplevelprefix\the\floatno}% \fi % % Start the printed caption with what we've constructed in % \floatident, but keep it separate; we need \floatident again. \let\captionline = \floatident % \ifx\thiscaption\empty \else \ifx\floatident\empty \else \appendtomacro\captionline{: }% had ident, so need a colon between \fi % % caption text. \appendtomacro\captionline{\scanexp\thiscaption}% \fi % % If we have anything to print, print it, with space before. % Eventually this needs to become an \insert. \ifx\captionline\empty \else \vskip.5\parskip \captionline % % Space below caption. \vskip\parskip \fi % % If have an xref label, write the list of floats info. Do this % after the caption, to avoid chance of it being a breakpoint. \ifx\floatlabel\empty \else % Write the text that goes in the lof to the aux file as % \floatlabel-lof. Besides \floatident, we include the short % caption if specified, else the full caption if specified, else nothing. {% \atdummies \turnoffactive \otherbackslash % since we read the caption text in the macro world, where ^^M % is turned into a normal character, we have to scan it back, so % we don't write the literal three characters "^^M" into the aux file. \scanexp{% \xdef\noexpand\gtemp{% \ifx\thisshortcaption\empty \thiscaption \else \thisshortcaption \fi }% }% \immediate\write\auxfile{@@xrdef{\floatlabel-lof}{\floatident \ifx\gtemp\empty \else : \gtemp \fi}}% }% \fi \egroup % end of \vtop % % place the captured inserts % % BEWARE: when the floats start float, we have to issue warning whenever an % insert appears inside a float which could possibly float. --kasal, 26may04 % \checkinserts } % Append the tokens #2 to the definition of macro #1, not expanding either. % \def\appendtomacro#1#2{% \expandafter\def\expandafter#1\expandafter{#1#2}% } % @@caption, @@shortcaption % \def\caption{\docaption\thiscaption} \def\shortcaption{\docaption\thisshortcaption} \def\docaption{\checkenv\float \bgroup\scanargctxt\defcaption} \def\defcaption#1#2{\egroup \def#1{#2}} % The parameter is the control sequence identifying the counter we are % going to use. Create it if it doesn't exist and assign it to \floatno. \def\getfloatno#1{% \ifx#1\relax % Haven't seen this figure type before. \csname newcount\endcsname #1% % % Remember to reset this floatno at the next chap. \expandafter\gdef\expandafter\resetallfloatnos \expandafter{\resetallfloatnos #1=0 }% \fi \let\floatno#1% } % \setref calls this to get the XREFLABEL-snt value. We want an @@xref % to the FLOATLABEL to expand to "Figure 3.1". We call \setref when we % first read the @@float command. % \def\Yfloat{\floattype@@tie \chaplevelprefix\the\floatno}% % Magic string used for the XREFLABEL-title value, so \xrefX can % distinguish floats from other xref types. \def\floatmagic{!!float!!} % #1 is the control sequence we are passed; we expand into a conditional % which is true if #1 represents a float ref. That is, the magic % \thissection value which we \setref above. % \def\iffloat#1{\expandafter\doiffloat#1==\finish} % % #1 is (maybe) the \floatmagic string. If so, #2 will be the % (safe) float type for this float. We set \iffloattype to #2. % \def\doiffloat#1=#2=#3\finish{% \def\temp{#1}% \def\iffloattype{#2}% \ifx\temp\floatmagic } % @@listoffloats FLOATTYPE - print a list of floats like a table of contents. % \parseargdef\listoffloats{% \def\floattype{#1}% floattype {% % the floattype might have accents or other special characters, % but we need to use it in a control sequence name. \indexnofonts \turnoffactive \xdef\safefloattype{\floattype}% }% % % \xrdef saves the floats as a \do-list in \floatlistSAFEFLOATTYPE. \expandafter\ifx\csname floatlist\safefloattype\endcsname \relax \ifhavexrefs % if the user said @@listoffloats foo but never @@float foo. \message{\linenumber No `\safefloattype' floats to list.}% \fi \else \begingroup \leftskip=\tocindent % indent these entries like a toc \let\do=\listoffloatsdo \csname floatlist\safefloattype\endcsname \endgroup \fi } % This is called on each entry in a list of floats. We're passed the % xref label, in the form LABEL-title, which is how we save it in the % aux file. We strip off the -title and look up \XRLABEL-lof, which % has the text we're supposed to typeset here. % % Figures without xref labels will not be included in the list (since % they won't appear in the aux file). % \def\listoffloatsdo#1{\listoffloatsdoentry#1\finish} \def\listoffloatsdoentry#1-title\finish{{% % Can't fully expand XR#1-lof because it can contain anything. Just % pass the control sequence. On the other hand, XR#1-pg is just the % page number, and we want to fully expand that so we can get a link % in pdf output. \toksA = \expandafter{\csname XR#1-lof\endcsname}% % % use the same \entry macro we use to generate the TOC and index. \edef\writeentry{\noexpand\entry{\the\toksA}{\csname XR#1-pg\endcsname}}% \writeentry }} \message{localization,} % and i18n. % @@documentlanguage is usually given very early, just after % @@setfilename. If done too late, it may not override everything % properly. Single argument is the language abbreviation. % It would be nice if we could set up a hyphenation file here. % \parseargdef\documentlanguage{% \tex % read txi-??.tex file in plain TeX. % Read the file if it exists. \openin 1 txi-#1.tex \ifeof 1 \errhelp = \nolanghelp \errmessage{Cannot read language file txi-#1.tex}% \else \input txi-#1.tex \fi \closein 1 \endgroup } \newhelp\nolanghelp{The given language definition file cannot be found or is empty. Maybe you need to install it? In the current directory should work if nowhere else does.} % @@documentencoding should change something in TeX eventually, most % likely, but for now just recognize it. \let\documentencoding = \comment % Page size parameters. % \newdimen\defaultparindent \defaultparindent = 15pt \chapheadingskip = 15pt plus 4pt minus 2pt \secheadingskip = 12pt plus 3pt minus 2pt \subsecheadingskip = 9pt plus 2pt minus 2pt % Prevent underfull vbox error messages. \vbadness = 10000 % Don't be so finicky about underfull hboxes, either. \hbadness = 2000 % Following George Bush, just get rid of widows and orphans. \widowpenalty=10000 \clubpenalty=10000 % Use TeX 3.0's \emergencystretch to help line breaking, but if we're % using an old version of TeX, don't do anything. We want the amount of % stretch added to depend on the line length, hence the dependence on % \hsize. We call this whenever the paper size is set. % \def\setemergencystretch{% \ifx\emergencystretch\thisisundefined % Allow us to assign to \emergencystretch anyway. \def\emergencystretch{\dimen0}% \else \emergencystretch = .15\hsize \fi } % Parameters in order: 1) textheight; 2) textwidth; 3) voffset; % 4) hoffset; 5) binding offset; 6) topskip; 7) physical page height; 8) % physical page width. % % We also call \setleading{\textleading}, so the caller should define % \textleading. The caller should also set \parskip. % \def\internalpagesizes#1#2#3#4#5#6#7#8{% \voffset = #3\relax \topskip = #6\relax \splittopskip = \topskip % \vsize = #1\relax \advance\vsize by \topskip \outervsize = \vsize \advance\outervsize by 2\topandbottommargin \pageheight = \vsize % \hsize = #2\relax \outerhsize = \hsize \advance\outerhsize by 0.5in \pagewidth = \hsize % \normaloffset = #4\relax \bindingoffset = #5\relax % \ifpdf \pdfpageheight #7\relax \pdfpagewidth #8\relax \fi % \setleading{\textleading} % \parindent = \defaultparindent \setemergencystretch } % @@letterpaper (the default). \def\letterpaper{{\globaldefs = 1 \parskip = 3pt plus 2pt minus 1pt \textleading = 13.2pt % % If page is nothing but text, make it come out even. \internalpagesizes{46\baselineskip}{6in}% {\voffset}{.25in}% {\bindingoffset}{36pt}% {11in}{8.5in}% }} % Use @@smallbook to reset parameters for 7x9.5 (or so) format. \def\smallbook{{\globaldefs = 1 \parskip = 2pt plus 1pt \textleading = 12pt % \internalpagesizes{7.5in}{5in}% {\voffset}{.25in}% {\bindingoffset}{16pt}% {9.25in}{7in}% % \lispnarrowing = 0.3in \tolerance = 700 \hfuzz = 1pt \contentsrightmargin = 0pt \defbodyindent = .5cm }} % Use @@afourpaper to print on European A4 paper. \def\afourpaper{{\globaldefs = 1 \parskip = 3pt plus 2pt minus 1pt \textleading = 13.2pt % % Double-side printing via postscript on Laserjet 4050 % prints double-sided nicely when \bindingoffset=10mm and \hoffset=-6mm. % To change the settings for a different printer or situation, adjust % \normaloffset until the front-side and back-side texts align. Then % do the same for \bindingoffset. You can set these for testing in % your texinfo source file like this: % @@tex % \global\normaloffset = -6mm % \global\bindingoffset = 10mm % @@end tex \internalpagesizes{51\baselineskip}{160mm} {\voffset}{\hoffset}% {\bindingoffset}{44pt}% {297mm}{210mm}% % \tolerance = 700 \hfuzz = 1pt \contentsrightmargin = 0pt \defbodyindent = 5mm }} % Use @@afivepaper to print on European A5 paper. % From romildo@@urano.iceb.ufop.br, 2 July 2000. % He also recommends making @@example and @@lisp be small. \def\afivepaper{{\globaldefs = 1 \parskip = 2pt plus 1pt minus 0.1pt \textleading = 12.5pt % \internalpagesizes{160mm}{120mm}% {\voffset}{\hoffset}% {\bindingoffset}{8pt}% {210mm}{148mm}% % \lispnarrowing = 0.2in \tolerance = 800 \hfuzz = 1.2pt \contentsrightmargin = 0pt \defbodyindent = 2mm \tableindent = 12mm }} % A specific text layout, 24x15cm overall, intended for A4 paper. \def\afourlatex{{\globaldefs = 1 \afourpaper \internalpagesizes{237mm}{150mm}% {\voffset}{4.6mm}% {\bindingoffset}{7mm}% {297mm}{210mm}% % % Must explicitly reset to 0 because we call \afourpaper. \globaldefs = 0 }} % Use @@afourwide to print on A4 paper in landscape format. \def\afourwide{{\globaldefs = 1 \afourpaper \internalpagesizes{241mm}{165mm}% {\voffset}{-2.95mm}% {\bindingoffset}{7mm}% {297mm}{210mm}% \globaldefs = 0 }} % @@pagesizes TEXTHEIGHT[,TEXTWIDTH] % Perhaps we should allow setting the margins, \topskip, \parskip, % and/or leading, also. Or perhaps we should compute them somehow. % \parseargdef\pagesizes{\pagesizesyyy #1,,\finish} \def\pagesizesyyy#1,#2,#3\finish{{% \setbox0 = \hbox{\ignorespaces #2}\ifdim\wd0 > 0pt \hsize=#2\relax \fi \globaldefs = 1 % \parskip = 3pt plus 2pt minus 1pt \setleading{\textleading}% % \dimen0 = #1 \advance\dimen0 by \voffset % \dimen2 = \hsize \advance\dimen2 by \normaloffset % \internalpagesizes{#1}{\hsize}% {\voffset}{\normaloffset}% {\bindingoffset}{44pt}% {\dimen0}{\dimen2}% }} % Set default to letter. % \letterpaper \message{and turning on texinfo input format.} % Define macros to output various characters with catcode for normal text. \catcode`\"=\other \catcode`\~=\other \catcode`\^=\other \catcode`\_=\other \catcode`\|=\other \catcode`\<=\other \catcode`\>=\other \catcode`\+=\other \catcode`\$=\other \def\normaldoublequote{"} \def\normaltilde{~} \def\normalcaret{^} \def\normalunderscore{_} \def\normalverticalbar{|} \def\normalless{<} \def\normalgreater{>} \def\normalplus{+} \def\normaldollar{$}%$ font-lock fix % This macro is used to make a character print one way in \tt % (where it can probably be output as-is), and another way in other fonts, % where something hairier probably needs to be done. % % #1 is what to print if we are indeed using \tt; #2 is what to print % otherwise. Since all the Computer Modern typewriter fonts have zero % interword stretch (and shrink), and it is reasonable to expect all % typewriter fonts to have this, we can check that font parameter. % \def\ifusingtt#1#2{\ifdim \fontdimen3\font=0pt #1\else #2\fi} % Same as above, but check for italic font. Actually this also catches % non-italic slanted fonts since it is impossible to distinguish them from % italic fonts. But since this is only used by $ and it uses \sl anyway % this is not a problem. \def\ifusingit#1#2{\ifdim \fontdimen1\font>0pt #1\else #2\fi} % Turn off all special characters except @@ % (and those which the user can use as if they were ordinary). % Most of these we simply print from the \tt font, but for some, we can % use math or other variants that look better in normal text. \catcode`\"=\active \def\activedoublequote{{\tt\char34}} \let"=\activedoublequote \catcode`\~=\active \def~{{\tt\char126}} \chardef\hat=`\^ \catcode`\^=\active \def^{{\tt \hat}} \catcode`\_=\active \def_{\ifusingtt\normalunderscore\_} % Subroutine for the previous macro. \def\_{\leavevmode \kern.07em \vbox{\hrule width.3em height.1ex}\kern .07em } \catcode`\|=\active \def|{{\tt\char124}} \chardef \less=`\< \catcode`\<=\active \def<{{\tt \less}} \chardef \gtr=`\> \catcode`\>=\active \def>{{\tt \gtr}} \catcode`\+=\active \def+{{\tt \char 43}} \catcode`\$=\active \def${\ifusingit{{\sl\$}}\normaldollar}%$ font-lock fix % If a .fmt file is being used, characters that might appear in a file % name cannot be active until we have parsed the command line. % So turn them off again, and have \everyjob (or @@setfilename) turn them on. % \otherifyactive is called near the end of this file. \def\otherifyactive{\catcode`+=\other \catcode`\_=\other} \catcode`\@@=0 % \backslashcurfont outputs one backslash character in current font, % as in \char`\\. \global\chardef\backslashcurfont=`\\ \global\let\rawbackslashxx=\backslashcurfont % let existing .??s files work % \rawbackslash defines an active \ to do \backslashcurfont. % \otherbackslash defines an active \ to be a literal `\' character with % catcode other. {\catcode`\\=\active @@gdef@@rawbackslash{@@let\=@@backslashcurfont} @@gdef@@otherbackslash{@@let\=@@realbackslash} } % \realbackslash is an actual character `\' with catcode other. {\catcode`\\=\other @@gdef@@realbackslash{\}} % \normalbackslash outputs one backslash in fixed width font. \def\normalbackslash{{\tt\backslashcurfont}} \catcode`\\=\active % Used sometimes to turn off (effectively) the active characters % even after parsing them. @@def@@turnoffactive{% @@let"=@@normaldoublequote @@let\=@@realbackslash @@let~=@@normaltilde @@let^=@@normalcaret @@let_=@@normalunderscore @@let|=@@normalverticalbar @@let<=@@normalless @@let>=@@normalgreater @@let+=@@normalplus @@let$=@@normaldollar %$ font-lock fix @@unsepspaces } % Same as @@turnoffactive except outputs \ as {\tt\char`\\} instead of % the literal character `\'. (Thus, \ is not expandable when this is in % effect.) % @@def@@normalturnoffactive{@@turnoffactive @@let\=@@normalbackslash} % Make _ and + \other characters, temporarily. % This is canceled by @@fixbackslash. @@otherifyactive % If a .fmt file is being used, we don't want the `\input texinfo' to show up. % That is what \eatinput is for; after that, the `\' should revert to printing % a backslash. % @@gdef@@eatinput input texinfo{@@fixbackslash} @@global@@let\ = @@eatinput % On the other hand, perhaps the file did not have a `\input texinfo'. Then % the first `\{ in the file would cause an error. This macro tries to fix % that, assuming it is called before the first `\' could plausibly occur. % Also back turn on active characters that might appear in the input % file name, in case not using a pre-dumped format. % @@gdef@@fixbackslash{% @@ifx\@@eatinput @@let\ = @@normalbackslash @@fi @@catcode`+=@@active @@catcode`@@_=@@active } % Say @@foo, not \foo, in error messages. @@escapechar = `@@@@ % These look ok in all fonts, so just make them not special. @@catcode`@@& = @@other @@catcode`@@# = @@other @@catcode`@@% = @@other @@c Local variables: @@c eval: (add-hook 'write-file-hooks 'time-stamp) @@c page-delimiter: "^\\\\message" @@c time-stamp-start: "def\\\\texinfoversion{" @@c time-stamp-format: "%:y-%02m-%02d.%02H" @@c time-stamp-end: "}" @@c End: @@c vim:sw=2: @@ignore arch-tag: e1b36e32-c96e-4135-a41a-0b2efa2ea115 @@end ignore @ gsl-1.0.8/doc/RCS/gsl.info,v0000644000175000017500000032636611201030376013224 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @# @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @This is gsl.info, produced by makeinfo version 4.11 from gsl.texi.  File: gsl.info, Node: Top, Up: (dir) Octave gsl ********** gsl_sf -*- texinfo -*- -- Loadable Function: gsl_sf () Octave bindings to the GNU Scientific Library. All GSL functions can be called with by the GSL names within octave. clausen -*- texinfo -*- -- Loadable Function: Y = clausen (X) -- Loadable Function: [Y, ERR] = clausen (...) The Clausen function is defined by the following integral, Cl_2(x) = - \\int_0^x dt \\log(2 \\sin(t/2)) It is related to the dilogarithm by Cl_2(\\theta) = \\Im Li_2(\\exp(i \\theta)). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. dawson -*- texinfo -*- -- Loadable Function: Y = dawson (X) -- Loadable Function: [Y, ERR] = dawson (...) The Dawson integral is defined by \\exp(-x^2) \\int_0^x dt \\exp(t^2). A table of Dawson integral can be found in Abramowitz & Stegun, Table 7.5. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. debye_1 -*- texinfo -*- -- Loadable Function: Y = debye_1 (X) -- Loadable Function: [Y, ERR] = debye_1 (...) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. debye_2 -*- texinfo -*- -- Loadable Function: Y = debye_2 (X) -- Loadable Function: [Y, ERR] = debye_2 (...) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. debye_3 -*- texinfo -*- -- Loadable Function: Y = debye_3 (X) -- Loadable Function: [Y, ERR] = debye_3 (...) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. debye_4 -*- texinfo -*- -- Loadable Function: Y = debye_4 (X) -- Loadable Function: [Y, ERR] = debye_4 (...) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. erf_gsl -*- texinfo -*- -- Loadable Function: Y = erf_gsl (X) -- Loadable Function: [Y, ERR] = erf_gsl (...) These routines compute the error function erf(x) = (2/\\sqrt(\\pi)) \\int_0^x dt \\exp(-t^2). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. erfc_gsl -*- texinfo -*- -- Loadable Function: Y = erfc_gsl (X) -- Loadable Function: [Y, ERR] = erfc_gsl (...) These routines compute the complementary error function erfc(x) = 1 - erf(x) = (2/\\sqrt(\\pi)) \\int_x^\\infty \\exp(-t^2). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. log_erfc -*- texinfo -*- -- Loadable Function: Y = log_erfc (X) -- Loadable Function: [Y, ERR] = log_erfc (...) These routines compute the logarithm of the complementary error function \\log(\\erfc(x)). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. erf_Z -*- texinfo -*- -- Loadable Function: Y = erf_Z (X) -- Loadable Function: [Y, ERR] = erf_Z (...) These routines compute the Gaussian probability function Z(x) = (1/(2\\pi)) \\exp(-x^2/2). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. erf_Q -*- texinfo -*- -- Loadable Function: Y = erf_Q (X) -- Loadable Function: [Y, ERR] = erf_Q (...) These routines compute the upper tail of the Gaussian probability function Q(x) = (1/(2\\pi)) \\int_x^\\infty dt \\exp(-t^2/2). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. hazard -*- texinfo -*- -- Loadable Function: Y = hazard (X) -- Loadable Function: [Y, ERR] = hazard (...) The hazard function for the normal distrbution, also known as the inverse Mill\\'s ratio, is defined as h(x) = Z(x)/Q(x) = \\sqrt{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2)}. It decreases rapidly as x approaches -\\infty and asymptotes to h(x) \\sim x as x approaches +\\infty. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. expm1 -*- texinfo -*- -- Loadable Function: Y = expm1 (X) -- Loadable Function: [Y, ERR] = expm1 (...) These routines compute the quantity \\exp(x)-1 using an algorithm that is accurate for small x. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. exprel -*- texinfo -*- -- Loadable Function: Y = exprel (X) -- Loadable Function: [Y, ERR] = exprel (...) These routines compute the quantity (\\exp(x)-1)/x using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion (\\exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\dots. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. exprel_2 -*- texinfo -*- -- Loadable Function: Y = exprel_2 (X) -- Loadable Function: [Y, ERR] = exprel_2 (...) These routines compute the quantity 2(\\exp(x)-1-x)/x^2 using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion 2(\\exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\dots. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. expint_E1 -*- texinfo -*- -- Loadable Function: Y = expint_E1 (X) -- Loadable Function: [Y, ERR] = expint_E1 (...) These routines compute the exponential integral E_1(x), E_1(x) := Re \\int_1^\\infty dt \\exp(-xt)/t. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. expint_E2 -*- texinfo -*- -- Loadable Function: Y = expint_E2 (X) -- Loadable Function: [Y, ERR] = expint_E2 (...) These routines compute the second-order exponential integral E_2(x), E_2(x) := \\Re \\int_1^\\infty dt \\exp(-xt)/t^2. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. expint_Ei -*- texinfo -*- -- Loadable Function: Y = expint_Ei (X) -- Loadable Function: [Y, ERR] = expint_Ei (...) These routines compute the exponential integral E_i(x), Ei(x) := - PV(\\int_{-x}^\\infty dt \\exp(-t)/t) where PV denotes the principal value of the integral. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. Shi -*- texinfo -*- -- Loadable Function: Y = Shi (X) -- Loadable Function: [Y, ERR] = Shi (...) These routines compute the integral Shi(x) = \\int_0^x dt \\sinh(t)/t. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. Chi -*- texinfo -*- -- Loadable Function: Y = Chi (X) -- Loadable Function: [Y, ERR] = Chi (...) These routines compute the integral Chi(x) := Re[ \\gamma_E + \\log(x) + \\int_0^x dt (\\cosh[t]-1)/t] , where \\gamma_E is the Euler constant. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. expint_3 -*- texinfo -*- -- Loadable Function: Y = expint_3 (X) -- Loadable Function: [Y, ERR] = expint_3 (...) These routines compute the exponential integral Ei_3(x) = \\int_0^x dt \\exp(-t^3) for x >= 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. Si -*- texinfo -*- -- Loadable Function: Y = Si (X) -- Loadable Function: [Y, ERR] = Si (...) These routines compute the Sine integral Si(x) = \\int_0^x dt \\sin(t)/t. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. Ci -*- texinfo -*- -- Loadable Function: Y = Ci (X) -- Loadable Function: [Y, ERR] = Ci (...) These routines compute the Cosine integral Ci(x) = -\\int_x^\\infty dt \\cos(t)/t for x > 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. atanint -*- texinfo -*- -- Loadable Function: Y = atanint (X) -- Loadable Function: [Y, ERR] = atanint (...) These routines compute the Arctangent integral AtanInt(x) = \\int_0^x dt \\arctan(t)/t. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. fermi_dirac_mhalf -*- texinfo -*- -- Loadable Function: Y = fermi_dirac_mhalf (X) -- Loadable Function: [Y, ERR] = fermi_dirac_mhalf (...) These routines compute the complete Fermi-Dirac integral F_{-1/2}(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. fermi_dirac_half -*- texinfo -*- -- Loadable Function: Y = fermi_dirac_half (X) -- Loadable Function: [Y, ERR] = fermi_dirac_half (...) These routines compute the complete Fermi-Dirac integral F_{1/2}(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. fermi_dirac_3half -*- texinfo -*- -- Loadable Function: Y = fermi_dirac_3half (X) -- Loadable Function: [Y, ERR] = fermi_dirac_3half (...) These routines compute the complete Fermi-Dirac integral F_{3/2}(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. gamma_gsl -*- texinfo -*- -- Loadable Function: Y = gamma_gsl (X) -- Loadable Function: [Y, ERR] = gamma_gsl (...) These routines compute the Gamma function \\Gamma(x), subject to x not being a negative integer. The function is computed using the real Lanczos method. The maximum value of x such that \\Gamma(x) is not considered an overflow is given by the macro GSL_SF_GAMMA_XMAX and is 171.0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. lngamma_gsl -*- texinfo -*- -- Loadable Function: Y = lngamma_gsl (X) -- Loadable Function: [Y, ERR] = lngamma_gsl (...) These routines compute the logarithm of the Gamma function, \\log(\\Gamma(x)), subject to x not a being negative integer. For x<0 the real part of \\log(\\Gamma(x)) is returned, which is equivalent to \\log(|\\Gamma(x)|). The function is computed using the real Lanczos method. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. gammastar -*- texinfo -*- -- Loadable Function: Y = gammastar (X) -- Loadable Function: [Y, ERR] = gammastar (...) These routines compute the regulated Gamma Function \\Gamma^*(x) for x > 0. The regulated gamma function is given by, \\Gamma^*(x) = \\Gamma(x)/(\\sqrt{2\\pi} x^{(x-1/2)} \\exp(-x)) = (1 + (1/12x) + ...) for x \\to \\infty and is a useful suggestion of Temme. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. gammainv_gsl -*- texinfo -*- -- Loadable Function: Y = gammainv_gsl (X) -- Loadable Function: [Y, ERR] = gammainv_gsl (...) These routines compute the reciprocal of the gamma function, 1/\\Gamma(x) using the real Lanczos method. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. lambert_W0 -*- texinfo -*- -- Loadable Function: Y = lambert_W0 (X) -- Loadable Function: [Y, ERR] = lambert_W0 (...) These compute the principal branch of the Lambert W function, W_0(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_{-1}(x) to be the other real branch, where W < -1 for x < 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. lambert_Wm1 -*- texinfo -*- -- Loadable Function: Y = lambert_Wm1 (X) -- Loadable Function: [Y, ERR] = lambert_Wm1 (...) These compute the secondary real-valued branch of the Lambert W function, W_{-1}(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_{-1}(x) to be the other real branch, where W < -1 for x < 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. log_1plusx -*- texinfo -*- -- Loadable Function: Y = log_1plusx (X) -- Loadable Function: [Y, ERR] = log_1plusx (...) These routines compute \\log(1 + x) for x > -1 using an algorithm that is accurate for small x. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. log_1plusx_mx -*- texinfo -*- -- Loadable Function: Y = log_1plusx_mx (X) -- Loadable Function: [Y, ERR] = log_1plusx_mx (...) These routines compute \\log(1 + x) - x for x > -1 using an algorithm that is accurate for small x. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. psi -*- texinfo -*- -- Loadable Function: Y = psi (X) -- Loadable Function: [Y, ERR] = psi (...) These routines compute the digamma function \\psi(x) for general x, x \ e 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. psi_1piy -*- texinfo -*- -- Loadable Function: Y = psi_1piy (X) -- Loadable Function: [Y, ERR] = psi_1piy (...) These routines compute the real part of the digamma function on the line 1+i y, Re[\\psi(1 + i y)]. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. synchrotron_1 -*- texinfo -*- -- Loadable Function: Y = synchrotron_1 (X) -- Loadable Function: [Y, ERR] = synchrotron_1 (...) These routines compute the first synchrotron function x \\int_x^\\infty dt K_{5/3}(t) for x >= 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. synchrotron_2 -*- texinfo -*- -- Loadable Function: Y = synchrotron_2 (X) -- Loadable Function: [Y, ERR] = synchrotron_2 (...) These routines compute the second synchrotron function x K_{2/3}(x) for x >= 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. transport_2 -*- texinfo -*- -- Loadable Function: Y = transport_2 (X) -- Loadable Function: [Y, ERR] = transport_2 (...) These routines compute the transport function J(2,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. transport_3 -*- texinfo -*- -- Loadable Function: Y = transport_3 (X) -- Loadable Function: [Y, ERR] = transport_3 (...) These routines compute the transport function J(3,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. transport_4 -*- texinfo -*- -- Loadable Function: Y = transport_4 (X) -- Loadable Function: [Y, ERR] = transport_4 (...) These routines compute the transport function J(4,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. transport_5 -*- texinfo -*- -- Loadable Function: Y = transport_5 (X) -- Loadable Function: [Y, ERR] = transport_5 (...) These routines compute the transport function J(5,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. sinc_gsl -*- texinfo -*- -- Loadable Function: Y = sinc_gsl (X) -- Loadable Function: [Y, ERR] = sinc_gsl (...) These routines compute \\sinc(x) = \\sin(\\pi x) / (\\pi x) for any value of x. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. lnsinh -*- texinfo -*- -- Loadable Function: Y = lnsinh (X) -- Loadable Function: [Y, ERR] = lnsinh (...) These routines compute \\log(\\sinh(x)) for x > 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. lncosh -*- texinfo -*- -- Loadable Function: Y = lncosh (X) -- Loadable Function: [Y, ERR] = lncosh (...) These routines compute \\log(\\cosh(x)) for any x. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. zeta -*- texinfo -*- -- Loadable Function: Y = zeta (X) -- Loadable Function: [Y, ERR] = zeta (...) These routines compute the Riemann zeta function \\zeta(s) for arbitrary s, s \ e 1. The Riemann zeta function is defined by the infinite sum \\zeta(s) = \\sum_{k=1}^\\infty k^{-s}. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. eta -*- texinfo -*- -- Loadable Function: Y = eta (X) -- Loadable Function: [Y, ERR] = eta (...) These routines compute the eta function \\eta(s) for arbitrary s. The eta function is defined by \\eta(s) = (1-2^{1-s}) \\zeta(s). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_Jn -*- texinfo -*- -- Loadable Function: Y = bessel_Jn (N, X) -- Loadable Function: [Y, ERR] = bessel_Jn (...) These routines compute the regular cylindrical Bessel function of order n, J_n(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_Yn -*- texinfo -*- -- Loadable Function: Y = bessel_Yn (N, X) -- Loadable Function: [Y, ERR] = bessel_Yn (...) These routines compute the irregular cylindrical Bessel function of order n, Y_n(x), for x>0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_In -*- texinfo -*- -- Loadable Function: Y = bessel_In (N, X) -- Loadable Function: [Y, ERR] = bessel_In (...) These routines compute the regular modified cylindrical Bessel function of order n, I_n(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_In_scaled -*- texinfo -*- -- Loadable Function: Y = bessel_In_scaled (N, X) -- Loadable Function: [Y, ERR] = bessel_In_scaled (...) These routines compute the scaled regular modified cylindrical Bessel function of order n, \\exp(-|x|) I_n(x) ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_Kn -*- texinfo -*- -- Loadable Function: Y = bessel_Kn (N, X) -- Loadable Function: [Y, ERR] = bessel_Kn (...) These routines compute the irregular modified cylindrical Bessel function of order n, K_n(x), for x > 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_Kn_scaled -*- texinfo -*- -- Loadable Function: Y = bessel_Kn_scaled (N, X) -- Loadable Function: [Y, ERR] = bessel_Kn_scaled (...) ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_jl -*- texinfo -*- -- Loadable Function: Y = bessel_jl (N, X) -- Loadable Function: [Y, ERR] = bessel_jl (...) These routines compute the regular spherical Bessel function of order l, j_l(x), for l >= 0 and x >= 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_yl -*- texinfo -*- -- Loadable Function: Y = bessel_yl (N, X) -- Loadable Function: [Y, ERR] = bessel_yl (...) These routines compute the irregular spherical Bessel function of order l, y_l(x), for l >= 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_il_scaled -*- texinfo -*- -- Loadable Function: Y = bessel_il_scaled (N, X) -- Loadable Function: [Y, ERR] = bessel_il_scaled (...) These routines compute the scaled regular modified spherical Bessel function of order l, \\exp(-|x|) i_l(x) ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_kl_scaled -*- texinfo -*- -- Loadable Function: Y = bessel_kl_scaled (N, X) -- Loadable Function: [Y, ERR] = bessel_kl_scaled (...) These routines compute the scaled irregular modified spherical Bessel function of order l, \\exp(x) k_l(x), for x>0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. exprel_n -*- texinfo -*- -- Loadable Function: Y = exprel_n (N, X) -- Loadable Function: [Y, ERR] = exprel_n (...) These routines compute the N-relative exponential, which is the n-th generalization of the functions gsl_sf_exprel and gsl_sf_exprel2. The N-relative exponential is given by, exprel_N(x) = N!/x^N (\\exp(x) - \\sum_{k=0}^{N-1} x^k/k!) = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ... = 1F1 (1,1+N,x) ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. fermi_dirac_int -*- texinfo -*- -- Loadable Function: Y = fermi_dirac_int (N, X) -- Loadable Function: [Y, ERR] = fermi_dirac_int (...) These routines compute the complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/\\Gamma(j+1)) \\int_0^\\infty dt (t^j /(\\exp(t-x)+1)). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. taylorcoeff -*- texinfo -*- -- Loadable Function: Y = taylorcoeff (N, X) -- Loadable Function: [Y, ERR] = taylorcoeff (...) These routines compute the Taylor coefficient x^n / n! for x >= 0, n >= 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. legendre_Pl -*- texinfo -*- -- Loadable Function: Y = legendre_Pl (N, X) -- Loadable Function: [Y, ERR] = legendre_Pl (...) These functions evaluate the Legendre polynomial P_l(x) for a specific value of l, x subject to l >= 0, |x| <= 1 ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. legendre_Ql -*- texinfo -*- -- Loadable Function: Y = legendre_Ql (N, X) -- Loadable Function: [Y, ERR] = legendre_Ql (...) These routines compute the Legendre function Q_l(x) for x > -1, x != 1 and l >= 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. psi_n -*- texinfo -*- -- Loadable Function: Y = psi_n (N, X) -- Loadable Function: [Y, ERR] = psi_n (...) These routines compute the polygamma function \\psi^{(m)}(x) for m >= 0, x > 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_Jnu -*- texinfo -*- -- Loadable Function: Z = bessel_Jnu (X, Y) -- Loadable Function: [Z, ERR] = bessel_Jnu (...) These routines compute the regular cylindrical Bessel function of fractional order nu, J_\ u(x). ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_Ynu -*- texinfo -*- -- Loadable Function: Z = bessel_Ynu (X, Y) -- Loadable Function: [Z, ERR] = bessel_Ynu (...) These routines compute the irregular cylindrical Bessel function of fractional order nu, Y_\ u(x). ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_Inu -*- texinfo -*- -- Loadable Function: Z = bessel_Inu (X, Y) -- Loadable Function: [Z, ERR] = bessel_Inu (...) These routines compute the regular modified Bessel function of fractional order nu, I_\ u(x) for x>0, \ u>0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_Inu_scaled -*- texinfo -*- -- Loadable Function: Z = bessel_Inu_scaled (X, Y) -- Loadable Function: [Z, ERR] = bessel_Inu_scaled (...) These routines compute the scaled regular modified Bessel function of fractional order nu, \\exp(-|x|)I_\ u(x) for x>0, \ u>0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_Knu -*- texinfo -*- -- Loadable Function: Z = bessel_Knu (X, Y) -- Loadable Function: [Z, ERR] = bessel_Knu (...) These routines compute the irregular modified Bessel function of fractional order nu, K_\ u(x) for x>0, \ u>0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_lnKnu -*- texinfo -*- -- Loadable Function: Z = bessel_lnKnu (X, Y) -- Loadable Function: [Z, ERR] = bessel_lnKnu (...) These routines compute the logarithm of the irregular modified Bessel function of fractional order nu, \\ln(K_\ u(x)) for x>0, \ u>0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_Knu_scaled -*- texinfo -*- -- Loadable Function: Z = bessel_Knu_scaled (X, Y) -- Loadable Function: [Z, ERR] = bessel_Knu_scaled (...) These routines compute the scaled irregular modified Bessel function of fractional order nu, \\exp(+|x|) K_\ u(x) for x>0, \ u>0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. exp_mult -*- texinfo -*- -- Loadable Function: Z = exp_mult (X, Y) -- Loadable Function: [Z, ERR] = exp_mult (...) These routines exponentiate x and multiply by the factor y to return the product y \\exp(x). ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. fermi_dirac_inc_0 -*- texinfo -*- -- Loadable Function: Z = fermi_dirac_inc_0 (X, Y) -- Loadable Function: [Z, ERR] = fermi_dirac_inc_0 (...) These routines compute the incomplete Fermi-Dirac integral with an index of zero, F_0(x,b) = \\ln(1 + e^{b-x}) - (b-x). ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. poch -*- texinfo -*- -- Loadable Function: Z = poch (X, Y) -- Loadable Function: [Z, ERR] = poch (...) These routines compute the Pochhammer symbol (a)_x := \\Gamma(a + x)/\\Gamma(a), subject to a and a+x not being negative integers. The Pochhammer symbol is also known as the Apell symbol. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. lnpoch -*- texinfo -*- -- Loadable Function: Z = lnpoch (X, Y) -- Loadable Function: [Z, ERR] = lnpoch (...) These routines compute the logarithm of the Pochhammer symbol, \\log((a)_x) = \\log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. pochrel -*- texinfo -*- -- Loadable Function: Z = pochrel (X, Y) -- Loadable Function: [Z, ERR] = pochrel (...) These routines compute the relative Pochhammer symbol ((a,x) - 1)/x where (a,x) = (a)_x := \\Gamma(a + x)/\\Gamma(a). ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. gamma_inc_Q -*- texinfo -*- -- Loadable Function: Z = gamma_inc_Q (X, Y) -- Loadable Function: [Z, ERR] = gamma_inc_Q (...) These routines compute the normalized incomplete Gamma Function Q(a,x) = 1/\\Gamma(a) \\int_x\\infty dt t^{a-1} \\exp(-t) for a > 0, x >= 0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. gamma_inc_P -*- texinfo -*- -- Loadable Function: Z = gamma_inc_P (X, Y) -- Loadable Function: [Z, ERR] = gamma_inc_P (...) These routines compute the complementary normalized incomplete Gamma Function P(a,x) = 1/\\Gamma(a) \\int_0^x dt t^{a-1} \\exp(-t) for a > 0, x >= 0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. gamma_inc -*- texinfo -*- -- Loadable Function: Z = gamma_inc (X, Y) -- Loadable Function: [Z, ERR] = gamma_inc (...) These functions compute the incomplete Gamma Function the normalization factor included in the previously defined functions: \\Gamma(a,x) = \\int_x\\infty dt t^{a-1} \\exp(-t) for a real and x >= 0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. beta_gsl -*- texinfo -*- -- Loadable Function: Z = beta_gsl (X, Y) -- Loadable Function: [Z, ERR] = beta_gsl (...) These routines compute the Beta Function, B(a,b) = \\Gamma(a)\\Gamma(b)/\\Gamma(a+b) for a > 0, b > 0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. lnbeta -*- texinfo -*- -- Loadable Function: Z = lnbeta (X, Y) -- Loadable Function: [Z, ERR] = lnbeta (...) These routines compute the logarithm of the Beta Function, \\log(B(a,b)) for a > 0, b > 0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. hyperg_0F1 -*- texinfo -*- -- Loadable Function: Z = hyperg_0F1 (X, Y) -- Loadable Function: [Z, ERR] = hyperg_0F1 (...) These routines compute the hypergeometric function 0F1(c,x). ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. conicalP_half -*- texinfo -*- -- Loadable Function: Z = conicalP_half (X, Y) -- Loadable Function: [Z, ERR] = conicalP_half (...) These routines compute the irregular Spherical Conical Function P^{1/2}_{-1/2 + i \\lambda}(x) for x > -1. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. conicalP_mhalf -*- texinfo -*- -- Loadable Function: Z = conicalP_mhalf (X, Y) -- Loadable Function: [Z, ERR] = conicalP_mhalf (...) These routines compute the regular Spherical Conical Function P^{-1/2}_{-1/2 + i \\lambda}(x) for x > -1. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. conicalP_0 -*- texinfo -*- -- Loadable Function: Z = conicalP_0 (X, Y) -- Loadable Function: [Z, ERR] = conicalP_0 (...) These routines compute the conical function P^0_{-1/2 + i \\lambda}(x) for x > -1. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. conicalP_1 -*- texinfo -*- -- Loadable Function: Z = conicalP_1 (X, Y) -- Loadable Function: [Z, ERR] = conicalP_1 (...) These routines compute the conical function P^1_{-1/2 + i \\lambda}(x) for x > -1. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. hzeta -*- texinfo -*- -- Loadable Function: Z = hzeta (X, Y) -- Loadable Function: [Z, ERR] = hzeta (...) These routines compute the Hurwitz zeta function \\zeta(s,q) for s > 1, q > 0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_Ai -*- texinfo -*- -- Loadable Function: Y = airy_Ai (X, MODE) -- Loadable Function: [Y, ERR] = airy_Ai (...) These routines compute the Airy function Ai(x) with an accuracy specified by mode. The second argument MODE must be an integer corresponding to 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately `2 * 10^-16'. 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately `10^-7'. 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately `5 * 10^-4'. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_Bi -*- texinfo -*- -- Loadable Function: Y = airy_Bi (X, MODE) -- Loadable Function: [Y, ERR] = airy_Bi (...) These routines compute the Airy function Bi(x) with an accuracy specified by mode. The second argument MODE must be an integer corresponding to 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately `2 * 10^-16'. 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately `10^-7'. 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately `5 * 10^-4'. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_Ai_scaled -*- texinfo -*- -- Loadable Function: Y = airy_Ai_scaled (X, MODE) -- Loadable Function: [Y, ERR] = airy_Ai_scaled (...) These routines compute a scaled version of the Airy function S_A(x) Ai(x). For x>0 the scaling factor S_A(x) is \\exp(+(2/3) x^(3/2)), and is 1 for x<0. The second argument MODE must be an integer corresponding to 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately `2 * 10^-16'. 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately `10^-7'. 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately `5 * 10^-4'. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_Bi_scaled -*- texinfo -*- -- Loadable Function: Y = airy_Bi_scaled (X, MODE) -- Loadable Function: [Y, ERR] = airy_Bi_scaled (...) These routines compute a scaled version of the Airy function S_B(x) Bi(x). For x>0 the scaling factor S_B(x) is exp(-(2/3) x^(3/2)), and is 1 for x<0. The second argument MODE must be an integer corresponding to 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately `2 * 10^-16'. 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately `10^-7'. 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately `5 * 10^-4'. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_Ai_deriv -*- texinfo -*- -- Loadable Function: Y = airy_Ai_deriv (X, MODE) -- Loadable Function: [Y, ERR] = airy_Ai_deriv (...) These routines compute the Airy function derivative Ai'(x) with an accuracy specified by mode. The second argument MODE must be an integer corresponding to 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately `2 * 10^-16'. 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately `10^-7'. 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately `5 * 10^-4'. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_Bi_deriv -*- texinfo -*- -- Loadable Function: Y = airy_Bi_deriv (X, MODE) -- Loadable Function: [Y, ERR] = airy_Bi_deriv (...) These routines compute the Airy function derivative Bi'(x) with an accuracy specified by mode. The second argument MODE must be an integer corresponding to 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately `2 * 10^-16'. 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately `10^-7'. 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately `5 * 10^-4'. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_Ai_deriv_scaled -*- texinfo -*- -- Loadable Function: Y = airy_Ai_deriv_scaled (X, MODE) -- Loadable Function: [Y, ERR] = airy_Ai_deriv_scaled (...) These routines compute the derivative of the scaled Airy function S_A(x) Ai(x). The second argument MODE must be an integer corresponding to 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately `2 * 10^-16'. 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately `10^-7'. 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately `5 * 10^-4'. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_Bi_deriv_scaled -*- texinfo -*- -- Loadable Function: Y = airy_Bi_deriv_scaled (X, MODE) -- Loadable Function: [Y, ERR] = airy_Bi_deriv_scaled (...) These routines compute the derivative of the scaled Airy function S_B(x) Bi(x). The second argument MODE must be an integer corresponding to 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately `2 * 10^-16'. 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately `10^-7'. 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately `5 * 10^-4'. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. ellint_Kcomp -*- texinfo -*- -- Loadable Function: Y = ellint_Kcomp (X, MODE) -- Loadable Function: [Y, ERR] = ellint_Kcomp (...) These routines compute the complete elliptic integral K(k) The notation used here is based on Carlson, `Numerische Mathematik' 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter m = k^2. The second argument MODE must be an integer corresponding to 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately `2 * 10^-16'. 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately `10^-7'. 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately `5 * 10^-4'. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. ellint_Ecomp -*- texinfo -*- -- Loadable Function: Y = ellint_Ecomp (X, MODE) -- Loadable Function: [Y, ERR] = ellint_Ecomp (...) These routines compute the complete elliptic integral E(k) to the accuracy specified by the mode variable mode. The notation used here is based on Carlson, `Numerische Mathematik' 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter m = k^2. The second argument MODE must be an integer corresponding to 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately `2 * 10^-16'. 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately `10^-7'. 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately `5 * 10^-4'. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_zero_Ai -*- texinfo -*- -- Loadable Function: Y = airy_zero_Ai (N) -- Loadable Function: [Y, ERR] = airy_zero_Ai (...) These routines compute the location of the s-th zero of the Airy function Ai(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_zero_Bi -*- texinfo -*- -- Loadable Function: Y = airy_zero_Bi (N) -- Loadable Function: [Y, ERR] = airy_zero_Bi (...) These routines compute the location of the s-th zero of the Airy function Bi(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_zero_Ai_deriv -*- texinfo -*- -- Loadable Function: Y = airy_zero_Ai_deriv (N) -- Loadable Function: [Y, ERR] = airy_zero_Ai_deriv (...) These routines compute the location of the s-th zero of the Airy function derivative Ai(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_zero_Bi_deriv -*- texinfo -*- -- Loadable Function: Y = airy_zero_Bi_deriv (N) -- Loadable Function: [Y, ERR] = airy_zero_Bi_deriv (...) These routines compute the location of the s-th zero of the Airy function derivative Bi(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_zero_J0 -*- texinfo -*- -- Loadable Function: Y = bessel_zero_J0 (N) -- Loadable Function: [Y, ERR] = bessel_zero_J0 (...) These routines compute the location of the s-th positive zero of the Bessel function J_0(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_zero_J1 -*- texinfo -*- -- Loadable Function: Y = bessel_zero_J1 (N) -- Loadable Function: [Y, ERR] = bessel_zero_J1 (...) These routines compute the location of the s-th positive zero of the Bessel function J_1(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. psi_1_int -*- texinfo -*- -- Loadable Function: Y = psi_1_int (N) -- Loadable Function: [Y, ERR] = psi_1_int (...) These routines compute the Trigamma function \\psi(n) for positive integer n. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. zeta_int -*- texinfo -*- -- Loadable Function: Y = zeta_int (N) -- Loadable Function: [Y, ERR] = zeta_int (...) These routines compute the Riemann zeta function \\zeta(n) for integer n, n \ e 1. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. eta_int -*- texinfo -*- -- Loadable Function: Y = eta_int (N) -- Loadable Function: [Y, ERR] = eta_int (...) These routines compute the eta function \\eta(n) for integer n. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. legendre_Plm -*- texinfo -*- -- Loadable Function: Y = legendre_Plm (N, M, X) -- Loadable Function: [Y, ERR] = legendre_Plm (...) These routines compute the associated Legendre polynomial P_l^m(x) for m >= 0, l >= m, |x| <= 1. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. legendre_sphPlm -*- texinfo -*- -- Loadable Function: Y = legendre_sphPlm (N, M, X) -- Loadable Function: [Y, ERR] = legendre_sphPlm (...) These routines compute the normalized associated Legendre polynomial $\\sqrt{(2l+1)/(4\\pi)} \\sqrt{(l-m)!/(l+m)!} P_l^m(x)$ suitable for use in spherical harmonics. The parameters must satisfy m >= 0, l >= m, |x| <= 1. Theses routines avoid the overflows that occur for the standard normalization of P_l^m(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. hyperg_U -*- texinfo -*- -- Loadable Function: OUT = hyperg_U (X0, X1, X2) -- Loadable Function: [OUT, ERR] = hyperg_U (...) Secondary Confluent Hypergoemetric U function A&E 13.1.3 All input are double as is the output. ERR contains an estimate of the absolute error in the value OUT.a. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. hyperg_1F1 -*- texinfo -*- -- Loadable Function: OUT = hyperg_1F1 (X0, X1, X2) -- Loadable Function: [OUT, ERR] = hyperg_1F1 (...) Primary Confluent Hypergoemetric U function A&E 13.1.3 All inputs are double as is the output. ERR contains an estimate of the absolute error in the value OUT.a. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. gsl_sf -*- texinfo -*- -- Loadable Function: gsl_sf () Octave bindings to the GNU Scientific Library. All GSL functions can be called with by the GSL names within octave. clausen -*- texinfo -*- -- Loadable Function: Y = clausen (X) -- Loadable Function: [Y, ERR] = clausen (...) The Clausen function is defined by the following integral, Cl_2(x) = - \\int_0^x dt \\log(2 \\sin(t/2)) It is related to the dilogarithm by Cl_2(\\theta) = \\Im Li_2(\\exp(i \\theta)). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. dawson -*- texinfo -*- -- Loadable Function: Y = dawson (X) -- Loadable Function: [Y, ERR] = dawson (...) The Dawson integral is defined by \\exp(-x^2) \\int_0^x dt \\exp(t^2). A table of Dawson integral can be found in Abramowitz & Stegun, Table 7.5. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. debye_1 -*- texinfo -*- -- Loadable Function: Y = debye_1 (X) -- Loadable Function: [Y, ERR] = debye_1 (...) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. debye_2 -*- texinfo -*- -- Loadable Function: Y = debye_2 (X) -- Loadable Function: [Y, ERR] = debye_2 (...) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. debye_3 -*- texinfo -*- -- Loadable Function: Y = debye_3 (X) -- Loadable Function: [Y, ERR] = debye_3 (...) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. debye_4 -*- texinfo -*- -- Loadable Function: Y = debye_4 (X) -- Loadable Function: [Y, ERR] = debye_4 (...) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. erf_gsl -*- texinfo -*- -- Loadable Function: Y = erf_gsl (X) -- Loadable Function: [Y, ERR] = erf_gsl (...) These routines compute the error function erf(x) = (2/\\sqrt(\\pi)) \\int_0^x dt \\exp(-t^2). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. erfc_gsl -*- texinfo -*- -- Loadable Function: Y = erfc_gsl (X) -- Loadable Function: [Y, ERR] = erfc_gsl (...) These routines compute the complementary error function erfc(x) = 1 - erf(x) = (2/\\sqrt(\\pi)) \\int_x^\\infty \\exp(-t^2). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. log_erfc -*- texinfo -*- -- Loadable Function: Y = log_erfc (X) -- Loadable Function: [Y, ERR] = log_erfc (...) These routines compute the logarithm of the complementary error function \\log(\\erfc(x)). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. erf_Z -*- texinfo -*- -- Loadable Function: Y = erf_Z (X) -- Loadable Function: [Y, ERR] = erf_Z (...) These routines compute the Gaussian probability function Z(x) = (1/(2\\pi)) \\exp(-x^2/2). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. erf_Q -*- texinfo -*- -- Loadable Function: Y = erf_Q (X) -- Loadable Function: [Y, ERR] = erf_Q (...) These routines compute the upper tail of the Gaussian probability function Q(x) = (1/(2\\pi)) \\int_x^\\infty dt \\exp(-t^2/2). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. hazard -*- texinfo -*- -- Loadable Function: Y = hazard (X) -- Loadable Function: [Y, ERR] = hazard (...) The hazard function for the normal distrbution, also known as the inverse Mill\\'s ratio, is defined as h(x) = Z(x)/Q(x) = \\sqrt{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2)}. It decreases rapidly as x approaches -\\infty and asymptotes to h(x) \\sim x as x approaches +\\infty. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. expm1 -*- texinfo -*- -- Loadable Function: Y = expm1 (X) -- Loadable Function: [Y, ERR] = expm1 (...) These routines compute the quantity \\exp(x)-1 using an algorithm that is accurate for small x. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. exprel -*- texinfo -*- -- Loadable Function: Y = exprel (X) -- Loadable Function: [Y, ERR] = exprel (...) These routines compute the quantity (\\exp(x)-1)/x using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion (\\exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\dots. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. exprel_2 -*- texinfo -*- -- Loadable Function: Y = exprel_2 (X) -- Loadable Function: [Y, ERR] = exprel_2 (...) These routines compute the quantity 2(\\exp(x)-1-x)/x^2 using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion 2(\\exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\dots. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. expint_E1 -*- texinfo -*- -- Loadable Function: Y = expint_E1 (X) -- Loadable Function: [Y, ERR] = expint_E1 (...) These routines compute the exponential integral E_1(x), E_1(x) := Re \\int_1^\\infty dt \\exp(-xt)/t. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. expint_E2 -*- texinfo -*- -- Loadable Function: Y = expint_E2 (X) -- Loadable Function: [Y, ERR] = expint_E2 (...) These routines compute the second-order exponential integral E_2(x), E_2(x) := \\Re \\int_1^\\infty dt \\exp(-xt)/t^2. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. expint_Ei -*- texinfo -*- -- Loadable Function: Y = expint_Ei (X) -- Loadable Function: [Y, ERR] = expint_Ei (...) These routines compute the exponential integral E_i(x), Ei(x) := - PV(\\int_{-x}^\\infty dt \\exp(-t)/t) where PV denotes the principal value of the integral. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. Shi -*- texinfo -*- -- Loadable Function: Y = Shi (X) -- Loadable Function: [Y, ERR] = Shi (...) These routines compute the integral Shi(x) = \\int_0^x dt \\sinh(t)/t. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. Chi -*- texinfo -*- -- Loadable Function: Y = Chi (X) -- Loadable Function: [Y, ERR] = Chi (...) These routines compute the integral Chi(x) := Re[ \\gamma_E + \\log(x) + \\int_0^x dt (\\cosh[t]-1)/t] , where \\gamma_E is the Euler constant. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. expint_3 -*- texinfo -*- -- Loadable Function: Y = expint_3 (X) -- Loadable Function: [Y, ERR] = expint_3 (...) These routines compute the exponential integral Ei_3(x) = \\int_0^x dt \\exp(-t^3) for x >= 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. Si -*- texinfo -*- -- Loadable Function: Y = Si (X) -- Loadable Function: [Y, ERR] = Si (...) These routines compute the Sine integral Si(x) = \\int_0^x dt \\sin(t)/t. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. Ci -*- texinfo -*- -- Loadable Function: Y = Ci (X) -- Loadable Function: [Y, ERR] = Ci (...) These routines compute the Cosine integral Ci(x) = -\\int_x^\\infty dt \\cos(t)/t for x > 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. atanint -*- texinfo -*- -- Loadable Function: Y = atanint (X) -- Loadable Function: [Y, ERR] = atanint (...) These routines compute the Arctangent integral AtanInt(x) = \\int_0^x dt \\arctan(t)/t. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. fermi_dirac_mhalf -*- texinfo -*- -- Loadable Function: Y = fermi_dirac_mhalf (X) -- Loadable Function: [Y, ERR] = fermi_dirac_mhalf (...) These routines compute the complete Fermi-Dirac integral F_{-1/2}(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. fermi_dirac_half -*- texinfo -*- -- Loadable Function: Y = fermi_dirac_half (X) -- Loadable Function: [Y, ERR] = fermi_dirac_half (...) These routines compute the complete Fermi-Dirac integral F_{1/2}(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. fermi_dirac_3half -*- texinfo -*- -- Loadable Function: Y = fermi_dirac_3half (X) -- Loadable Function: [Y, ERR] = fermi_dirac_3half (...) These routines compute the complete Fermi-Dirac integral F_{3/2}(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. gamma_gsl -*- texinfo -*- -- Loadable Function: Y = gamma_gsl (X) -- Loadable Function: [Y, ERR] = gamma_gsl (...) These routines compute the Gamma function \\Gamma(x), subject to x not being a negative integer. The function is computed using the real Lanczos method. The maximum value of x such that \\Gamma(x) is not considered an overflow is given by the macro GSL_SF_GAMMA_XMAX and is 171.0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. lngamma_gsl -*- texinfo -*- -- Loadable Function: Y = lngamma_gsl (X) -- Loadable Function: [Y, ERR] = lngamma_gsl (...) These routines compute the logarithm of the Gamma function, \\log(\\Gamma(x)), subject to x not a being negative integer. For x<0 the real part of \\log(\\Gamma(x)) is returned, which is equivalent to \\log(|\\Gamma(x)|). The function is computed using the real Lanczos method. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. gammastar -*- texinfo -*- -- Loadable Function: Y = gammastar (X) -- Loadable Function: [Y, ERR] = gammastar (...) These routines compute the regulated Gamma Function \\Gamma^*(x) for x > 0. The regulated gamma function is given by, \\Gamma^*(x) = \\Gamma(x)/(\\sqrt{2\\pi} x^{(x-1/2)} \\exp(-x)) = (1 + (1/12x) + ...) for x \\to \\infty and is a useful suggestion of Temme. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. gammainv_gsl -*- texinfo -*- -- Loadable Function: Y = gammainv_gsl (X) -- Loadable Function: [Y, ERR] = gammainv_gsl (...) These routines compute the reciprocal of the gamma function, 1/\\Gamma(x) using the real Lanczos method. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. lambert_W0 -*- texinfo -*- -- Loadable Function: Y = lambert_W0 (X) -- Loadable Function: [Y, ERR] = lambert_W0 (...) These compute the principal branch of the Lambert W function, W_0(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_{-1}(x) to be the other real branch, where W < -1 for x < 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. lambert_Wm1 -*- texinfo -*- -- Loadable Function: Y = lambert_Wm1 (X) -- Loadable Function: [Y, ERR] = lambert_Wm1 (...) These compute the secondary real-valued branch of the Lambert W function, W_{-1}(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_{-1}(x) to be the other real branch, where W < -1 for x < 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. log_1plusx -*- texinfo -*- -- Loadable Function: Y = log_1plusx (X) -- Loadable Function: [Y, ERR] = log_1plusx (...) These routines compute \\log(1 + x) for x > -1 using an algorithm that is accurate for small x. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. log_1plusx_mx -*- texinfo -*- -- Loadable Function: Y = log_1plusx_mx (X) -- Loadable Function: [Y, ERR] = log_1plusx_mx (...) These routines compute \\log(1 + x) - x for x > -1 using an algorithm that is accurate for small x. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. psi -*- texinfo -*- -- Loadable Function: Y = psi (X) -- Loadable Function: [Y, ERR] = psi (...) These routines compute the digamma function \\psi(x) for general x, x \ e 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. psi_1piy -*- texinfo -*- -- Loadable Function: Y = psi_1piy (X) -- Loadable Function: [Y, ERR] = psi_1piy (...) These routines compute the real part of the digamma function on the line 1+i y, Re[\\psi(1 + i y)]. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. synchrotron_1 -*- texinfo -*- -- Loadable Function: Y = synchrotron_1 (X) -- Loadable Function: [Y, ERR] = synchrotron_1 (...) These routines compute the first synchrotron function x \\int_x^\\infty dt K_{5/3}(t) for x >= 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. synchrotron_2 -*- texinfo -*- -- Loadable Function: Y = synchrotron_2 (X) -- Loadable Function: [Y, ERR] = synchrotron_2 (...) These routines compute the second synchrotron function x K_{2/3}(x) for x >= 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. transport_2 -*- texinfo -*- -- Loadable Function: Y = transport_2 (X) -- Loadable Function: [Y, ERR] = transport_2 (...) These routines compute the transport function J(2,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. transport_3 -*- texinfo -*- -- Loadable Function: Y = transport_3 (X) -- Loadable Function: [Y, ERR] = transport_3 (...) These routines compute the transport function J(3,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. transport_4 -*- texinfo -*- -- Loadable Function: Y = transport_4 (X) -- Loadable Function: [Y, ERR] = transport_4 (...) These routines compute the transport function J(4,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. transport_5 -*- texinfo -*- -- Loadable Function: Y = transport_5 (X) -- Loadable Function: [Y, ERR] = transport_5 (...) These routines compute the transport function J(5,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. sinc_gsl -*- texinfo -*- -- Loadable Function: Y = sinc_gsl (X) -- Loadable Function: [Y, ERR] = sinc_gsl (...) These routines compute \\sinc(x) = \\sin(\\pi x) / (\\pi x) for any value of x. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. lnsinh -*- texinfo -*- -- Loadable Function: Y = lnsinh (X) -- Loadable Function: [Y, ERR] = lnsinh (...) These routines compute \\log(\\sinh(x)) for x > 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. lncosh -*- texinfo -*- -- Loadable Function: Y = lncosh (X) -- Loadable Function: [Y, ERR] = lncosh (...) These routines compute \\log(\\cosh(x)) for any x. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. zeta -*- texinfo -*- -- Loadable Function: Y = zeta (X) -- Loadable Function: [Y, ERR] = zeta (...) These routines compute the Riemann zeta function \\zeta(s) for arbitrary s, s \ e 1. The Riemann zeta function is defined by the infinite sum \\zeta(s) = \\sum_{k=1}^\\infty k^{-s}. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. eta -*- texinfo -*- -- Loadable Function: Y = eta (X) -- Loadable Function: [Y, ERR] = eta (...) These routines compute the eta function \\eta(s) for arbitrary s. The eta function is defined by \\eta(s) = (1-2^{1-s}) \\zeta(s). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_Jn -*- texinfo -*- -- Loadable Function: Y = bessel_Jn (N, X) -- Loadable Function: [Y, ERR] = bessel_Jn (...) These routines compute the regular cylindrical Bessel function of order n, J_n(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_Yn -*- texinfo -*- -- Loadable Function: Y = bessel_Yn (N, X) -- Loadable Function: [Y, ERR] = bessel_Yn (...) These routines compute the irregular cylindrical Bessel function of order n, Y_n(x), for x>0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_In -*- texinfo -*- -- Loadable Function: Y = bessel_In (N, X) -- Loadable Function: [Y, ERR] = bessel_In (...) These routines compute the regular modified cylindrical Bessel function of order n, I_n(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_In_scaled -*- texinfo -*- -- Loadable Function: Y = bessel_In_scaled (N, X) -- Loadable Function: [Y, ERR] = bessel_In_scaled (...) These routines compute the scaled regular modified cylindrical Bessel function of order n, \\exp(-|x|) I_n(x) ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_Kn -*- texinfo -*- -- Loadable Function: Y = bessel_Kn (N, X) -- Loadable Function: [Y, ERR] = bessel_Kn (...) These routines compute the irregular modified cylindrical Bessel function of order n, K_n(x), for x > 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_Kn_scaled -*- texinfo -*- -- Loadable Function: Y = bessel_Kn_scaled (N, X) -- Loadable Function: [Y, ERR] = bessel_Kn_scaled (...) ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_jl -*- texinfo -*- -- Loadable Function: Y = bessel_jl (N, X) -- Loadable Function: [Y, ERR] = bessel_jl (...) These routines compute the regular spherical Bessel function of order l, j_l(x), for l >= 0 and x >= 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_yl -*- texinfo -*- -- Loadable Function: Y = bessel_yl (N, X) -- Loadable Function: [Y, ERR] = bessel_yl (...) These routines compute the irregular spherical Bessel function of order l, y_l(x), for l >= 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_il_scaled -*- texinfo -*- -- Loadable Function: Y = bessel_il_scaled (N, X) -- Loadable Function: [Y, ERR] = bessel_il_scaled (...) These routines compute the scaled regular modified spherical Bessel function of order l, \\exp(-|x|) i_l(x) ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_kl_scaled -*- texinfo -*- -- Loadable Function: Y = bessel_kl_scaled (N, X) -- Loadable Function: [Y, ERR] = bessel_kl_scaled (...) These routines compute the scaled irregular modified spherical Bessel function of order l, \\exp(x) k_l(x), for x>0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. exprel_n -*- texinfo -*- -- Loadable Function: Y = exprel_n (N, X) -- Loadable Function: [Y, ERR] = exprel_n (...) These routines compute the N-relative exponential, which is the n-th generalization of the functions gsl_sf_exprel and gsl_sf_exprel2. The N-relative exponential is given by, exprel_N(x) = N!/x^N (\\exp(x) - \\sum_{k=0}^{N-1} x^k/k!) = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ... = 1F1 (1,1+N,x) ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. fermi_dirac_int -*- texinfo -*- -- Loadable Function: Y = fermi_dirac_int (N, X) -- Loadable Function: [Y, ERR] = fermi_dirac_int (...) These routines compute the complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/\\Gamma(j+1)) \\int_0^\\infty dt (t^j /(\\exp(t-x)+1)). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. taylorcoeff -*- texinfo -*- -- Loadable Function: Y = taylorcoeff (N, X) -- Loadable Function: [Y, ERR] = taylorcoeff (...) These routines compute the Taylor coefficient x^n / n! for x >= 0, n >= 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. legendre_Pl -*- texinfo -*- -- Loadable Function: Y = legendre_Pl (N, X) -- Loadable Function: [Y, ERR] = legendre_Pl (...) These functions evaluate the Legendre polynomial P_l(x) for a specific value of l, x subject to l >= 0, |x| <= 1 ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. legendre_Ql -*- texinfo -*- -- Loadable Function: Y = legendre_Ql (N, X) -- Loadable Function: [Y, ERR] = legendre_Ql (...) These routines compute the Legendre function Q_l(x) for x > -1, x != 1 and l >= 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. psi_n -*- texinfo -*- -- Loadable Function: Y = psi_n (N, X) -- Loadable Function: [Y, ERR] = psi_n (...) These routines compute the polygamma function \\psi^{(m)}(x) for m >= 0, x > 0. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_Jnu -*- texinfo -*- -- Loadable Function: Z = bessel_Jnu (X, Y) -- Loadable Function: [Z, ERR] = bessel_Jnu (...) These routines compute the regular cylindrical Bessel function of fractional order nu, J_\ u(x). ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_Ynu -*- texinfo -*- -- Loadable Function: Z = bessel_Ynu (X, Y) -- Loadable Function: [Z, ERR] = bessel_Ynu (...) These routines compute the irregular cylindrical Bessel function of fractional order nu, Y_\ u(x). ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_Inu -*- texinfo -*- -- Loadable Function: Z = bessel_Inu (X, Y) -- Loadable Function: [Z, ERR] = bessel_Inu (...) These routines compute the regular modified Bessel function of fractional order nu, I_\ u(x) for x>0, \ u>0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_Inu_scaled -*- texinfo -*- -- Loadable Function: Z = bessel_Inu_scaled (X, Y) -- Loadable Function: [Z, ERR] = bessel_Inu_scaled (...) These routines compute the scaled regular modified Bessel function of fractional order nu, \\exp(-|x|)I_\ u(x) for x>0, \ u>0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_Knu -*- texinfo -*- -- Loadable Function: Z = bessel_Knu (X, Y) -- Loadable Function: [Z, ERR] = bessel_Knu (...) These routines compute the irregular modified Bessel function of fractional order nu, K_\ u(x) for x>0, \ u>0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_lnKnu -*- texinfo -*- -- Loadable Function: Z = bessel_lnKnu (X, Y) -- Loadable Function: [Z, ERR] = bessel_lnKnu (...) These routines compute the logarithm of the irregular modified Bessel function of fractional order nu, \\ln(K_\ u(x)) for x>0, \ u>0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_Knu_scaled -*- texinfo -*- -- Loadable Function: Z = bessel_Knu_scaled (X, Y) -- Loadable Function: [Z, ERR] = bessel_Knu_scaled (...) These routines compute the scaled irregular modified Bessel function of fractional order nu, \\exp(+|x|) K_\ u(x) for x>0, \ u>0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. exp_mult -*- texinfo -*- -- Loadable Function: Z = exp_mult (X, Y) -- Loadable Function: [Z, ERR] = exp_mult (...) These routines exponentiate x and multiply by the factor y to return the product y \\exp(x). ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. fermi_dirac_inc_0 -*- texinfo -*- -- Loadable Function: Z = fermi_dirac_inc_0 (X, Y) -- Loadable Function: [Z, ERR] = fermi_dirac_inc_0 (...) These routines compute the incomplete Fermi-Dirac integral with an index of zero, F_0(x,b) = \\ln(1 + e^{b-x}) - (b-x). ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. poch -*- texinfo -*- -- Loadable Function: Z = poch (X, Y) -- Loadable Function: [Z, ERR] = poch (...) These routines compute the Pochhammer symbol (a)_x := \\Gamma(a + x)/\\Gamma(a), subject to a and a+x not being negative integers. The Pochhammer symbol is also known as the Apell symbol. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. lnpoch -*- texinfo -*- -- Loadable Function: Z = lnpoch (X, Y) -- Loadable Function: [Z, ERR] = lnpoch (...) These routines compute the logarithm of the Pochhammer symbol, \\log((a)_x) = \\log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. pochrel -*- texinfo -*- -- Loadable Function: Z = pochrel (X, Y) -- Loadable Function: [Z, ERR] = pochrel (...) These routines compute the relative Pochhammer symbol ((a,x) - 1)/x where (a,x) = (a)_x := \\Gamma(a + x)/\\Gamma(a). ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. gamma_inc_Q -*- texinfo -*- -- Loadable Function: Z = gamma_inc_Q (X, Y) -- Loadable Function: [Z, ERR] = gamma_inc_Q (...) These routines compute the normalized incomplete Gamma Function Q(a,x) = 1/\\Gamma(a) \\int_x\\infty dt t^{a-1} \\exp(-t) for a > 0, x >= 0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. gamma_inc_P -*- texinfo -*- -- Loadable Function: Z = gamma_inc_P (X, Y) -- Loadable Function: [Z, ERR] = gamma_inc_P (...) These routines compute the complementary normalized incomplete Gamma Function P(a,x) = 1/\\Gamma(a) \\int_0^x dt t^{a-1} \\exp(-t) for a > 0, x >= 0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. gamma_inc -*- texinfo -*- -- Loadable Function: Z = gamma_inc (X, Y) -- Loadable Function: [Z, ERR] = gamma_inc (...) These functions compute the incomplete Gamma Function the normalization factor included in the previously defined functions: \\Gamma(a,x) = \\int_x\\infty dt t^{a-1} \\exp(-t) for a real and x >= 0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. beta_gsl -*- texinfo -*- -- Loadable Function: Z = beta_gsl (X, Y) -- Loadable Function: [Z, ERR] = beta_gsl (...) These routines compute the Beta Function, B(a,b) = \\Gamma(a)\\Gamma(b)/\\Gamma(a+b) for a > 0, b > 0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. lnbeta -*- texinfo -*- -- Loadable Function: Z = lnbeta (X, Y) -- Loadable Function: [Z, ERR] = lnbeta (...) These routines compute the logarithm of the Beta Function, \\log(B(a,b)) for a > 0, b > 0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. hyperg_0F1 -*- texinfo -*- -- Loadable Function: Z = hyperg_0F1 (X, Y) -- Loadable Function: [Z, ERR] = hyperg_0F1 (...) These routines compute the hypergeometric function 0F1(c,x). ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. conicalP_half -*- texinfo -*- -- Loadable Function: Z = conicalP_half (X, Y) -- Loadable Function: [Z, ERR] = conicalP_half (...) These routines compute the irregular Spherical Conical Function P^{1/2}_{-1/2 + i \\lambda}(x) for x > -1. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. conicalP_mhalf -*- texinfo -*- -- Loadable Function: Z = conicalP_mhalf (X, Y) -- Loadable Function: [Z, ERR] = conicalP_mhalf (...) These routines compute the regular Spherical Conical Function P^{-1/2}_{-1/2 + i \\lambda}(x) for x > -1. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. conicalP_0 -*- texinfo -*- -- Loadable Function: Z = conicalP_0 (X, Y) -- Loadable Function: [Z, ERR] = conicalP_0 (...) These routines compute the conical function P^0_{-1/2 + i \\lambda}(x) for x > -1. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. conicalP_1 -*- texinfo -*- -- Loadable Function: Z = conicalP_1 (X, Y) -- Loadable Function: [Z, ERR] = conicalP_1 (...) These routines compute the conical function P^1_{-1/2 + i \\lambda}(x) for x > -1. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. hzeta -*- texinfo -*- -- Loadable Function: Z = hzeta (X, Y) -- Loadable Function: [Z, ERR] = hzeta (...) These routines compute the Hurwitz zeta function \\zeta(s,q) for s > 1, q > 0. ERR contains an estimate of the absolute error in the value Z. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_Ai -*- texinfo -*- -- Loadable Function: Y = airy_Ai (X, MODE) -- Loadable Function: [Y, ERR] = airy_Ai (...) These routines compute the Airy function Ai(x) with an accuracy specified by mode. The second argument MODE must be an integer corresponding to 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately `2 * 10^-16'. 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately `10^-7'. 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately `5 * 10^-4'. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_Bi -*- texinfo -*- -- Loadable Function: Y = airy_Bi (X, MODE) -- Loadable Function: [Y, ERR] = airy_Bi (...) These routines compute the Airy function Bi(x) with an accuracy specified by mode. The second argument MODE must be an integer corresponding to 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately `2 * 10^-16'. 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately `10^-7'. 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately `5 * 10^-4'. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_Ai_scaled -*- texinfo -*- -- Loadable Function: Y = airy_Ai_scaled (X, MODE) -- Loadable Function: [Y, ERR] = airy_Ai_scaled (...) These routines compute a scaled version of the Airy function S_A(x) Ai(x). For x>0 the scaling factor S_A(x) is \\exp(+(2/3) x^(3/2)), and is 1 for x<0. The second argument MODE must be an integer corresponding to 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately `2 * 10^-16'. 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately `10^-7'. 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately `5 * 10^-4'. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_Bi_scaled -*- texinfo -*- -- Loadable Function: Y = airy_Bi_scaled (X, MODE) -- Loadable Function: [Y, ERR] = airy_Bi_scaled (...) These routines compute a scaled version of the Airy function S_B(x) Bi(x). For x>0 the scaling factor S_B(x) is exp(-(2/3) x^(3/2)), and is 1 for x<0. The second argument MODE must be an integer corresponding to 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately `2 * 10^-16'. 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately `10^-7'. 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately `5 * 10^-4'. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_Ai_deriv -*- texinfo -*- -- Loadable Function: Y = airy_Ai_deriv (X, MODE) -- Loadable Function: [Y, ERR] = airy_Ai_deriv (...) These routines compute the Airy function derivative Ai'(x) with an accuracy specified by mode. The second argument MODE must be an integer corresponding to 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately `2 * 10^-16'. 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately `10^-7'. 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately `5 * 10^-4'. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_Bi_deriv -*- texinfo -*- -- Loadable Function: Y = airy_Bi_deriv (X, MODE) -- Loadable Function: [Y, ERR] = airy_Bi_deriv (...) These routines compute the Airy function derivative Bi'(x) with an accuracy specified by mode. The second argument MODE must be an integer corresponding to 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately `2 * 10^-16'. 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately `10^-7'. 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately `5 * 10^-4'. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_Ai_deriv_scaled -*- texinfo -*- -- Loadable Function: Y = airy_Ai_deriv_scaled (X, MODE) -- Loadable Function: [Y, ERR] = airy_Ai_deriv_scaled (...) These routines compute the derivative of the scaled Airy function S_A(x) Ai(x). The second argument MODE must be an integer corresponding to 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately `2 * 10^-16'. 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately `10^-7'. 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately `5 * 10^-4'. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_Bi_deriv_scaled -*- texinfo -*- -- Loadable Function: Y = airy_Bi_deriv_scaled (X, MODE) -- Loadable Function: [Y, ERR] = airy_Bi_deriv_scaled (...) These routines compute the derivative of the scaled Airy function S_B(x) Bi(x). The second argument MODE must be an integer corresponding to 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately `2 * 10^-16'. 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately `10^-7'. 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately `5 * 10^-4'. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. ellint_Kcomp -*- texinfo -*- -- Loadable Function: Y = ellint_Kcomp (X, MODE) -- Loadable Function: [Y, ERR] = ellint_Kcomp (...) These routines compute the complete elliptic integral K(k) The notation used here is based on Carlson, `Numerische Mathematik' 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter m = k^2. The second argument MODE must be an integer corresponding to 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately `2 * 10^-16'. 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately `10^-7'. 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately `5 * 10^-4'. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. ellint_Ecomp -*- texinfo -*- -- Loadable Function: Y = ellint_Ecomp (X, MODE) -- Loadable Function: [Y, ERR] = ellint_Ecomp (...) These routines compute the complete elliptic integral E(k) to the accuracy specified by the mode variable mode. The notation used here is based on Carlson, `Numerische Mathematik' 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter m = k^2. The second argument MODE must be an integer corresponding to 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately `2 * 10^-16'. 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately `10^-7'. 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately `5 * 10^-4'. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_zero_Ai -*- texinfo -*- -- Loadable Function: Y = airy_zero_Ai (N) -- Loadable Function: [Y, ERR] = airy_zero_Ai (...) These routines compute the location of the s-th zero of the Airy function Ai(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_zero_Bi -*- texinfo -*- -- Loadable Function: Y = airy_zero_Bi (N) -- Loadable Function: [Y, ERR] = airy_zero_Bi (...) These routines compute the location of the s-th zero of the Airy function Bi(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_zero_Ai_deriv -*- texinfo -*- -- Loadable Function: Y = airy_zero_Ai_deriv (N) -- Loadable Function: [Y, ERR] = airy_zero_Ai_deriv (...) These routines compute the location of the s-th zero of the Airy function derivative Ai(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. airy_zero_Bi_deriv -*- texinfo -*- -- Loadable Function: Y = airy_zero_Bi_deriv (N) -- Loadable Function: [Y, ERR] = airy_zero_Bi_deriv (...) These routines compute the location of the s-th zero of the Airy function derivative Bi(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_zero_J0 -*- texinfo -*- -- Loadable Function: Y = bessel_zero_J0 (N) -- Loadable Function: [Y, ERR] = bessel_zero_J0 (...) These routines compute the location of the s-th positive zero of the Bessel function J_0(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. bessel_zero_J1 -*- texinfo -*- -- Loadable Function: Y = bessel_zero_J1 (N) -- Loadable Function: [Y, ERR] = bessel_zero_J1 (...) These routines compute the location of the s-th positive zero of the Bessel function J_1(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. psi_1_int -*- texinfo -*- -- Loadable Function: Y = psi_1_int (N) -- Loadable Function: [Y, ERR] = psi_1_int (...) These routines compute the Trigamma function \\psi(n) for positive integer n. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. zeta_int -*- texinfo -*- -- Loadable Function: Y = zeta_int (N) -- Loadable Function: [Y, ERR] = zeta_int (...) These routines compute the Riemann zeta function \\zeta(n) for integer n, n \ e 1. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. eta_int -*- texinfo -*- -- Loadable Function: Y = eta_int (N) -- Loadable Function: [Y, ERR] = eta_int (...) These routines compute the eta function \\eta(n) for integer n. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. legendre_Plm -*- texinfo -*- -- Loadable Function: Y = legendre_Plm (N, M, X) -- Loadable Function: [Y, ERR] = legendre_Plm (...) These routines compute the associated Legendre polynomial P_l^m(x) for m >= 0, l >= m, |x| <= 1. ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. legendre_sphPlm -*- texinfo -*- -- Loadable Function: Y = legendre_sphPlm (N, M, X) -- Loadable Function: [Y, ERR] = legendre_sphPlm (...) These routines compute the normalized associated Legendre polynomial $\\sqrt{(2l+1)/(4\\pi)} \\sqrt{(l-m)!/(l+m)!} P_l^m(x)$ suitable for use in spherical harmonics. The parameters must satisfy m >= 0, l >= m, |x| <= 1. Theses routines avoid the overflows that occur for the standard normalization of P_l^m(x). ERR contains an estimate of the absolute error in the value Y. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. hyperg_U -*- texinfo -*- -- Loadable Function: OUT = hyperg_U (X0, X1, X2) -- Loadable Function: [OUT, ERR] = hyperg_U (...) Secondary Confluent Hypergoemetric U function A&E 13.1.3 All input are double as is the output. ERR contains an estimate of the absolute error in the value OUT.a. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation. hyperg_1F1 -*- texinfo -*- -- Loadable Function: OUT = hyperg_1F1 (X0, X1, X2) -- Loadable Function: [OUT, ERR] = hyperg_1F1 (...) Primary Confluent Hypergoemetric U function A&E 13.1.3 All inputs are double as is the output. ERR contains an estimate of the absolute error in the value OUT.a. This function is from the GNU Scientific Library, see `http://www.gnu.org/software/gsl/' for documentation.  Tag Table: Node: Top0  End Tag Table @ gsl-1.0.8/doc/RCS/DOSCSTRINGS.old,v0000755000175000017500000017047511201030376014065 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @# @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @gsl_sf -*- texinfo -*- @@deftypefn {Loadable Function} {} gsl_sf () Octave bindings to the GNU Scientific Library. All GSL functions can be called with by the GSL names within octave. @@end deftypefn clausen -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} clausen (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} clausen (@@dots{}) The Clausen function is defined by the following integral, Cl_2(x) = - \\int_0^x dt \\log(2 \\sin(t/2)) It is related to the dilogarithm by Cl_2(\\theta) = \\Im Li_2(\\exp(i \\theta)). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn dawson -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} dawson (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} dawson (@@dots{}) The Dawson integral is defined by \\exp(-x^2) \\int_0^x dt \\exp(t^2). A table of Dawson integral can be found in Abramowitz & Stegun, Table 7.5. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn debye_1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} debye_1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_1 (@@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn debye_2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} debye_2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_2 (@@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn debye_3 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} debye_3 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_3 (@@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn debye_4 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} debye_4 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} debye_4 (@@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn erf_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} erf_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erf_gsl (@@dots{}) These routines compute the error function erf(x) = (2/\\sqrt(\\pi)) \\int_0^x dt \\exp(-t^2). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn erfc_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} erfc_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erfc_gsl (@@dots{}) These routines compute the complementary error function erfc(x) = 1 - erf(x) = (2/\\sqrt(\\pi)) \\int_x^\\infty \\exp(-t^2). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn log_erfc -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} log_erfc (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} log_erfc (@@dots{}) These routines compute the logarithm of the complementary error function \\log(\\erfc(x)). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn erf_Z -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} erf_Z (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erf_Z (@@dots{}) These routines compute the Gaussian probability function Z(x) = (1/(2\\pi)) \\exp(-x^2/2). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn erf_Q -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} erf_Q (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} erf_Q (@@dots{}) These routines compute the upper tail of the Gaussian probability function Q(x) = (1/(2\\pi)) \\int_x^\\infty dt \\exp(-t^2/2). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hazard -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} hazard (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} hazard (@@dots{}) The hazard function for the normal distrbution, also known as the inverse Mill\\'s ratio, is defined as h(x) = Z(x)/Q(x) = \\sqrt@@{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2)@@}. It decreases rapidly as x approaches -\\infty and asymptotes to h(x) \\sim x as x approaches +\\infty. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expm1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expm1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expm1 (@@dots{}) These routines compute the quantity \\exp(x)-1 using an algorithm that is accurate for small x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn exprel -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} exprel (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} exprel (@@dots{}) These routines compute the quantity (\\exp(x)-1)/x using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion (\\exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\dots. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn exprel_2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} exprel_2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} exprel_2 (@@dots{}) These routines compute the quantity 2(\\exp(x)-1-x)/x^2 using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion 2(\\exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\dots. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expint_E1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expint_E1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_E1 (@@dots{}) These routines compute the exponential integral E_1(x), E_1(x) := Re \\int_1^\\infty dt \\exp(-xt)/t. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expint_E2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expint_E2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_E2 (@@dots{}) These routines compute the second-order exponential integral E_2(x), E_2(x) := \\Re \\int_1^\\infty dt \\exp(-xt)/t^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expint_Ei -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expint_Ei (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_Ei (@@dots{}) These routines compute the exponential integral E_i(x), Ei(x) := - PV(\\int_@@{-x@@}^\\infty dt \\exp(-t)/t) where PV denotes the principal value of the integral. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn Shi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} Shi (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Shi (@@dots{}) These routines compute the integral Shi(x) = \\int_0^x dt \\sinh(t)/t. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn Chi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} Chi (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Chi (@@dots{}) These routines compute the integral Chi(x) := Re[ \\gamma_E + \\log(x) + \\int_0^x dt (\\cosh[t]-1)/t] , where \\gamma_E is the Euler constant. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn expint_3 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} expint_3 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} expint_3 (@@dots{}) These routines compute the exponential integral Ei_3(x) = \\int_0^x dt \\exp(-t^3) for x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn Si -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} Si (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Si (@@dots{}) These routines compute the Sine integral Si(x) = \\int_0^x dt \\sin(t)/t. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn Ci -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} Ci (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} Ci (@@dots{}) These routines compute the Cosine integral Ci(x) = -\\int_x^\\infty dt \\cos(t)/t for x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn atanint -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} atanint (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} atanint (@@dots{}) These routines compute the Arctangent integral AtanInt(x) = \\int_0^x dt \\arctan(t)/t. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_mhalf -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_mhalf (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_mhalf (@@dots{}) These routines compute the complete Fermi-Dirac integral F_@@{-1/2@@}(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_half -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_half (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_half (@@dots{}) These routines compute the complete Fermi-Dirac integral F_@@{1/2@@}(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_3half -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_3half (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_3half (@@dots{}) These routines compute the complete Fermi-Dirac integral F_@@{3/2@@}(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gamma_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} gamma_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} gamma_gsl (@@dots{}) These routines compute the Gamma function \\Gamma(x), subject to x not being a negative integer. The function is computed using the real Lanczos method. The maximum value of x such that \\Gamma(x) is not considered an overflow is given by the macro GSL_SF_GAMMA_XMAX and is 171.0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lngamma_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lngamma_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lngamma_gsl (@@dots{}) These routines compute the logarithm of the Gamma function, \\log(\\Gamma(x)), subject to x not a being negative integer. For x<0 the real part of \\log(\\Gamma(x)) is returned, which is equivalent to \\log(|\\Gamma(x)|). The function is computed using the real Lanczos method. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gammastar -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} gammastar (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} gammastar (@@dots{}) These routines compute the regulated Gamma Function \\Gamma^*(x) for x > 0. The regulated gamma function is given by, \\Gamma^*(x) = \\Gamma(x)/(\\sqrt@@{2\\pi@@} x^@@{(x-1/2)@@} \\exp(-x)) = (1 + (1/12x) + ...) for x \\to \\infty and is a useful suggestion of Temme. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gammainv_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} gammainv_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} gammainv_gsl (@@dots{}) These routines compute the reciprocal of the gamma function, 1/\\Gamma(x) using the real Lanczos method. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lambert_W0 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lambert_W0 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lambert_W0 (@@dots{}) These compute the principal branch of the Lambert W function, W_0(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@@{-1@@}(x) to be the other real branch, where W < -1 for x < 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lambert_Wm1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lambert_Wm1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lambert_Wm1 (@@dots{}) These compute the secondary real-valued branch of the Lambert W function, W_@@{-1@@}(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@@{-1@@}(x) to be the other real branch, where W < -1 for x < 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn log_1plusx -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} log_1plusx (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} log_1plusx (@@dots{}) These routines compute \\log(1 + x) for x > -1 using an algorithm that is accurate for small x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn log_1plusx_mx -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} log_1plusx_mx (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} log_1plusx_mx (@@dots{}) These routines compute \\log(1 + x) - x for x > -1 using an algorithm that is accurate for small x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn psi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} psi (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi (@@dots{}) These routines compute the digamma function \\psi(x) for general x, x \ e 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn psi_1piy -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} psi_1piy (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi_1piy (@@dots{}) These routines compute the real part of the digamma function on the line 1+i y, Re[\\psi(1 + i y)]. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn synchrotron_1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} synchrotron_1 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} synchrotron_1 (@@dots{}) These routines compute the first synchrotron function x \\int_x^\\infty dt K_@@{5/3@@}(t) for x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn synchrotron_2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} synchrotron_2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} synchrotron_2 (@@dots{}) These routines compute the second synchrotron function x K_@@{2/3@@}(x) for x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn transport_2 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} transport_2 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_2 (@@dots{}) These routines compute the transport function J(2,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn transport_3 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} transport_3 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_3 (@@dots{}) These routines compute the transport function J(3,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn transport_4 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} transport_4 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_4 (@@dots{}) These routines compute the transport function J(4,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn transport_5 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} transport_5 (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} transport_5 (@@dots{}) These routines compute the transport function J(5,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn sinc_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} sinc_gsl (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} sinc_gsl (@@dots{}) These routines compute \\sinc(x) = \\sin(\\pi x) / (\\pi x) for any value of x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lnsinh -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lnsinh (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lnsinh (@@dots{}) These routines compute \\log(\\sinh(x)) for x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lncosh -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} lncosh (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} lncosh (@@dots{}) These routines compute \\log(\\cosh(x)) for any x. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn zeta -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} zeta (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} zeta (@@dots{}) These routines compute the Riemann zeta function \\zeta(s) for arbitrary s, s \ e 1. The Riemann zeta function is defined by the infinite sum \\zeta(s) = \\sum_@@{k=1@@}^\\infty k^@@{-s@@}. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn eta -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} eta (@@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} eta (@@dots{}) These routines compute the eta function \\eta(s) for arbitrary s. The eta function is defined by \\eta(s) = (1-2^@@{1-s@@}) \\zeta(s). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Jn -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_Jn (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Jn (@@dots{}) These routines compute the regular cylindrical Bessel function of order n, J_n(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Yn -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_Yn (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Yn (@@dots{}) These routines compute the irregular cylindrical Bessel function of order n, Y_n(x), for x>0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_In -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_In (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_In (@@dots{}) These routines compute the regular modified cylindrical Bessel function of order n, I_n(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_In_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_In_scaled (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_In_scaled (@@dots{}) These routines compute the scaled regular modified cylindrical Bessel function of order n, \\exp(-|x|) I_n(x) @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Kn -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_Kn (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Kn (@@dots{}) These routines compute the irregular modified cylindrical Bessel function of order n, K_n(x), for x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Kn_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_Kn_scaled (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_Kn_scaled (@@dots{}) @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_jl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_jl (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_jl (@@dots{}) These routines compute the regular spherical Bessel function of order l, j_l(x), for l >= 0 and x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_yl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_yl (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_yl (@@dots{}) These routines compute the irregular spherical Bessel function of order l, y_l(x), for l >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_il_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_il_scaled (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_il_scaled (@@dots{}) These routines compute the scaled regular modified spherical Bessel function of order l, \\exp(-|x|) i_l(x) @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_kl_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_kl_scaled (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_kl_scaled (@@dots{}) These routines compute the scaled irregular modified spherical Bessel function of order l, \\exp(x) k_l(x), for x>0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn exprel_n -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} exprel_n (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} exprel_n (@@dots{}) These routines compute the N-relative exponential, which is the n-th generalization of the functions gsl_sf_exprel and gsl_sf_exprel2. The N-relative exponential is given by, exprel_N(x) = N!/x^N (\\exp(x) - \\sum_@@{k=0@@}^@@{N-1@@} x^k/k!) = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ... = 1F1 (1,1+N,x) @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_int -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} fermi_dirac_int (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} fermi_dirac_int (@@dots{}) These routines compute the complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/\\Gamma(j+1)) \\int_0^\\infty dt (t^j /(\\exp(t-x)+1)). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn taylorcoeff -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} taylorcoeff (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} taylorcoeff (@@dots{}) These routines compute the Taylor coefficient x^n / n! for x >= 0, n >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn legendre_Pl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} legendre_Pl (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_Pl (@@dots{}) These functions evaluate the Legendre polynomial P_l(x) for a specific value of l, x subject to l >= 0, |x| <= 1 @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn legendre_Ql -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} legendre_Ql (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_Ql (@@dots{}) These routines compute the Legendre function Q_l(x) for x > -1, x != 1 and l >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn psi_n -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} psi_n (@@var{n}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi_n (@@dots{}) These routines compute the polygamma function \\psi^@@{(m)@@}(x) for m >= 0, x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Jnu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Jnu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Jnu (@@dots{}) These routines compute the regular cylindrical Bessel function of fractional order nu, J_\ u(x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Ynu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Ynu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Ynu (@@dots{}) These routines compute the irregular cylindrical Bessel function of fractional order nu, Y_\ u(x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Inu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Inu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Inu (@@dots{}) These routines compute the regular modified Bessel function of fractional order nu, I_\ u(x) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Inu_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Inu_scaled (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Inu_scaled (@@dots{}) These routines compute the scaled regular modified Bessel function of fractional order nu, \\exp(-|x|)I_\ u(x) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Knu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Knu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Knu (@@dots{}) These routines compute the irregular modified Bessel function of fractional order nu, K_\ u(x) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_lnKnu -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_lnKnu (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_lnKnu (@@dots{}) These routines compute the logarithm of the irregular modified Bessel function of fractional order nu, \\ln(K_\ u(x)) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_Knu_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} bessel_Knu_scaled (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} bessel_Knu_scaled (@@dots{}) These routines compute the scaled irregular modified Bessel function of fractional order nu, \\exp(+|x|) K_\ u(x) for x>0, \ u>0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn exp_mult -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} exp_mult (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} exp_mult (@@dots{}) These routines exponentiate x and multiply by the factor y to return the product y \\exp(x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn fermi_dirac_inc_0 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} fermi_dirac_inc_0 (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} fermi_dirac_inc_0 (@@dots{}) These routines compute the incomplete Fermi-Dirac integral with an index of zero, F_0(x,b) = \\ln(1 + e^@@{b-x@@}) - (b-x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn poch -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} poch (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} poch (@@dots{}) These routines compute the Pochhammer symbol (a)_x := \\Gamma(a + x)/\\Gamma(a), subject to a and a+x not being negative integers. The Pochhammer symbol is also known as the Apell symbol. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lnpoch -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} lnpoch (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} lnpoch (@@dots{}) These routines compute the logarithm of the Pochhammer symbol, \\log((a)_x) = \\log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn pochrel -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} pochrel (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} pochrel (@@dots{}) These routines compute the relative Pochhammer symbol ((a,x) - 1)/x where (a,x) = (a)_x := \\Gamma(a + x)/\\Gamma(a). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gamma_inc_Q -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} gamma_inc_Q (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} gamma_inc_Q (@@dots{}) These routines compute the normalized incomplete Gamma Function Q(a,x) = 1/\\Gamma(a) \\int_x\\infty dt t^@@{a-1@@} \\exp(-t) for a > 0, x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gamma_inc_P -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} gamma_inc_P (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} gamma_inc_P (@@dots{}) These routines compute the complementary normalized incomplete Gamma Function P(a,x) = 1/\\Gamma(a) \\int_0^x dt t^@@{a-1@@} \\exp(-t) for a > 0, x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn gamma_inc -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} gamma_inc (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} gamma_inc (@@dots{}) These functions compute the incomplete Gamma Function the normalization factor included in the previously defined functions: \\Gamma(a,x) = \\int_x\\infty dt t^@@{a-1@@} \\exp(-t) for a real and x >= 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn beta_gsl -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} beta_gsl (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} beta_gsl (@@dots{}) These routines compute the Beta Function, B(a,b) = \\Gamma(a)\\Gamma(b)/\\Gamma(a+b) for a > 0, b > 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn lnbeta -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} lnbeta (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} lnbeta (@@dots{}) These routines compute the logarithm of the Beta Function, \\log(B(a,b)) for a > 0, b > 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hyperg_0F1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} hyperg_0F1 (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} hyperg_0F1 (@@dots{}) These routines compute the hypergeometric function 0F1(c,x). @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn conicalP_half -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} conicalP_half (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_half (@@dots{}) These routines compute the irregular Spherical Conical Function P^@@{1/2@@}_@@{-1/2 + i \\lambda@@}(x) for x > -1. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn conicalP_mhalf -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} conicalP_mhalf (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_mhalf (@@dots{}) These routines compute the regular Spherical Conical Function P^@@{-1/2@@}_@@{-1/2 + i \\lambda@@}(x) for x > -1. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn conicalP_0 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} conicalP_0 (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_0 (@@dots{}) These routines compute the conical function P^0_@@{-1/2 + i \\lambda@@}(x) for x > -1. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn conicalP_1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} conicalP_1 (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} conicalP_1 (@@dots{}) These routines compute the conical function P^1_@@{-1/2 + i \\lambda@@}(x) for x > -1. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hzeta -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{z} =} hzeta (@@var{x}, @@var{y}) @@deftypefnx {Loadable Function} {[@@var{z}, @@var{err}] =} hzeta (@@dots{}) These routines compute the Hurwitz zeta function \\zeta(s,q) for s > 1, q > 0. @@var{err} contains an estimate of the absolute error in the value @@var{z}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Ai -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai (@@dots{}) These routines compute the Airy function Ai(x) with an accuracy specified by mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Bi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi (@@dots{}) These routines compute the Airy function Bi(x) with an accuracy specified by mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Ai_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai_scaled (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai_scaled (@@dots{}) These routines compute a scaled version of the Airy function S_A(x) Ai(x). For x>0 the scaling factor S_A(x) is \\exp(+(2/3) x^(3/2)), and is 1 for x<0. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Bi_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi_scaled (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi_scaled (@@dots{}) These routines compute a scaled version of the Airy function S_B(x) Bi(x). For x>0 the scaling factor S_B(x) is exp(-(2/3) x^(3/2)), and is 1 for x<0. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Ai_deriv -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai_deriv (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai_deriv (@@dots{}) These routines compute the Airy function derivative Ai'(x) with an accuracy specified by mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Bi_deriv -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi_deriv (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi_deriv (@@dots{}) These routines compute the Airy function derivative Bi'(x) with an accuracy specified by mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Ai_deriv_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Ai_deriv_scaled (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Ai_deriv_scaled (@@dots{}) These routines compute the derivative of the scaled Airy function S_A(x) Ai(x). The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_Bi_deriv_scaled -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_Bi_deriv_scaled (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_Bi_deriv_scaled (@@dots{}) These routines compute the derivative of the scaled Airy function S_B(x) Bi(x). The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn ellint_Kcomp -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} ellint_Kcomp (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} ellint_Kcomp (@@dots{}) These routines compute the complete elliptic integral K(k) to the accuracy specified by the mode variable mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn ellint_Ecomp -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} ellint_Ecomp (@@var{x}, @@var{mode}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} ellint_Ecomp (@@dots{}) These routines compute the complete elliptic integral E(k) to the accuracy specified by the mode variable mode. The second argument @@var{mode} must be an integer corresponding to @@table @@asis @@item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @@code{2 * 10^-16}. @@item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @@code{10^-7}. @@item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @@code{5 * 10^-4}. @@end table @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_zero_Ai -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Ai (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Ai (@@dots{}) These routines compute the location of the s-th zero of the Airy function Ai(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_zero_Bi -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Bi (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Bi (@@dots{}) These routines compute the location of the s-th zero of the Airy function Bi(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_zero_Ai_deriv -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Ai_deriv (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Ai_deriv (@@dots{}) These routines compute the location of the s-th zero of the Airy function derivative Ai(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn airy_zero_Bi_deriv -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} airy_zero_Bi_deriv (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} airy_zero_Bi_deriv (@@dots{}) These routines compute the location of the s-th zero of the Airy function derivative Bi(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_zero_J0 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_zero_J0 (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_zero_J0 (@@dots{}) These routines compute the location of the s-th positive zero of the Bessel function J_0(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn bessel_zero_J1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} bessel_zero_J1 (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} bessel_zero_J1 (@@dots{}) These routines compute the location of the s-th positive zero of the Bessel function J_1(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn psi_1_int -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} psi_1_int (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} psi_1_int (@@dots{}) These routines compute the Trigamma function \\psi(n) for positive integer n. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn zeta_int -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} zeta_int (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} zeta_int (@@dots{}) These routines compute the Riemann zeta function \\zeta(n) for integer n, n \ e 1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn eta_int -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} eta_int (@@var{n}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} eta_int (@@dots{}) These routines compute the eta function \\eta(n) for integer n. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn legendre_Plm -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} legendre_Plm (@@var{n}, @@var{m}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_Plm (@@dots{}) These routines compute the associated Legendre polynomial P_l^m(x) for m >= 0, l >= m, |x| <= 1. @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn legendre_sphPlm -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{y} =} legendre_sphPlm (@@var{n}, @@var{m}, @@var{x}) @@deftypefnx {Loadable Function} {[@@var{y}, @@var{err}] =} legendre_sphPlm (@@dots{}) These routines compute the normalized associated Legendre polynomial $\\sqrt@@{(2l+1)/(4\\pi)@@} \\sqrt@@{(l-m)!/(l+m)!@@} P_l^m(x)$ suitable for use in spherical harmonics. The parameters must satisfy m >= 0, l >= m, |x| <= 1. Theses routines avoid the overflows that occur for the standard normalization of P_l^m(x). @@var{err} contains an estimate of the absolute error in the value @@var{y}. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hyperg_U -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{out} =} hyperg_U (@@var{x0}, @@var{x1}, @@var{x2}) @@deftypefnx {Loadable Function} {[@@var{out}, @@var{err}] =} hyperg_U (@@dots{}) @@var{err} contains an estimate of the absolute error in the value @@var{out}.a. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn hyperg_1F1 -*- texinfo -*- @@deftypefn {Loadable Function} {@@var{out} =} hyperg_1F1 (@@var{x0}, @@var{x1}, @@var{x2}) @@deftypefnx {Loadable Function} {[@@var{out}, @@var{err}] =} hyperg_1F1 (@@dots{}) @@var{err} contains an estimate of the absolute error in the value @@var{out}.a. This function is from the GNU Scientific Library, see @@url{http://www.gnu.org/software/gsl/} for documentation. @@end deftypefn @ gsl-1.0.8/doc/RCS/#mktexi#,v0000755000175000017500000003070111201030376013100 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @# @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @#!/usr/bin/env perl # # David Bateman Feb 02 2003 # # Extracts the help in texinfo format for particular function for use # in documentation. Based on make_index script from octave_forge. use strict; use File::Find; use File::Basename; use Text::Wrap; use FileHandle; use IPC::Open3; use POSIX ":sys_wait_h"; my $file = shift @@ARGV; my $docfile = shift @@ARGV; my $indexfile = shift @@ARGV; my $line; print("\input texinfo") if ( open(IN,$file) ) { $line = ; my $tex = 0; while ($line) { if ($line =~ /^\@@DOCSTRING/) { my $found = 0; my $func = $line; $func =~ s/\@@DOCSTRING\(//; $func =~ s/\)[\n\r]+//; my $func0 = $func; my $func1 = $func; $func0 =~ s/,.*$//; $func1 =~ s/^.*,//; if ( open(DOC,$docfile) ) { while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func0$/) { my $desc = ""; my $docline; my $doctex = 0; while (($docline = ) && ($docline !~ /^\037/)) { $docline =~ s/^\s*-[*]- texinfo -[*]-\s*//; if ($docline =~ /\@@tex/) { $doctex = 1; } if ($doctex) { $docline =~ s/\\\\/\\/g; } if ($docline =~ /\@@end tex/) { $doctex = 0; } $desc .= $docline; } $desc =~ s/$func0/$func1/g; $desc =~ s/\@@seealso\{(.*[^}])\}/See also: \1/g; print "$desc", "\n"; $found = 1; last; } } close (DOC); if (! $found) { print "\@@emph{Not implemented}\n"; } } else { print STDERR "Could not open file $docfile\n"; exit 1; } } elsif ($line =~ /^\@@REFERENCE_SECTION/) { my $secfound = 0; my $sec = $line; $sec =~ s/\@@REFERENCE_SECTION\(//; $sec =~ s/\)[\n\r]+//; my @@listfunc = (); my $nfunc = 0; my $seccat = 0; if ( open(IND,$indexfile) ) { while () { next unless /^[^ ]/; my $section = $_; $section =~ s/[\n\r]+//; if ($section =~ /^(.*?)\s*>>\s*(.*?)$/) { $section =~ s/.*>>(.*)/\1/; $seccat = 1; } $section =~ s/^ *//; $section =~ s/ *$//; if ($section =~ /^$sec$/) { if ($seccat) { print "\@@iftex\n"; print "\@@section Functions by Category\n"; # Get the list of categories to index my $firstcat = 1; my $category; while () { last if />>/; if (/^[^ ]/) { if (! $firstcat) { print "\@@end table\n"; } else { $firstcat = 0; } $category = $_; $category =~ s/[\n\r]+//; print "\@@subsection $category\n"; print "\@@table \@@asis\n"; } elsif (/^\s+(\S.*\S)\s*=\s*(\S.*\S)\s*$/) { my $func = $1; my $desc = $2; print "\@@item $func\n"; print "$desc\n"; print "\n"; } else { if ($firstcat) { print STDERR "Error parsing index file\n"; exit 1; } s/^\s+//; my @@funcs = split /\s+/; while ($#funcs >= 0) { my $func = shift @@funcs; $func =~ s/^ *//; $func =~ s/[\n\r]+//; push @@listfunc, $func; $nfunc = $nfunc + 1; print "\@@item $func\n"; print func_summary($func, $docfile); print "\n"; } } } if (! $firstcat) { print "\@@end table\n"; } print "\n\@@section Functions Alphabetically\n"; print "\@@end iftex\n\n"; } else { # Get the list of functions to index my $indline; while (($indline = ) && ($indline =~ /^ /)) { if ($indline =~ /^\s+(\S.*\S)\s*=\s*(\S.*\S)\s*$/) { next; } $indline =~ s/^\s+//; my @@funcs = split(/\s+/,$indline); while ($#funcs >= 0) { my $func = shift @@funcs; $func =~ s/^ *//; $func =~ s/[\n\r]+//; push @@listfunc, $func; $nfunc = $nfunc + 1; } } } $secfound = 1; last; } } close (IND); if (! $secfound) { print STDERR "Did not find section $sec\n"; } } else { print STDERR "Could not open file $indexfile\n"; exit 1; } @@listfunc = sort(@@listfunc); my @@listfunc2 = (); my $indent = 16 - 3; print "\@@menu\n"; foreach my $func (@@listfunc) { if ( open(DOC,$docfile) ) { my $found = 0; while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func$/) { $found = 1; last; } } close (DOC); if ($found) { push @@listfunc2, $func; my $func0 = "${func}::"; my $entry = sprintf("* %-*s %s",$indent,$func0,func_summary($func,$docfile)); print wrap("","\t\t","$entry"), "\n"; } } else { print STDERR "Could not open file $indexfile\n"; exit 1; } } print "\@@end menu\n"; my $up = "Function Reference"; my $next; my $prev; my $mfunc = 1; foreach my $func (@@listfunc2) { if ($mfunc == $nfunc) { $next = ""; } else { $next = @@listfunc2[$mfunc]; $mfunc = $mfunc + 1; } print "\n\@@node $func, $next, $prev, $up\n"; if ($seccat) { print "\@@subsection $func\n\n"; } else { print "\@@section $func\n\n"; } $prev = $func; my $found = 0; my $desc = ""; if ( open(DOC,$docfile) ) { while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func$/) { my $docline; my $doctex = 0; while (($docline = ) && ($docline !~ /^\037/)) { $docline =~ s/^\s*-[*]- texinfo -[*]-\s*//; if ($docline =~ /\@@tex/) { $doctex = 1; } if ($doctex) { $docline =~ s/\\\\/\\/g; } if ($docline =~ /\@@end tex/) { $doctex = 0; } $desc .= $docline; } $desc =~ s/\@@seealso\{(.*[^}])\}/See also: \1/g; print "$desc", "\n"; $found = 1; last; } } close (DOC); if (! $found) { print "\@@emph{Not implemented}\n"; } } else { print STDERR "Could not open file $docfile\n"; exit 1; } } } else { if ($line =~ /\@@tex/) { $tex = 1; } if ($tex) { $line =~ s/\\\\/\\/g; } print "$line"; if ($line =~ /\@@end tex/) { $tex = 0; } } $line = ; } } else { print STDERR "Could not open file $file\n"; exit 1; } print("@@bye") sub func_summary { # {{{1 my ($func, # in function name $docfile # in DOCSTRINGS ) = @@_; my $desc = ""; my $found = 0; if ( open(DOC,$docfile) ) { while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func$/) { my $docline; my $doctex = 0; while (($docline = ) && ($docline !~ /^\037/)) { if ($docline =~ /\@@tex/) { $doctex = 1; } if ($doctex) { $docline =~ s/\\\\/\\/g; } if ($docline =~ /\@@end tex/) { $doctex = 0; } $desc .= $docline; } $desc =~ s/\@@seealso\{(.*[^}])\}/See also: \1/g; $found = 1; last; } } close (DOC); if (! $found) { $desc = "\@@emph{Not implemented}"; } } else { print STDERR "Could not open file $docfile\n"; exit 1; } return first_sentence($desc); } # 1}}} sub first_sentence { # {{{1 # grab the first real sentence from the function documentation my ($desc) = @@_; my $retval = ''; my $line; my $next; my @@lines; my $trace = 0; # $trace = 1 if $desc =~ /Levenberg/; return "" unless defined $desc; if ($desc =~ /^\s*-[*]- texinfo -[*]-/) { # help text contains texinfo. Strip the indicator and run it # through makeinfo. (XXX FIXME XXX this needs to be a function) $desc =~ s/^\s*-[*]- texinfo -[*]-\s*//; my $cmd = "makeinfo --fill-column 1600 --no-warn --no-validate --no-headers --force --ifinfo"; open3(*Writer, *Reader, *Errer, $cmd) or die "Could not run info"; print Writer "\@@macro seealso {args}\n\n\@@noindent\nSee also: \\args\\.\n\@@end macro\n"; print Writer "$desc"; close(Writer); @@lines = ; close(Reader); my @@err = ; close(Errer); waitpid(-1,&WNOHANG); # Display source and errors, if any if (@@err) { my $n = 1; foreach $line ( split(/\n/,$desc) ) { printf "%2d: %s\n",$n++,$line; } print ">>> @@err"; } # Print trace showing formatted output # print "\n"; # Skip prototype and blank lines while (1) { return "" unless @@lines; $line = shift @@lines; next if $line =~ /^\s*-/; next if $line =~ /^\s*$/; last; } } else { # print "\n"; # Skip prototype and blank lines @@lines = split(/\n/,$desc); while (1) { return "" if ($#lines < 0); $line = shift @@lines; next if $line =~ /^\s*[Uu][Ss][Aa][Gg][Ee]/; # skip " usage " $line =~ s/^\s*\w+\s*://; # chop " blah : " print "strip blah: $line\n" if $trace; $line =~ s/^\s*[Ff]unction\s+//; # chop " function " print "strip function $line\n" if $trace; $line =~ s/^\s*\[.*\]\s*=\s*//; # chop " [a,b] = " print "strip []= $line\n" if $trace; $line =~ s/^\s*\w+\s*=\s*//; # chop " a = " print "strip a= $line\n" if $trace; $line =~ s/^\s*\w+\s*\([^\)]*\)\s*//; # chop " f(x) " print "strip f(x) $line\n" if $trace; $line =~ s/^\s*[;:]\s*//; # chop " ; " print "strip ; $line\n" if $trace; $line =~ s/^\s*[[:upper:]][[:upper:]0-9_]+//; # chop " BLAH" print "strip BLAH $line\n" if $trace; $line =~ s/^\s*\w*\s*[-]+\s+//; # chop " blah --- " print "strip blah --- $line\n" if $trace; $line =~ s/^\s*\w+ *\t\s*//; # chop " blah " print "strip blah $line\n" if $trace; $line =~ s/^\s*\w+\s\s+//; # chop " blah " print "strip blah $line\n" if $trace; # next if $line =~ /^\s*\[/; # skip [a,b] = f(x) # next if $line =~ /^\s*\w+\s*(=|\()/; # skip a = f(x) OR f(x) next if $line =~ /^\s*or\s*$/; # skip blah \n or \n blah next if $line =~ /^\s*$/; # skip blank line next if $line =~ /^\s?!\//; # skip # !/usr/bin/octave # XXX FIXME XXX should be testing for unmatched () in proto # before going to the next line! last; } } # Try to make a complete sentence, including the '.' if ( "$line " !~ /[^.][.]\s/ && $#lines >= 0) { my $next = $lines[0]; $line =~ s/\s*$//; # trim trailing blanks on last $next =~ s/^\s*//; # trim leading blanks on next $line .= " $next" if "$next " =~ /[^.][.]\s/; # ends the sentence } # Tidy up the sentence. chomp $line; # trim trailing newline, if there is one $line =~ s/^\s*//; # trim leading blanks on line $line =~ s/([^.][.])\s.*$/$1/; # trim everything after the sentence print "Skipping:\n$desc---\n" if $line eq ""; # And return it. return $line; } # 1}}} __END__ This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, see . This program is granted to the public domain. THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. @ gsl-1.0.8/doc/RCS/mktexi,v0000644000175000017500000003105711201030376012774 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @# @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @#!/usr/bin/env perl # # David Bateman Feb 02 2003 # # Extracts the help in texinfo format for particular function for use # in documentation. Based on make_index script from octave_forge. use strict; use File::Find; use File::Basename; use Text::Wrap; use FileHandle; use IPC::Open3; use POSIX ":sys_wait_h"; my $file = shift @@ARGV; my $docfile = shift @@ARGV; my $indexfile = shift @@ARGV; my $line; print("\\input texinfo \n"); print("\@@ifnottex \n"); print("\@@node Top \n"); print("print("\@@top Octave gsl \n"); @@end ifnottex if ( open(IN,$file) ) { $line = ; my $tex = 0; while ($line) { if ($line =~ /^\@@DOCSTRING/) { my $found = 0; my $func = $line; $func =~ s/\@@DOCSTRING\(//; $func =~ s/\)[\n\r]+//; my $func0 = $func; my $func1 = $func; $func0 =~ s/,.*$//; $func1 =~ s/^.*,//; if ( open(DOC,$docfile) ) { while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func0$/) { my $desc = ""; my $docline; my $doctex = 0; while (($docline = ) && ($docline !~ /^\037/)) { $docline =~ s/^\s*-[*]- texinfo -[*]-\s*//; if ($docline =~ /\@@tex/) { $doctex = 1; } if ($doctex) { $docline =~ s/\\\\/\\/g; } if ($docline =~ /\@@end tex/) { $doctex = 0; } $desc .= $docline; } $desc =~ s/$func0/$func1/g; $desc =~ s/\@@seealso\{(.*[^}])\}/See also: \1/g; print "$desc", "\n"; $found = 1; last; } } close (DOC); if (! $found) { print "\@@emph{Not implemented}\n"; } } else { print STDERR "Could not open file $docfile\n"; exit 1; } } elsif ($line =~ /^\@@REFERENCE_SECTION/) { my $secfound = 0; my $sec = $line; $sec =~ s/\@@REFERENCE_SECTION\(//; $sec =~ s/\)[\n\r]+//; my @@listfunc = (); my $nfunc = 0; my $seccat = 0; if ( open(IND,$indexfile) ) { while () { next unless /^[^ ]/; my $section = $_; $section =~ s/[\n\r]+//; if ($section =~ /^(.*?)\s*>>\s*(.*?)$/) { $section =~ s/.*>>(.*)/\1/; $seccat = 1; } $section =~ s/^ *//; $section =~ s/ *$//; if ($section =~ /^$sec$/) { if ($seccat) { print "\@@iftex\n"; print "\@@section Functions by Category\n"; # Get the list of categories to index my $firstcat = 1; my $category; while () { last if />>/; if (/^[^ ]/) { if (! $firstcat) { print "\@@end table\n"; } else { $firstcat = 0; } $category = $_; $category =~ s/[\n\r]+//; print "\@@subsection $category\n"; print "\@@table \@@asis\n"; } elsif (/^\s+(\S.*\S)\s*=\s*(\S.*\S)\s*$/) { my $func = $1; my $desc = $2; print "\@@item $func\n"; print "$desc\n"; print "\n"; } else { if ($firstcat) { print STDERR "Error parsing index file\n"; exit 1; } s/^\s+//; my @@funcs = split /\s+/; while ($#funcs >= 0) { my $func = shift @@funcs; $func =~ s/^ *//; $func =~ s/[\n\r]+//; push @@listfunc, $func; $nfunc = $nfunc + 1; print "\@@item $func\n"; print func_summary($func, $docfile); print "\n"; } } } if (! $firstcat) { print "\@@end table\n"; } print "\n\@@section Functions Alphabetically\n"; print "\@@end iftex\n\n"; } else { # Get the list of functions to index my $indline; while (($indline = ) && ($indline =~ /^ /)) { if ($indline =~ /^\s+(\S.*\S)\s*=\s*(\S.*\S)\s*$/) { next; } $indline =~ s/^\s+//; my @@funcs = split(/\s+/,$indline); while ($#funcs >= 0) { my $func = shift @@funcs; $func =~ s/^ *//; $func =~ s/[\n\r]+//; push @@listfunc, $func; $nfunc = $nfunc + 1; } } } $secfound = 1; last; } } close (IND); if (! $secfound) { print STDERR "Did not find section $sec\n"; } } else { print STDERR "Could not open file $indexfile\n"; exit 1; } @@listfunc = sort(@@listfunc); my @@listfunc2 = (); my $indent = 16 - 3; print "\@@menu\n"; foreach my $func (@@listfunc) { if ( open(DOC,$docfile) ) { my $found = 0; while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func$/) { $found = 1; last; } } close (DOC); if ($found) { push @@listfunc2, $func; my $func0 = "${func}::"; my $entry = sprintf("* %-*s %s",$indent,$func0,func_summary($func,$docfile)); print wrap("","\t\t","$entry"), "\n"; } } else { print STDERR "Could not open file $indexfile\n"; exit 1; } } print "\@@end menu\n"; my $up = "Function Reference"; my $next; my $prev; my $mfunc = 1; foreach my $func (@@listfunc2) { if ($mfunc == $nfunc) { $next = ""; } else { $next = @@listfunc2[$mfunc]; $mfunc = $mfunc + 1; } print "\n\@@node $func, $next, $prev, $up\n"; if ($seccat) { print "\@@subsection $func\n\n"; } else { print "\@@section $func\n\n"; } $prev = $func; my $found = 0; my $desc = ""; if ( open(DOC,$docfile) ) { while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func$/) { my $docline; my $doctex = 0; while (($docline = ) && ($docline !~ /^\037/)) { $docline =~ s/^\s*-[*]- texinfo -[*]-\s*//; if ($docline =~ /\@@tex/) { $doctex = 1; } if ($doctex) { $docline =~ s/\\\\/\\/g; } if ($docline =~ /\@@end tex/) { $doctex = 0; } $desc .= $docline; } $desc =~ s/\@@seealso\{(.*[^}])\}/See also: \1/g; print "$desc", "\n"; $found = 1; last; } } close (DOC); if (! $found) { print "\@@emph{Not implemented}\n"; } } else { print STDERR "Could not open file $docfile\n"; exit 1; } } } else { if ($line =~ /\@@tex/) { $tex = 1; } if ($tex) { $line =~ s/\\\\/\\/g; } print "$line"; if ($line =~ /\@@end tex/) { $tex = 0; } } $line = ; } } else { print STDERR "Could not open file $file\n"; exit 1; }; print("\@@bye"); sub func_summary { # {{{1 my ($func, # in function name $docfile # in DOCSTRINGS ) = @@_; my $desc = ""; my $found = 0; if ( open(DOC,$docfile) ) { while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func$/) { my $docline; my $doctex = 0; while (($docline = ) && ($docline !~ /^\037/)) { if ($docline =~ /\@@tex/) { $doctex = 1; } if ($doctex) { $docline =~ s/\\\\/\\/g; } if ($docline =~ /\@@end tex/) { $doctex = 0; } $desc .= $docline; } $desc =~ s/\@@seealso\{(.*[^}])\}/See also: \1/g; $found = 1; last; } } close (DOC); if (! $found) { $desc = "\@@emph{Not implemented}"; } } else { print STDERR "Could not open file $docfile\n"; exit 1; } return first_sentence($desc); } # 1}}} sub first_sentence { # {{{1 # grab the first real sentence from the function documentation my ($desc) = @@_; my $retval = ''; my $line; my $next; my @@lines; my $trace = 0; # $trace = 1 if $desc =~ /Levenberg/; return "" unless defined $desc; if ($desc =~ /^\s*-[*]- texinfo -[*]-/) { # help text contains texinfo. Strip the indicator and run it # through makeinfo. (XXX FIXME XXX this needs to be a function) $desc =~ s/^\s*-[*]- texinfo -[*]-\s*//; my $cmd = "makeinfo --fill-column 1600 --no-warn --no-validate --no-headers --force --ifinfo"; open3(*Writer, *Reader, *Errer, $cmd) or die "Could not run info"; print Writer "\@@macro seealso {args}\n\n\@@noindent\nSee also: \\args\\.\n\@@end macro\n"; print Writer "$desc"; close(Writer); @@lines = ; close(Reader); my @@err = ; close(Errer); waitpid(-1,&WNOHANG); # Display source and errors, if any if (@@err) { my $n = 1; foreach $line ( split(/\n/,$desc) ) { printf "%2d: %s\n",$n++,$line; } print ">>> @@err"; } # Print trace showing formatted output # print "\n"; # Skip prototype and blank lines while (1) { return "" unless @@lines; $line = shift @@lines; next if $line =~ /^\s*-/; next if $line =~ /^\s*$/; last; } } else { # print "\n"; # Skip prototype and blank lines @@lines = split(/\n/,$desc); while (1) { return "" if ($#lines < 0); $line = shift @@lines; next if $line =~ /^\s*[Uu][Ss][Aa][Gg][Ee]/; # skip " usage " $line =~ s/^\s*\w+\s*://; # chop " blah : " print "strip blah: $line\n" if $trace; $line =~ s/^\s*[Ff]unction\s+//; # chop " function " print "strip function $line\n" if $trace; $line =~ s/^\s*\[.*\]\s*=\s*//; # chop " [a,b] = " print "strip []= $line\n" if $trace; $line =~ s/^\s*\w+\s*=\s*//; # chop " a = " print "strip a= $line\n" if $trace; $line =~ s/^\s*\w+\s*\([^\)]*\)\s*//; # chop " f(x) " print "strip f(x) $line\n" if $trace; $line =~ s/^\s*[;:]\s*//; # chop " ; " print "strip ; $line\n" if $trace; $line =~ s/^\s*[[:upper:]][[:upper:]0-9_]+//; # chop " BLAH" print "strip BLAH $line\n" if $trace; $line =~ s/^\s*\w*\s*[-]+\s+//; # chop " blah --- " print "strip blah --- $line\n" if $trace; $line =~ s/^\s*\w+ *\t\s*//; # chop " blah " print "strip blah $line\n" if $trace; $line =~ s/^\s*\w+\s\s+//; # chop " blah " print "strip blah $line\n" if $trace; # next if $line =~ /^\s*\[/; # skip [a,b] = f(x) # next if $line =~ /^\s*\w+\s*(=|\()/; # skip a = f(x) OR f(x) next if $line =~ /^\s*or\s*$/; # skip blah \n or \n blah next if $line =~ /^\s*$/; # skip blank line next if $line =~ /^\s?!\//; # skip # !/usr/bin/octave # XXX FIXME XXX should be testing for unmatched () in proto # before going to the next line! last; } } # Try to make a complete sentence, including the '.' if ( "$line " !~ /[^.][.]\s/ && $#lines >= 0) { my $next = $lines[0]; $line =~ s/\s*$//; # trim trailing blanks on last $next =~ s/^\s*//; # trim leading blanks on next $line .= " $next" if "$next " =~ /[^.][.]\s/; # ends the sentence } # Tidy up the sentence. chomp $line; # trim trailing newline, if there is one $line =~ s/^\s*//; # trim leading blanks on line $line =~ s/([^.][.])\s.*$/$1/; # trim everything after the sentence print "Skipping:\n$desc---\n" if $line eq ""; # And return it. return $line; } # 1}}} __END__ This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, see . This program is granted to the public domain. THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. @ gsl-1.0.8/doc/RCS/mk_pdf_dvi~,v0000755000175000017500000000050211201030376013765 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @# @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @./mkdoc >$1.doc ./mktexi_inc $1.doc >$1.texi tex -interaction batchmode $1.texi texi2pdf -b $1.texi dvips -o $1.ps $1.dvi @ gsl-1.0.8/doc/RCS/mkdoc,v0000755000175000017500000001267611201030376012601 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @# @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @#!/usr/bin/env perl # # David Bateman Feb 02 2003 # # Extracts the help in texinfo format from *.cc and *.m files for use # in documentation. Based on make_index script from octave_forge. use strict; use File::Find; use File::Basename; use FileHandle; my $docdir = "."; if (@@ARGV) { $docdir = @@ARGV[0]; } # locate all C++ and m-files in current directory my @@m_files = (); my @@C_files = (); find(\&cc_and_m_files, $docdir); sub cc_and_m_files { # {{{1 populates global array @@files return unless -f and /\.(m|cc)$/; # .m and .cc files my $path = "$File::Find::dir/$_"; $path =~ s|^[.]/||; if (/\.m$/) { push @@m_files, $path; } else { push @@C_files, $path; } } # 1}}} # grab help from C++ files foreach my $f ( @@C_files ) { # XXX FIXME XXX. Should run the preprocessor over the file first, since # the help might include defines that are compile dependent. if ( open(IN,$f) ) { while () { # skip to the next function next unless /^DEFUN_DLD/; # extract function name to pattern space /\((\w*)\s*,/; # remember function name my $function = $1; # skip to next line if comment doesn't start on this line # XXX FIXME XXX maybe we want a loop here? $_ = unless /\"/; # skip to the beginning of the comment string by # chopping everything up to opening " my $desc = $_; $desc =~ s/^[^\"]*\"//; # join lines until you get the end of the comment string # plus a bit more. You need the "plus a bit more" because # C compilers allow implicitly concatenated string constants # "A" "B" ==> "AB". while ($desc !~ /[^\\]\"\s*\S/ && $desc !~ /^\"/) { # if line ends in '\', chop it and the following '\n' $desc =~ s/\\\s*\n//; # join with the next line $desc .= ; # eliminate consecutive quotes, being careful to ignore # preceding slashes. XXX FIXME XXX what about \\" ? $desc =~ s/([^\\])\"\s*\"/$1/; } $desc = "" if $desc =~ /^\"/; # chop everything if it was "" $desc =~ s/\\n/\n/g; # insert fake line ends $desc =~ s/([^\"])\".*$/$1/; # chop everything after final '"' $desc =~ s/\\\"/\"/; # convert \"; XXX FIXME XXX \\" $desc =~ s/$//g; # chop trailing ... if (!($desc =~ /^\s*-[*]- texinfo -[*]-/)) { my $err = sprintf("Function %s, does not contain texinfo help\n", $function); print STDERR "$err"; } my $entry = sprintf("\037%s\n%s", $function, $desc); print "$entry", "\n"; } close (IN); } else { print STDERR "Could not open file ($f): $!\n"; } } # grab help from m-files foreach my $f ( @@m_files ) { my $desc = extract_description($f); my $function = basename($f, ('.m')); die "Null function?? [$f]\n" unless $function; if (!($desc =~ /^\s*-[*]- texinfo -[*]-/)) { my $err = sprintf("Function %s, does not contain texinfo help\n", $function); print STDERR "$err"; } my $entry = sprintf("\037%s\n%s", $function, $desc); print "$entry", "\n"; } sub extract_description { # {{{1 # grab the entire documentation comment from an m-file my ($file) = @@_; my $retval = ''; if( open( IN, "$file")) { # skip leading blank lines while () { last if /\S/; } if( m/\s*[%\#][\s\#%]* Copyright/) { # next block is copyright statement, skip it while () { last unless /^\s*[%\#]/; } } # Skip everything until the next comment block while ( !/^\s*[\#%]/ ) { $_ = ; last if not defined $_; } # Return the next comment block as the documentation while (/^\s*[\#%]/) { s/^[\s%\#]*//; # strip leading comment characters s/[\cM\s]*$//; # strip trailing spaces. s/[\.*]$//; $retval .= "$_\n"; $_ = ; last if not defined $_; } close(IN); return $retval; } else { print STDERR "Could not open file ($file): $!\n"; } } # 1}}} __END__ This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, see . This program is granted to the public domain. THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. @ gsl-1.0.8/doc/RCS/mk.tgz,v0000755000175000017500000001306711201030376012711 0ustar shshhead 1.1; access; symbols; locks rrogers:1.1; strict; comment @# @; 1.1 date 2008.06.11.13.20.31; author rrogers; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @‹%a(Hí;sÚH²û¯ùÙYÁ€ÚÝz8Á€ªð¼I aNˆÁè'‰8TÖ÷Ù_÷üÒHlïÕÞÕÕ3åÂÒLOwOwOOwÏ°øÒïÎOé§ Ÿß~ù…ý‡OâÿëòÉɯ?—OÊ¿–O^¿þ©|\þí·“ŸHù¯e‹VAhù„üä{^¸ î¡þÿÒÏþ‹Ò*ðKcÇ-Q÷YRžÙÏ쓆õÍ™3+¤ Ë%çtLÊ'ä´}ð×üú–$œQ2£ó%q\‚–äN=2õü…â?²´üбWsñtåڡ㹬}PÀc&ž½ZP7´°«:!´°¾Ò‘ãNèwؾ³t¾· žZßèPÜÒb&hHúŽVÙó¹3§•Ê9ŒÓß©k-(oëÓïa¥òÉ·–ÌËÌEëª^©t–Ô}Í߯:½ÖgbT‚u0º³œp43ª™ÌbM¦0’¼%ÁÌ™†ä}­{ñ{•µÃœ¶u±mëœ;.ðq¦$K<` Ûj‘É‘Â!`ä›Vû´ ï8„-e|½›!â,ƒâAdbØ?IéÆ|ßèÔ{ýn«}Q’ ÏÔ[¹‰I5‚ΠMpÆÛEã?IPÒ°™ÙR) "70]Ó¾Šz%Þ2"ƇdÇq²C‚#ÂB1 tÌ{nŠùBÔ X,H•pAî A½®SÖ@@ˆ VAVîœ)™å׿¦½ˆ'f¸ÀÖˆµjMl’^JëÑ&¿'t¡”nøÔJ‚ NpB”ºaTµ6ÏæJÐ[”îY£˜UV¢¡ðþü3‰Z_0;@@–sŠ*!Ñ &K3È òÃ#µ¦Ù´Š©(ÓÒ†94ŸÊ^ÄÞ±pŸ tDÝ„|•n·ÔhR0Û4ºåÍÑ\²Å·Iq !xdë…ÿ;VŒhæû€Rkxæl1?¸¹æÌûRR‚bF£–¾ã†Ä`ƒ1LW*V-:)£¹„ìñ^˜1ãÍž{à‡ÐsЉ"x!†  ‹Årö£í…ÄY,çý*Üszã=¡sÀãø¨^¿Ñìv‰Q÷Vó qa,®Â|”\6XBˆœJ¾¶ Ómž7»Ív½9ê5ëýV§ð5µSÝ ´oxÖÆ%¾6æt"ÀTŸó~î¡ðgÙœNÕ­IVlØÃXë†Kiµ…È•'œ t¦:•›Á F^$œŠjÙâ9´þÒ Ý»¬ÇÓSøb/š‰£*@@äJ`“Õ€OïX˜Û7D®õx;áþ7•)|ÓØ@@Ió4ÊXa÷£ß£Å õH¤çÂWd¼&uˆEn=­Ø'4d1j—xSbs(‡Bhâ¦# Ì·l?õ™Ë1n­7Ô¹‡‹çT:=E°…(´ {Чü""ÃÆæÆÜ•5–‹jO_‘Â)D<–ûV­ &1Pº4ñðJNk·àe/6Ž‚Õbaùk°ÔVK"RVŒjIݯ“ëAîlÛ–D…"”æjóåÌSÈ1¬ù|êL»p5Qd@@ÛÉTÑHó#РÅZì%:xÞ±—jE/IDàÅH¼ë‘k ÷•*—÷žŽ@@·× kÍ2k-Hx¦ÈV»ÓfÓ-v»½î°Ö-¶š4¥ûhãÚ4íEÑH_‹–ä°XÀ$}CÃáÏDC”Ÿ„‡!rRÑAzì$ô $ðü0«ri¡ËÉFì‚d\¶›ýJŽÈkÙ¥ŒBÀ〷CÞL-{)W#ˆÛ™5m䉑ÛÓ3©­¹Ô¶ljW>õ@@Fµ=§Ò”8[3aZì+hKäšÝ$-ù$2e}~˜Ú?ðñ¾RÑÓ8PÛ¿¦¡iÖÈ“—Gù€¼ Œ‚Pf£(¤xa¥\,µ¸ó­eÖ0 †š!üãTŒœ–kàÒÐ\ÞÓ XÛïc@@ÂÓ*ƒÓŒtµDyH§MºtJ}êÚÔˆEá̧EïKŸ~Óßb™?–O”1ËaÒ½=2j2ÅÖ#;"TŽbÈCaÉ…xx%²§mR®7¡D®À'S@@ApanÆ©‘ßœ…ÚО'Ç!3{Œ^TEÙK®Ûd‘áeÿß±È7«$[ê$ºR²÷¤"ÉÞÎú!ñ ÛË7ê"ɺŒ^‰ØZ! ð˜aKd£TòÔRÇ®bÇ¿æ†ÇÕu¥éI_l›OÕ g$ñU–± ßÌpïïaeò¥ƒ‹ç>¹õ­1˃àµæDÁ±#8Ö)í3v|—«BÐkS.`ñ {K£Æ¨ÔyÖãÒ@@’ì¤Ë·l¹²ý¨åÕ¡ì tI¿QwLý[±¨„p C®ã …TNøHŸ†-[;7Ð}~à¢c°=˜»ƒEW$¤úÎ’I BhB<Ï'Ø™¿r‰âðpæ{«Û;ã䃲Ÿ?&ç­Ï›ŸÂ™€ã¡V|ƒù*‰çbÿ@@ › 4qCÒ"GG`Fó#Û›¯.¤å24¹ÞÑ"bO %gb…”¿Í¨5¡~€ã<ßÆFgŠˆp_Dó|Íòú’ï2Xxhú>þGâ9óŸ8T7k& ƒ›>GÁ2VËö="Ö1ùaù·Á=†¶XóÉtµm"€i€å8œïÚqÌ<"©ò•œå­^p3C?ɹ?• ü5ÇÅøžú>°‰)ö†x.¼t&Ù£ãÂÏŸÚµö4£®N°œ[kÈîW(=4Š¥È €&g¹k}#þØ «…I2ÓáÛuV•sÜRA¬4ëñœ’/O&È(A …÷Õ«ÂÁæQ—ˆ#NOOÙÔxÞ€ü^±¾°‚™w‡ÕR~žâÁü*\®Â̾ÌwÞ³;zàÃ"GÉ…­°<4Z9åy%0Ùû +lé{¡®—\¨ã¹å~% ³Ú•D7<€äaOƒDKïb»?:½F—?*íì>Ý"ºååñ5ùm8'|Ö£…Ç(<^tj9lYu§\™ÿÜçƒßrîÏŠvp½zÁpP³†ƒ‹Ûá I‡¥*8ûýÖ-ø’L ½t…æÝ+ø®€ï#úgŸØ3ÃLg¤£õ50]ŽdÅøb‹ šJhp> ‡Ì ® BjL#¥:KÍóæP„£É)j«0¢“O!6¾}<&¾8Žµ…†õTfvpcæ†y3'hE‚ËB$™*4ìx´zª•ar‰¹TS©TSI¤ÓTVË%õ+ÃaôX>úŸ æ#Bg—µi¤°ý bË#É£á+ÝÜ’– «}«m³Î'h‰äÍp«!0„oúµ³Óíôx÷“ì">·MŠ;ˆµ/ÓiŸÜîkÌAŒšð1j9¡ÉíÏŒ9ûö3›‹|”%†’N—£ØÁóùvc€ÍÈt1n‚o|{`³!›“ˆ|úŽ±ï^˜ ý²±û$ºÈïÛqû$¥Bx€„§! 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notation---the left quote is % in some cases the escape char. \chardef\colonChar = `\: \chardef\commaChar = `\, \chardef\dotChar = `\. \chardef\exclamChar= `\! \chardef\questChar = `\? \chardef\semiChar = `\; \chardef\underChar = `\_ \chardef\spaceChar = `\ % \chardef\spacecat = 10 \def\spaceisspace{\catcode\spaceChar=\spacecat} % Ignore a token. % \def\gobble#1{} % The following is used inside several \edef's. \def\makecsname#1{\expandafter\noexpand\csname#1\endcsname} % Hyphenation fixes. \hyphenation{ Flor-i-da Ghost-script Ghost-view Mac-OS Post-Script ap-pen-dix bit-map bit-maps data-base data-bases eshell fall-ing half-way long-est man-u-script man-u-scripts mini-buf-fer mini-buf-fers over-view par-a-digm par-a-digms rath-er rec-tan-gu-lar ro-bot-ics se-vere-ly set-up spa-ces spell-ing spell-ings stand-alone strong-est time-stamp time-stamps which-ever white-space wide-spread wrap-around } % Margin to add to right of even pages, to left of odd pages. \newdimen\bindingoffset \newdimen\normaloffset \newdimen\pagewidth \newdimen\pageheight % For a final copy, take out the rectangles % that mark overfull boxes (in case you have decided % that the text looks ok even though it passes the margin). % \def\finalout{\overfullrule=0pt} % @| inserts a changebar to the left of the current line. It should % surround any changed text. This approach does *not* work if the % change spans more than two lines of output. To handle that, we would % have adopt a much more difficult approach (putting marks into the main % vertical list for the beginning and end of each change). % \def\|{% % \vadjust can only be used in horizontal mode. \leavevmode % % Append this vertical mode material after the current line in the output. \vadjust{% % We want to insert a rule with the height and depth of the current % leading; that is exactly what \strutbox is supposed to record. \vskip-\baselineskip % % \vadjust-items are inserted at the left edge of the type. So % the \llap here moves out into the left-hand margin. \llap{% % % For a thicker or thinner bar, change the `1pt'. \vrule height\baselineskip width1pt % % This is the space between the bar and the text. \hskip 12pt }% }% } % Sometimes it is convenient to have everything in the transcript file % and nothing on the terminal. We don't just call \tracingall here, % since that produces some useless output on the terminal. We also make % some effort to order the tracing commands to reduce output in the log % file; cf. trace.sty in LaTeX. % \def\gloggingall{\begingroup \globaldefs = 1 \loggingall \endgroup}% \def\loggingall{% \tracingstats2 \tracingpages1 \tracinglostchars2 % 2 gives us more in etex \tracingparagraphs1 \tracingoutput1 \tracingmacros2 \tracingrestores1 \showboxbreadth\maxdimen \showboxdepth\maxdimen \ifx\eTeXversion\undefined\else % etex gives us more logging \tracingscantokens1 \tracingifs1 \tracinggroups1 \tracingnesting2 \tracingassigns1 \fi \tracingcommands3 % 3 gives us more in etex \errorcontextlines16 }% % add check for \lastpenalty to plain's definitions. If the last thing % we did was a \nobreak, we don't want to insert more space. % \def\smallbreak{\ifnum\lastpenalty<10000\par\ifdim\lastskip<\smallskipamount \removelastskip\penalty-50\smallskip\fi\fi} \def\medbreak{\ifnum\lastpenalty<10000\par\ifdim\lastskip<\medskipamount \removelastskip\penalty-100\medskip\fi\fi} \def\bigbreak{\ifnum\lastpenalty<10000\par\ifdim\lastskip<\bigskipamount \removelastskip\penalty-200\bigskip\fi\fi} % For @cropmarks command. % Do @cropmarks to get crop marks. % \newif\ifcropmarks \let\cropmarks = \cropmarkstrue % % Dimensions to add cropmarks at corners. % Added by P. A. MacKay, 12 Nov. 1986 % \newdimen\outerhsize \newdimen\outervsize % set by the paper size routines \newdimen\cornerlong \cornerlong=1pc \newdimen\cornerthick \cornerthick=.3pt \newdimen\topandbottommargin \topandbottommargin=.75in % Main output routine. \chardef\PAGE = 255 \output = {\onepageout{\pagecontents\PAGE}} \newbox\headlinebox \newbox\footlinebox % \onepageout takes a vbox as an argument. Note that \pagecontents % does insertions, but you have to call it yourself. \def\onepageout#1{% \ifcropmarks \hoffset=0pt \else \hoffset=\normaloffset \fi % \ifodd\pageno \advance\hoffset by \bindingoffset \else \advance\hoffset by -\bindingoffset\fi % % Do this outside of the \shipout so @code etc. will be expanded in % the headline as they should be, not taken literally (outputting ''code). \setbox\headlinebox = \vbox{\let\hsize=\pagewidth \makeheadline}% \setbox\footlinebox = \vbox{\let\hsize=\pagewidth \makefootline}% % {% % Have to do this stuff outside the \shipout because we want it to % take effect in \write's, yet the group defined by the \vbox ends % before the \shipout runs. % \escapechar = `\\ % use backslash in output files. \indexdummies % don't expand commands in the output. \normalturnoffactive % \ in index entries must not stay \, e.g., if % the page break happens to be in the middle of an example. \shipout\vbox{% % Do this early so pdf references go to the beginning of the page. \ifpdfmakepagedest \pdfdest name{\the\pageno} xyz\fi % \ifcropmarks \vbox to \outervsize\bgroup \hsize = \outerhsize \vskip-\topandbottommargin \vtop to0pt{% \line{\ewtop\hfil\ewtop}% \nointerlineskip \line{% \vbox{\moveleft\cornerthick\nstop}% \hfill \vbox{\moveright\cornerthick\nstop}% }% \vss}% \vskip\topandbottommargin \line\bgroup \hfil % center the page within the outer (page) hsize. \ifodd\pageno\hskip\bindingoffset\fi \vbox\bgroup \fi % \unvbox\headlinebox \pagebody{#1}% \ifdim\ht\footlinebox > 0pt % Only leave this space if the footline is nonempty. % (We lessened \vsize for it in \oddfootingxxx.) % The \baselineskip=24pt in plain's \makefootline has no effect. \vskip 2\baselineskip \unvbox\footlinebox \fi % \ifcropmarks \egroup % end of \vbox\bgroup \hfil\egroup % end of (centering) \line\bgroup \vskip\topandbottommargin plus1fill minus1fill \boxmaxdepth = \cornerthick \vbox to0pt{\vss \line{% \vbox{\moveleft\cornerthick\nsbot}% \hfill \vbox{\moveright\cornerthick\nsbot}% }% \nointerlineskip \line{\ewbot\hfil\ewbot}% }% \egroup % \vbox from first cropmarks clause \fi }% end of \shipout\vbox }% end of group with \normalturnoffactive \advancepageno \ifnum\outputpenalty>-20000 \else\dosupereject\fi } \newinsert\margin \dimen\margin=\maxdimen \def\pagebody#1{\vbox to\pageheight{\boxmaxdepth=\maxdepth #1}} {\catcode`\@ =11 \gdef\pagecontents#1{\ifvoid\topins\else\unvbox\topins\fi % marginal hacks, juha@viisa.uucp (Juha Takala) \ifvoid\margin\else % marginal info is present \rlap{\kern\hsize\vbox to\z@{\kern1pt\box\margin \vss}}\fi \dimen@=\dp#1 \unvbox#1 \ifvoid\footins\else\vskip\skip\footins\footnoterule \unvbox\footins\fi \ifr@ggedbottom \kern-\dimen@ \vfil \fi} } % Here are the rules for the cropmarks. Note that they are % offset so that the space between them is truly \outerhsize or \outervsize % (P. A. MacKay, 12 November, 1986) % \def\ewtop{\vrule height\cornerthick depth0pt width\cornerlong} \def\nstop{\vbox {\hrule height\cornerthick depth\cornerlong width\cornerthick}} \def\ewbot{\vrule height0pt depth\cornerthick width\cornerlong} \def\nsbot{\vbox {\hrule height\cornerlong depth\cornerthick width\cornerthick}} % Parse an argument, then pass it to #1. The argument is the rest of % the input line (except we remove a trailing comment). #1 should be a % macro which expects an ordinary undelimited TeX argument. % \def\parsearg{\parseargusing{}} \def\parseargusing#1#2{% \def\next{#2}% \begingroup \obeylines \spaceisspace #1% \parseargline\empty% Insert the \empty token, see \finishparsearg below. } {\obeylines % \gdef\parseargline#1^^M{% \endgroup % End of the group started in \parsearg. \argremovecomment #1\comment\ArgTerm% }% } % First remove any @comment, then any @c comment. \def\argremovecomment#1\comment#2\ArgTerm{\argremovec #1\c\ArgTerm} \def\argremovec#1\c#2\ArgTerm{\argcheckspaces#1\^^M\ArgTerm} % Each occurence of `\^^M' or `\^^M' is replaced by a single space. % % \argremovec might leave us with trailing space, e.g., % @end itemize @c foo % This space token undergoes the same procedure and is eventually removed % by \finishparsearg. % \def\argcheckspaces#1\^^M{\argcheckspacesX#1\^^M \^^M} \def\argcheckspacesX#1 \^^M{\argcheckspacesY#1\^^M} \def\argcheckspacesY#1\^^M#2\^^M#3\ArgTerm{% \def\temp{#3}% \ifx\temp\empty % We cannot use \next here, as it holds the macro to run; % thus we reuse \temp. \let\temp\finishparsearg \else \let\temp\argcheckspaces \fi % Put the space token in: \temp#1 #3\ArgTerm } % If a _delimited_ argument is enclosed in braces, they get stripped; so % to get _exactly_ the rest of the line, we had to prevent such situation. % We prepended an \empty token at the very beginning and we expand it now, % just before passing the control to \next. % (Similarily, we have to think about #3 of \argcheckspacesY above: it is % either the null string, or it ends with \^^M---thus there is no danger % that a pair of braces would be stripped. % % But first, we have to remove the trailing space token. % \def\finishparsearg#1 \ArgTerm{\expandafter\next\expandafter{#1}} % \parseargdef\foo{...} % is roughly equivalent to % \def\foo{\parsearg\Xfoo} % \def\Xfoo#1{...} % % Actually, I use \csname\string\foo\endcsname, ie. \\foo, as it is my % favourite TeX trick. --kasal, 16nov03 \def\parseargdef#1{% \expandafter \doparseargdef \csname\string#1\endcsname #1% } \def\doparseargdef#1#2{% \def#2{\parsearg#1}% \def#1##1% } % Several utility definitions with active space: { \obeyspaces \gdef\obeyedspace{ } % Make each space character in the input produce a normal interword % space in the output. Don't allow a line break at this space, as this % is used only in environments like @example, where each line of input % should produce a line of output anyway. % \gdef\sepspaces{\obeyspaces\let =\tie} % If an index command is used in an @example environment, any spaces % therein should become regular spaces in the raw index file, not the % expansion of \tie (\leavevmode \penalty \@M \ ). \gdef\unsepspaces{\let =\space} } \def\flushcr{\ifx\par\lisppar \def\next##1{}\else \let\next=\relax \fi \next} % Define the framework for environments in texinfo.tex. It's used like this: % % \envdef\foo{...} % \def\Efoo{...} % % It's the responsibility of \envdef to insert \begingroup before the % actual body; @end closes the group after calling \Efoo. \envdef also % defines \thisenv, so the current environment is known; @end checks % whether the environment name matches. The \checkenv macro can also be % used to check whether the current environment is the one expected. % % Non-false conditionals (@iftex, @ifset) don't fit into this, so they % are not treated as enviroments; they don't open a group. (The % implementation of @end takes care not to call \endgroup in this % special case.) % At runtime, environments start with this: \def\startenvironment#1{\begingroup\def\thisenv{#1}} % initialize \let\thisenv\empty % ... but they get defined via ``\envdef\foo{...}'': \long\def\envdef#1#2{\def#1{\startenvironment#1#2}} \def\envparseargdef#1#2{\parseargdef#1{\startenvironment#1#2}} % Check whether we're in the right environment: \def\checkenv#1{% \def\temp{#1}% \ifx\thisenv\temp \else \badenverr \fi } % Evironment mismatch, #1 expected: \def\badenverr{% \errhelp = \EMsimple \errmessage{This command can appear only \inenvironment\temp, not \inenvironment\thisenv}% } \def\inenvironment#1{% \ifx#1\empty out of any environment% \else in environment \expandafter\string#1% \fi } % @end foo executes the definition of \Efoo. % But first, it executes a specialized version of \checkenv % \parseargdef\end{% \if 1\csname iscond.#1\endcsname \else % The general wording of \badenverr may not be ideal, but... --kasal, 06nov03 \expandafter\checkenv\csname#1\endcsname \csname E#1\endcsname \endgroup \fi } \newhelp\EMsimple{Press RETURN to continue.} %% Simple single-character @ commands % @@ prints an @ % Kludge this until the fonts are right (grr). \def\@{{\tt\char64}} % This is turned off because it was never documented % and you can use @w{...} around a quote to suppress ligatures. %% Define @` and @' to be the same as ` and ' %% but suppressing ligatures. %\def\`{{`}} %\def\'{{'}} % Used to generate quoted braces. \def\mylbrace {{\tt\char123}} \def\myrbrace {{\tt\char125}} \let\{=\mylbrace \let\}=\myrbrace \begingroup % Definitions to produce \{ and \} commands for indices, % and @{ and @} for the aux file. \catcode`\{ = \other \catcode`\} = \other \catcode`\[ = 1 \catcode`\] = 2 \catcode`\! = 0 \catcode`\\ = \other !gdef!lbracecmd[\{]% !gdef!rbracecmd[\}]% !gdef!lbraceatcmd[@{]% !gdef!rbraceatcmd[@}]% !endgroup % @comma{} to avoid , parsing problems. \let\comma = , % Accents: @, @dotaccent @ringaccent @ubaraccent @udotaccent % Others are defined by plain TeX: @` @' @" @^ @~ @= @u @v @H. \let\, = \c \let\dotaccent = \. \def\ringaccent#1{{\accent23 #1}} \let\tieaccent = \t \let\ubaraccent = \b \let\udotaccent = \d % Other special characters: @questiondown @exclamdown @ordf @ordm % Plain TeX defines: @AA @AE @O @OE @L (plus lowercase versions) @ss. \def\questiondown{?`} \def\exclamdown{!`} \def\ordf{\leavevmode\raise1ex\hbox{\selectfonts\lllsize \underbar{a}}} \def\ordm{\leavevmode\raise1ex\hbox{\selectfonts\lllsize \underbar{o}}} % Dotless i and dotless j, used for accents. \def\imacro{i} \def\jmacro{j} \def\dotless#1{% \def\temp{#1}% \ifx\temp\imacro \ptexi \else\ifx\temp\jmacro \j \else \errmessage{@dotless can be used only with i or j}% \fi\fi } % The \TeX{} logo, as in plain, but resetting the spacing so that a % period following counts as ending a sentence. (Idea found in latex.) % \edef\TeX{\TeX \spacefactor=1000 } % @LaTeX{} logo. Not quite the same results as the definition in % latex.ltx, since we use a different font for the raised A; it's most % convenient for us to use an explicitly smaller font, rather than using % the \scriptstyle font (since we don't reset \scriptstyle and % \scriptscriptstyle). % \def\LaTeX{% L\kern-.36em {\setbox0=\hbox{T}% \vbox to \ht0{\hbox{\selectfonts\lllsize A}\vss}}% \kern-.15em \TeX } % Be sure we're in horizontal mode when doing a tie, since we make space % equivalent to this in @example-like environments. Otherwise, a space % at the beginning of a line will start with \penalty -- and % since \penalty is valid in vertical mode, we'd end up putting the % penalty on the vertical list instead of in the new paragraph. {\catcode`@ = 11 % Avoid using \@M directly, because that causes trouble % if the definition is written into an index file. \global\let\tiepenalty = \@M \gdef\tie{\leavevmode\penalty\tiepenalty\ } } % @: forces normal size whitespace following. \def\:{\spacefactor=1000 } % @* forces a line break. \def\*{\hfil\break\hbox{}\ignorespaces} % @/ allows a line break. \let\/=\allowbreak % @. is an end-of-sentence period. \def\.{.\spacefactor=3000 } % @! is an end-of-sentence bang. \def\!{!\spacefactor=3000 } % @? is an end-of-sentence query. \def\?{?\spacefactor=3000 } % @w prevents a word break. Without the \leavevmode, @w at the % beginning of a paragraph, when TeX is still in vertical mode, would % produce a whole line of output instead of starting the paragraph. \def\w#1{\leavevmode\hbox{#1}} % @group ... @end group forces ... to be all on one page, by enclosing % it in a TeX vbox. We use \vtop instead of \vbox to construct the box % to keep its height that of a normal line. According to the rules for % \topskip (p.114 of the TeXbook), the glue inserted is % max (\topskip - \ht (first item), 0). If that height is large, % therefore, no glue is inserted, and the space between the headline and % the text is small, which looks bad. % % Another complication is that the group might be very large. This can % cause the glue on the previous page to be unduly stretched, because it % does not have much material. In this case, it's better to add an % explicit \vfill so that the extra space is at the bottom. The % threshold for doing this is if the group is more than \vfilllimit % percent of a page (\vfilllimit can be changed inside of @tex). % \newbox\groupbox \def\vfilllimit{0.7} % \envdef\group{% \ifnum\catcode`\^^M=\active \else \errhelp = \groupinvalidhelp \errmessage{@group invalid in context where filling is enabled}% \fi \startsavinginserts % \setbox\groupbox = \vtop\bgroup % Do @comment since we are called inside an environment such as % @example, where each end-of-line in the input causes an % end-of-line in the output. We don't want the end-of-line after % the `@group' to put extra space in the output. Since @group % should appear on a line by itself (according to the Texinfo % manual), we don't worry about eating any user text. \comment } % % The \vtop produces a box with normal height and large depth; thus, TeX puts % \baselineskip glue before it, and (when the next line of text is done) % \lineskip glue after it. Thus, space below is not quite equal to space % above. But it's pretty close. \def\Egroup{% % To get correct interline space between the last line of the group % and the first line afterwards, we have to propagate \prevdepth. \endgraf % Not \par, as it may have been set to \lisppar. \global\dimen1 = \prevdepth \egroup % End the \vtop. % \dimen0 is the vertical size of the group's box. \dimen0 = \ht\groupbox \advance\dimen0 by \dp\groupbox % \dimen2 is how much space is left on the page (more or less). \dimen2 = \pageheight \advance\dimen2 by -\pagetotal % if the group doesn't fit on the current page, and it's a big big % group, force a page break. \ifdim \dimen0 > \dimen2 \ifdim \pagetotal < \vfilllimit\pageheight \page \fi \fi \box\groupbox \prevdepth = \dimen1 \checkinserts } % % TeX puts in an \escapechar (i.e., `@') at the beginning of the help % message, so this ends up printing `@group can only ...'. % \newhelp\groupinvalidhelp{% group can only be used in environments such as @example,^^J% where each line of input produces a line of output.} % @need space-in-mils % forces a page break if there is not space-in-mils remaining. \newdimen\mil \mil=0.001in % Old definition--didn't work. %\parseargdef\need{\par % %% This method tries to make TeX break the page naturally %% if the depth of the box does not fit. %{\baselineskip=0pt% %\vtop to #1\mil{\vfil}\kern -#1\mil\nobreak %\prevdepth=-1000pt %}} \parseargdef\need{% % Ensure vertical mode, so we don't make a big box in the middle of a % paragraph. \par % % If the @need value is less than one line space, it's useless. \dimen0 = #1\mil \dimen2 = \ht\strutbox \advance\dimen2 by \dp\strutbox \ifdim\dimen0 > \dimen2 % % Do a \strut just to make the height of this box be normal, so the % normal leading is inserted relative to the preceding line. % And a page break here is fine. \vtop to #1\mil{\strut\vfil}% % % TeX does not even consider page breaks if a penalty added to the % main vertical list is 10000 or more. But in order to see if the % empty box we just added fits on the page, we must make it consider % page breaks. On the other hand, we don't want to actually break the % page after the empty box. So we use a penalty of 9999. % % There is an extremely small chance that TeX will actually break the % page at this \penalty, if there are no other feasible breakpoints in % sight. (If the user is using lots of big @group commands, which % almost-but-not-quite fill up a page, TeX will have a hard time doing % good page breaking, for example.) However, I could not construct an % example where a page broke at this \penalty; if it happens in a real % document, then we can reconsider our strategy. \penalty9999 % % Back up by the size of the box, whether we did a page break or not. \kern -#1\mil % % Do not allow a page break right after this kern. \nobreak \fi } % @br forces paragraph break (and is undocumented). \let\br = \par % @page forces the start of a new page. % \def\page{\par\vfill\supereject} % @exdent text.... % outputs text on separate line in roman font, starting at standard page margin % This records the amount of indent in the innermost environment. % That's how much \exdent should take out. \newskip\exdentamount % This defn is used inside fill environments such as @defun. \parseargdef\exdent{\hfil\break\hbox{\kern -\exdentamount{\rm#1}}\hfil\break} % This defn is used inside nofill environments such as @example. \parseargdef\nofillexdent{{\advance \leftskip by -\exdentamount \leftline{\hskip\leftskip{\rm#1}}}} % @inmargin{WHICH}{TEXT} puts TEXT in the WHICH margin next to the current % paragraph. For more general purposes, use the \margin insertion % class. WHICH is `l' or `r'. % \newskip\inmarginspacing \inmarginspacing=1cm \def\strutdepth{\dp\strutbox} % \def\doinmargin#1#2{\strut\vadjust{% \nobreak \kern-\strutdepth \vtop to \strutdepth{% \baselineskip=\strutdepth \vss % if you have multiple lines of stuff to put here, you'll need to % make the vbox yourself of the appropriate size. \ifx#1l% \llap{\ignorespaces #2\hskip\inmarginspacing}% \else \rlap{\hskip\hsize \hskip\inmarginspacing \ignorespaces #2}% \fi \null }% }} \def\inleftmargin{\doinmargin l} \def\inrightmargin{\doinmargin r} % % @inmargin{TEXT [, RIGHT-TEXT]} % (if RIGHT-TEXT is given, use TEXT for left page, RIGHT-TEXT for right; % else use TEXT for both). % \def\inmargin#1{\parseinmargin #1,,\finish} \def\parseinmargin#1,#2,#3\finish{% not perfect, but better than nothing. \setbox0 = \hbox{\ignorespaces #2}% \ifdim\wd0 > 0pt \def\lefttext{#1}% have both texts \def\righttext{#2}% \else \def\lefttext{#1}% have only one text \def\righttext{#1}% \fi % \ifodd\pageno \def\temp{\inrightmargin\righttext}% odd page -> outside is right margin \else \def\temp{\inleftmargin\lefttext}% \fi \temp } % @include file insert text of that file as input. % \def\include{\parseargusing\filenamecatcodes\includezzz} \def\includezzz#1{% \pushthisfilestack \def\thisfile{#1}% {% \makevalueexpandable \def\temp{\input #1 }% \expandafter }\temp \popthisfilestack } \def\filenamecatcodes{% \catcode`\\=\other \catcode`~=\other \catcode`^=\other \catcode`_=\other \catcode`|=\other \catcode`<=\other \catcode`>=\other \catcode`+=\other \catcode`-=\other } \def\pushthisfilestack{% \expandafter\pushthisfilestackX\popthisfilestack\StackTerm } \def\pushthisfilestackX{% \expandafter\pushthisfilestackY\thisfile\StackTerm } \def\pushthisfilestackY #1\StackTerm #2\StackTerm {% \gdef\popthisfilestack{\gdef\thisfile{#1}\gdef\popthisfilestack{#2}}% } \def\popthisfilestack{\errthisfilestackempty} \def\errthisfilestackempty{\errmessage{Internal error: the stack of filenames is empty.}} \def\thisfile{} % @center line % outputs that line, centered. % \parseargdef\center{% \ifhmode \let\next\centerH \else \let\next\centerV \fi \next{\hfil \ignorespaces#1\unskip \hfil}% } \def\centerH#1{% {% \hfil\break \advance\hsize by -\leftskip \advance\hsize by -\rightskip \line{#1}% \break }% } \def\centerV#1{\line{\kern\leftskip #1\kern\rightskip}} % @sp n outputs n lines of vertical space \parseargdef\sp{\vskip #1\baselineskip} % @comment ...line which is ignored... % @c is the same as @comment % @ignore ... @end ignore is another way to write a comment \def\comment{\begingroup \catcode`\^^M=\other% \catcode`\@=\other \catcode`\{=\other \catcode`\}=\other% \commentxxx} {\catcode`\^^M=\other \gdef\commentxxx#1^^M{\endgroup}} \let\c=\comment % @paragraphindent NCHARS % We'll use ems for NCHARS, close enough. % NCHARS can also be the word `asis' or `none'. % We cannot feasibly implement @paragraphindent asis, though. % \def\asisword{asis} % no translation, these are keywords \def\noneword{none} % \parseargdef\paragraphindent{% \def\temp{#1}% \ifx\temp\asisword \else \ifx\temp\noneword \defaultparindent = 0pt \else \defaultparindent = #1em \fi \fi \parindent = \defaultparindent } % @exampleindent NCHARS % We'll use ems for NCHARS like @paragraphindent. % It seems @exampleindent asis isn't necessary, but % I preserve it to make it similar to @paragraphindent. \parseargdef\exampleindent{% \def\temp{#1}% \ifx\temp\asisword \else \ifx\temp\noneword \lispnarrowing = 0pt \else \lispnarrowing = #1em \fi \fi } % @firstparagraphindent WORD % If WORD is `none', then suppress indentation of the first paragraph % after a section heading. If WORD is `insert', then do indent at such % paragraphs. % % The paragraph indentation is suppressed or not by calling % \suppressfirstparagraphindent, which the sectioning commands do. % We switch the definition of this back and forth according to WORD. % By default, we suppress indentation. % \def\suppressfirstparagraphindent{\dosuppressfirstparagraphindent} \def\insertword{insert} % \parseargdef\firstparagraphindent{% \def\temp{#1}% \ifx\temp\noneword \let\suppressfirstparagraphindent = \dosuppressfirstparagraphindent \else\ifx\temp\insertword \let\suppressfirstparagraphindent = \relax \else \errhelp = \EMsimple \errmessage{Unknown @firstparagraphindent option `\temp'}% \fi\fi } % Here is how we actually suppress indentation. Redefine \everypar to % \kern backwards by \parindent, and then reset itself to empty. % % We also make \indent itself not actually do anything until the next % paragraph. % \gdef\dosuppressfirstparagraphindent{% \gdef\indent{% \restorefirstparagraphindent \indent }% \gdef\noindent{% \restorefirstparagraphindent \noindent }% \global\everypar = {% \kern -\parindent \restorefirstparagraphindent }% } \gdef\restorefirstparagraphindent{% \global \let \indent = \ptexindent \global \let \noindent = \ptexnoindent \global \everypar = {}% } % @asis just yields its argument. Used with @table, for example. % \def\asis#1{#1} % @math outputs its argument in math mode. % % One complication: _ usually means subscripts, but it could also mean % an actual _ character, as in @math{@var{some_variable} + 1}. So make % _ active, and distinguish by seeing if the current family is \slfam, % which is what @var uses. { \catcode\underChar = \active \gdef\mathunderscore{% \catcode\underChar=\active \def_{\ifnum\fam=\slfam \_\else\sb\fi}% } } % Another complication: we want \\ (and @\) to output a \ character. % FYI, plain.tex uses \\ as a temporary control sequence (why?), but % this is not advertised and we don't care. Texinfo does not % otherwise define @\. % % The \mathchar is class=0=ordinary, family=7=ttfam, position=5C=\. \def\mathbackslash{\ifnum\fam=\ttfam \mathchar"075C \else\backslash \fi} % \def\math{% \tex \mathunderscore \let\\ = \mathbackslash \mathactive $\finishmath } \def\finishmath#1{#1$\endgroup} % Close the group opened by \tex. % Some active characters (such as <) are spaced differently in math. % We have to reset their definitions in case the @math was an argument % to a command which sets the catcodes (such as @item or @section). % { \catcode`^ = \active \catcode`< = \active \catcode`> = \active \catcode`+ = \active \gdef\mathactive{% \let^ = \ptexhat \let< = \ptexless \let> = \ptexgtr \let+ = \ptexplus } } % @bullet and @minus need the same treatment as @math, just above. \def\bullet{$\ptexbullet$} \def\minus{$-$} % @dots{} outputs an ellipsis using the current font. % We do .5em per period so that it has the same spacing in a typewriter % font as three actual period characters. % \def\dots{% \leavevmode \hbox to 1.5em{% \hskip 0pt plus 0.25fil .\hfil.\hfil.% \hskip 0pt plus 0.5fil }% } % @enddots{} is an end-of-sentence ellipsis. % \def\enddots{% \dots \spacefactor=3000 } % @comma{} is so commas can be inserted into text without messing up % Texinfo's parsing. % \let\comma = , % @refill is a no-op. \let\refill=\relax % If working on a large document in chapters, it is convenient to % be able to disable indexing, cross-referencing, and contents, for test runs. % This is done with @novalidate (before @setfilename). % \newif\iflinks \linkstrue % by default we want the aux files. \let\novalidate = \linksfalse % @setfilename is done at the beginning of every texinfo file. % So open here the files we need to have open while reading the input. % This makes it possible to make a .fmt file for texinfo. \def\setfilename{% \fixbackslash % Turn off hack to swallow `\input texinfo'. \iflinks \tryauxfile % Open the new aux file. TeX will close it automatically at exit. \immediate\openout\auxfile=\jobname.aux \fi % \openindices needs to do some work in any case. \openindices \let\setfilename=\comment % Ignore extra @setfilename cmds. % % If texinfo.cnf is present on the system, read it. % Useful for site-wide @afourpaper, etc. \openin 1 texinfo.cnf \ifeof 1 \else \input texinfo.cnf \fi \closein 1 % \comment % Ignore the actual filename. } % Called from \setfilename. % \def\openindices{% \newindex{cp}% \newcodeindex{fn}% \newcodeindex{vr}% \newcodeindex{tp}% \newcodeindex{ky}% \newcodeindex{pg}% } % @bye. \outer\def\bye{\pagealignmacro\tracingstats=1\ptexend} \message{pdf,} % adobe `portable' document format \newcount\tempnum \newcount\lnkcount \newtoks\filename \newcount\filenamelength \newcount\pgn \newtoks\toksA \newtoks\toksB \newtoks\toksC \newtoks\toksD \newbox\boxA \newcount\countA \newif\ifpdf \newif\ifpdfmakepagedest % when pdftex is run in dvi mode, \pdfoutput is defined (so \pdfoutput=1 % can be set). So we test for \relax and 0 as well as \undefined, % borrowed from ifpdf.sty. \ifx\pdfoutput\undefined \else \ifx\pdfoutput\relax \else \ifcase\pdfoutput \else \pdftrue \fi \fi \fi % \ifpdf \input pdfcolor \pdfcatalog{/PageMode /UseOutlines}% \def\dopdfimage#1#2#3{% \def\imagewidth{#2}% \def\imageheight{#3}% % without \immediate, pdftex seg faults when the same image is % included twice. (Version 3.14159-pre-1.0-unofficial-20010704.) \ifnum\pdftexversion < 14 \immediate\pdfimage \else \immediate\pdfximage \fi \ifx\empty\imagewidth\else width \imagewidth \fi \ifx\empty\imageheight\else height \imageheight \fi \ifnum\pdftexversion<13 #1.pdf% \else {#1.pdf}% \fi \ifnum\pdftexversion < 14 \else \pdfrefximage \pdflastximage \fi} \def\pdfmkdest#1{{% % We have to set dummies so commands such as @code in a section title % aren't expanded. \atdummies \normalturnoffactive \pdfdest name{#1} xyz% }} \def\pdfmkpgn#1{#1} \let\linkcolor = \Blue % was Cyan, but that seems light? \def\endlink{\Black\pdfendlink} % Adding outlines to PDF; macros for calculating structure of outlines % come from Petr Olsak \def\expnumber#1{\expandafter\ifx\csname#1\endcsname\relax 0% \else \csname#1\endcsname \fi} \def\advancenumber#1{\tempnum=\expnumber{#1}\relax \advance\tempnum by 1 \expandafter\xdef\csname#1\endcsname{\the\tempnum}} % % #1 is the section text. #2 is the pdf expression for the number % of subentries (or empty, for subsubsections). #3 is the node % text, which might be empty if this toc entry had no % corresponding node. #4 is the page number. % \def\dopdfoutline#1#2#3#4{% % Generate a link to the node text if that exists; else, use the % page number. We could generate a destination for the section % text in the case where a section has no node, but it doesn't % seem worthwhile, since most documents are normally structured. \def\pdfoutlinedest{#3}% \ifx\pdfoutlinedest\empty \def\pdfoutlinedest{#4}\fi % \pdfoutline goto name{\pdfmkpgn{\pdfoutlinedest}}#2{#1}% } % \def\pdfmakeoutlines{% \begingroup % Thanh's hack / proper braces in bookmarks \edef\mylbrace{\iftrue \string{\else}\fi}\let\{=\mylbrace \edef\myrbrace{\iffalse{\else\string}\fi}\let\}=\myrbrace % % Read toc silently, to get counts of subentries for \pdfoutline. \def\numchapentry##1##2##3##4{% \def\thischapnum{##2}% \def\thissecnum{0}% \def\thissubsecnum{0}% }% \def\numsecentry##1##2##3##4{% \advancenumber{chap\thischapnum}% \def\thissecnum{##2}% \def\thissubsecnum{0}% }% \def\numsubsecentry##1##2##3##4{% \advancenumber{sec\thissecnum}% \def\thissubsecnum{##2}% }% \def\numsubsubsecentry##1##2##3##4{% \advancenumber{subsec\thissubsecnum}% }% \def\thischapnum{0}% \def\thissecnum{0}% \def\thissubsecnum{0}% % % use \def rather than \let here because we redefine \chapentry et % al. a second time, below. \def\appentry{\numchapentry}% \def\appsecentry{\numsecentry}% \def\appsubsecentry{\numsubsecentry}% \def\appsubsubsecentry{\numsubsubsecentry}% \def\unnchapentry{\numchapentry}% \def\unnsecentry{\numsecentry}% \def\unnsubsecentry{\numsubsecentry}% \def\unnsubsubsecentry{\numsubsubsecentry}% \input \jobname.toc % % Read toc second time, this time actually producing the outlines. % The `-' means take the \expnumber as the absolute number of % subentries, which we calculated on our first read of the .toc above. % % We use the node names as the destinations. \def\numchapentry##1##2##3##4{% \dopdfoutline{##1}{count-\expnumber{chap##2}}{##3}{##4}}% \def\numsecentry##1##2##3##4{% \dopdfoutline{##1}{count-\expnumber{sec##2}}{##3}{##4}}% \def\numsubsecentry##1##2##3##4{% \dopdfoutline{##1}{count-\expnumber{subsec##2}}{##3}{##4}}% \def\numsubsubsecentry##1##2##3##4{% count is always zero \dopdfoutline{##1}{}{##3}{##4}}% % % PDF outlines are displayed using system fonts, instead of % document fonts. Therefore we cannot use special characters, % since the encoding is unknown. For example, the eogonek from % Latin 2 (0xea) gets translated to a | character. Info from % Staszek Wawrykiewicz, 19 Jan 2004 04:09:24 +0100. % % xx to do this right, we have to translate 8-bit characters to % their "best" equivalent, based on the @documentencoding. Right % now, I guess we'll just let the pdf reader have its way. \indexnofonts \turnoffactive \input \jobname.toc \endgroup } % \def\makelinks #1,{% \def\params{#1}\def\E{END}% \ifx\params\E \let\nextmakelinks=\relax \else \let\nextmakelinks=\makelinks \ifnum\lnkcount>0,\fi \picknum{#1}% \startlink attr{/Border [0 0 0]} goto name{\pdfmkpgn{\the\pgn}}% \linkcolor #1% \advance\lnkcount by 1% \endlink \fi \nextmakelinks } \def\picknum#1{\expandafter\pn#1} \def\pn#1{% \def\p{#1}% \ifx\p\lbrace \let\nextpn=\ppn \else \let\nextpn=\ppnn \def\first{#1} \fi \nextpn } \def\ppn#1{\pgn=#1\gobble} \def\ppnn{\pgn=\first} \def\pdfmklnk#1{\lnkcount=0\makelinks #1,END,} \def\skipspaces#1{\def\PP{#1}\def\D{|}% \ifx\PP\D\let\nextsp\relax \else\let\nextsp\skipspaces \ifx\p\space\else\addtokens{\filename}{\PP}% \advance\filenamelength by 1 \fi \fi \nextsp} \def\getfilename#1{\filenamelength=0\expandafter\skipspaces#1|\relax} \ifnum\pdftexversion < 14 \let \startlink \pdfannotlink \else \let \startlink \pdfstartlink \fi \def\pdfurl#1{% \begingroup \normalturnoffactive\def\@{@}% \makevalueexpandable \leavevmode\Red \startlink attr{/Border [0 0 0]}% user{/Subtype /Link /A << /S /URI /URI (#1) >>}% \endgroup} \def\pdfgettoks#1.{\setbox\boxA=\hbox{\toksA={#1.}\toksB={}\maketoks}} \def\addtokens#1#2{\edef\addtoks{\noexpand#1={\the#1#2}}\addtoks} \def\adn#1{\addtokens{\toksC}{#1}\global\countA=1\let\next=\maketoks} \def\poptoks#1#2|ENDTOKS|{\let\first=#1\toksD={#1}\toksA={#2}} \def\maketoks{% \expandafter\poptoks\the\toksA|ENDTOKS|\relax \ifx\first0\adn0 \else\ifx\first1\adn1 \else\ifx\first2\adn2 \else\ifx\first3\adn3 \else\ifx\first4\adn4 \else\ifx\first5\adn5 \else\ifx\first6\adn6 \else\ifx\first7\adn7 \else\ifx\first8\adn8 \else\ifx\first9\adn9 \else \ifnum0=\countA\else\makelink\fi \ifx\first.\let\next=\done\else \let\next=\maketoks \addtokens{\toksB}{\the\toksD} \ifx\first,\addtokens{\toksB}{\space}\fi \fi \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi \next} \def\makelink{\addtokens{\toksB}% {\noexpand\pdflink{\the\toksC}}\toksC={}\global\countA=0} \def\pdflink#1{% \startlink attr{/Border [0 0 0]} goto name{\pdfmkpgn{#1}} \linkcolor #1\endlink} \def\done{\edef\st{\global\noexpand\toksA={\the\toksB}}\st} \else \let\pdfmkdest = \gobble \let\pdfurl = \gobble \let\endlink = \relax \let\linkcolor = \relax \let\pdfmakeoutlines = \relax \fi % \ifx\pdfoutput \message{fonts,} % Change the current font style to #1, remembering it in \curfontstyle. % For now, we do not accumulate font styles: @b{@i{foo}} prints foo in % italics, not bold italics. % \def\setfontstyle#1{% \def\curfontstyle{#1}% not as a control sequence, because we are \edef'd. \csname ten#1\endcsname % change the current font } % Select #1 fonts with the current style. % \def\selectfonts#1{\csname #1fonts\endcsname \csname\curfontstyle\endcsname} \def\rm{\fam=0 \setfontstyle{rm}} \def\it{\fam=\itfam \setfontstyle{it}} \def\sl{\fam=\slfam \setfontstyle{sl}} \def\bf{\fam=\bffam \setfontstyle{bf}}\def\bfstylename{bf} \def\tt{\fam=\ttfam \setfontstyle{tt}} % Texinfo sort of supports the sans serif font style, which plain TeX does not. % So we set up a \sf. \newfam\sffam \def\sf{\fam=\sffam \setfontstyle{sf}} \let\li = \sf % Sometimes we call it \li, not \sf. % We don't need math for this font style. \def\ttsl{\setfontstyle{ttsl}} % Default leading. \newdimen\textleading \textleading = 13.2pt % Set the baselineskip to #1, and the lineskip and strut size % correspondingly. There is no deep meaning behind these magic numbers % used as factors; they just match (closely enough) what Knuth defined. % \def\lineskipfactor{.08333} \def\strutheightpercent{.70833} \def\strutdepthpercent {.29167} % \def\setleading#1{% \normalbaselineskip = #1\relax \normallineskip = \lineskipfactor\normalbaselineskip \normalbaselines \setbox\strutbox =\hbox{% \vrule width0pt height\strutheightpercent\baselineskip depth \strutdepthpercent \baselineskip }% } % Set the font macro #1 to the font named #2, adding on the % specified font prefix (normally `cm'). % #3 is the font's design size, #4 is a scale factor \def\setfont#1#2#3#4{\font#1=\fontprefix#2#3 scaled #4} % Use cm as the default font prefix. % To specify the font prefix, you must define \fontprefix % before you read in texinfo.tex. \ifx\fontprefix\undefined \def\fontprefix{cm} \fi % Support font families that don't use the same naming scheme as CM. \def\rmshape{r} \def\rmbshape{bx} %where the normal face is bold \def\bfshape{b} \def\bxshape{bx} \def\ttshape{tt} \def\ttbshape{tt} \def\ttslshape{sltt} \def\itshape{ti} \def\itbshape{bxti} \def\slshape{sl} \def\slbshape{bxsl} \def\sfshape{ss} \def\sfbshape{ss} \def\scshape{csc} \def\scbshape{csc} % Text fonts (11.2pt, magstep1). \def\textnominalsize{11pt} \edef\mainmagstep{\magstephalf} \setfont\textrm\rmshape{10}{\mainmagstep} \setfont\texttt\ttshape{10}{\mainmagstep} \setfont\textbf\bfshape{10}{\mainmagstep} \setfont\textit\itshape{10}{\mainmagstep} \setfont\textsl\slshape{10}{\mainmagstep} \setfont\textsf\sfshape{10}{\mainmagstep} \setfont\textsc\scshape{10}{\mainmagstep} \setfont\textttsl\ttslshape{10}{\mainmagstep} \font\texti=cmmi10 scaled \mainmagstep \font\textsy=cmsy10 scaled \mainmagstep % A few fonts for @defun names and args. \setfont\defbf\bfshape{10}{\magstep1} \setfont\deftt\ttshape{10}{\magstep1} \setfont\defttsl\ttslshape{10}{\magstep1} \def\df{\let\tentt=\deftt \let\tenbf = \defbf \let\tenttsl=\defttsl \bf} % Fonts for indices, footnotes, small examples (9pt). \def\smallnominalsize{9pt} \setfont\smallrm\rmshape{9}{1000} \setfont\smalltt\ttshape{9}{1000} \setfont\smallbf\bfshape{10}{900} \setfont\smallit\itshape{9}{1000} \setfont\smallsl\slshape{9}{1000} \setfont\smallsf\sfshape{9}{1000} \setfont\smallsc\scshape{10}{900} \setfont\smallttsl\ttslshape{10}{900} \font\smalli=cmmi9 \font\smallsy=cmsy9 % Fonts for small examples (8pt). \def\smallernominalsize{8pt} \setfont\smallerrm\rmshape{8}{1000} \setfont\smallertt\ttshape{8}{1000} \setfont\smallerbf\bfshape{10}{800} \setfont\smallerit\itshape{8}{1000} \setfont\smallersl\slshape{8}{1000} \setfont\smallersf\sfshape{8}{1000} \setfont\smallersc\scshape{10}{800} \setfont\smallerttsl\ttslshape{10}{800} \font\smalleri=cmmi8 \font\smallersy=cmsy8 % Fonts for title page (20.4pt): \def\titlenominalsize{20pt} \setfont\titlerm\rmbshape{12}{\magstep3} \setfont\titleit\itbshape{10}{\magstep4} \setfont\titlesl\slbshape{10}{\magstep4} \setfont\titlett\ttbshape{12}{\magstep3} \setfont\titlettsl\ttslshape{10}{\magstep4} \setfont\titlesf\sfbshape{17}{\magstep1} \let\titlebf=\titlerm \setfont\titlesc\scbshape{10}{\magstep4} \font\titlei=cmmi12 scaled \magstep3 \font\titlesy=cmsy10 scaled \magstep4 \def\authorrm{\secrm} \def\authortt{\sectt} % Chapter (and unnumbered) fonts (17.28pt). \def\chapnominalsize{17pt} \setfont\chaprm\rmbshape{12}{\magstep2} \setfont\chapit\itbshape{10}{\magstep3} \setfont\chapsl\slbshape{10}{\magstep3} \setfont\chaptt\ttbshape{12}{\magstep2} \setfont\chapttsl\ttslshape{10}{\magstep3} \setfont\chapsf\sfbshape{17}{1000} \let\chapbf=\chaprm \setfont\chapsc\scbshape{10}{\magstep3} \font\chapi=cmmi12 scaled \magstep2 \font\chapsy=cmsy10 scaled \magstep3 % Section fonts (14.4pt). \def\secnominalsize{14pt} \setfont\secrm\rmbshape{12}{\magstep1} \setfont\secit\itbshape{10}{\magstep2} \setfont\secsl\slbshape{10}{\magstep2} \setfont\sectt\ttbshape{12}{\magstep1} \setfont\secttsl\ttslshape{10}{\magstep2} \setfont\secsf\sfbshape{12}{\magstep1} \let\secbf\secrm \setfont\secsc\scbshape{10}{\magstep2} \font\seci=cmmi12 scaled \magstep1 \font\secsy=cmsy10 scaled \magstep2 % Subsection fonts (13.15pt). \def\ssecnominalsize{13pt} \setfont\ssecrm\rmbshape{12}{\magstephalf} \setfont\ssecit\itbshape{10}{1315} \setfont\ssecsl\slbshape{10}{1315} \setfont\ssectt\ttbshape{12}{\magstephalf} \setfont\ssecttsl\ttslshape{10}{1315} \setfont\ssecsf\sfbshape{12}{\magstephalf} \let\ssecbf\ssecrm \setfont\ssecsc\scbshape{10}{1315} \font\sseci=cmmi12 scaled \magstephalf \font\ssecsy=cmsy10 scaled 1315 % Reduced fonts for @acro in text (10pt). \def\reducednominalsize{10pt} \setfont\reducedrm\rmshape{10}{1000} \setfont\reducedtt\ttshape{10}{1000} \setfont\reducedbf\bfshape{10}{1000} \setfont\reducedit\itshape{10}{1000} \setfont\reducedsl\slshape{10}{1000} \setfont\reducedsf\sfshape{10}{1000} \setfont\reducedsc\scshape{10}{1000} \setfont\reducedttsl\ttslshape{10}{1000} \font\reducedi=cmmi10 \font\reducedsy=cmsy10 % In order for the font changes to affect most math symbols and letters, % we have to define the \textfont of the standard families. Since % texinfo doesn't allow for producing subscripts and superscripts except % in the main text, we don't bother to reset \scriptfont and % \scriptscriptfont (which would also require loading a lot more fonts). % \def\resetmathfonts{% \textfont0=\tenrm \textfont1=\teni \textfont2=\tensy \textfont\itfam=\tenit \textfont\slfam=\tensl \textfont\bffam=\tenbf \textfont\ttfam=\tentt \textfont\sffam=\tensf } % The font-changing commands redefine the meanings of \tenSTYLE, instead % of just \STYLE. We do this because \STYLE needs to also set the % current \fam for math mode. Our \STYLE (e.g., \rm) commands hardwire % \tenSTYLE to set the current font. % % Each font-changing command also sets the names \lsize (one size lower) % and \lllsize (three sizes lower). These relative commands are used in % the LaTeX logo and acronyms. % % This all needs generalizing, badly. % \def\textfonts{% \let\tenrm=\textrm \let\tenit=\textit \let\tensl=\textsl \let\tenbf=\textbf \let\tentt=\texttt \let\smallcaps=\textsc \let\tensf=\textsf \let\teni=\texti \let\tensy=\textsy \let\tenttsl=\textttsl \def\curfontsize{text}% \def\lsize{reduced}\def\lllsize{smaller}% \resetmathfonts \setleading{\textleading}} \def\titlefonts{% \let\tenrm=\titlerm \let\tenit=\titleit \let\tensl=\titlesl \let\tenbf=\titlebf \let\tentt=\titlett \let\smallcaps=\titlesc \let\tensf=\titlesf \let\teni=\titlei \let\tensy=\titlesy \let\tenttsl=\titlettsl \def\curfontsize{title}% \def\lsize{chap}\def\lllsize{subsec}% \resetmathfonts \setleading{25pt}} \def\titlefont#1{{\titlefonts\rm #1}} \def\chapfonts{% \let\tenrm=\chaprm \let\tenit=\chapit \let\tensl=\chapsl \let\tenbf=\chapbf \let\tentt=\chaptt \let\smallcaps=\chapsc \let\tensf=\chapsf \let\teni=\chapi \let\tensy=\chapsy \let\tenttsl=\chapttsl \def\curfontsize{chap}% \def\lsize{sec}\def\lllsize{text}% \resetmathfonts \setleading{19pt}} \def\secfonts{% \let\tenrm=\secrm \let\tenit=\secit \let\tensl=\secsl \let\tenbf=\secbf \let\tentt=\sectt \let\smallcaps=\secsc \let\tensf=\secsf \let\teni=\seci \let\tensy=\secsy \let\tenttsl=\secttsl \def\curfontsize{sec}% \def\lsize{subsec}\def\lllsize{reduced}% \resetmathfonts \setleading{16pt}} \def\subsecfonts{% \let\tenrm=\ssecrm \let\tenit=\ssecit \let\tensl=\ssecsl \let\tenbf=\ssecbf \let\tentt=\ssectt \let\smallcaps=\ssecsc \let\tensf=\ssecsf \let\teni=\sseci \let\tensy=\ssecsy \let\tenttsl=\ssecttsl \def\curfontsize{ssec}% \def\lsize{text}\def\lllsize{small}% \resetmathfonts \setleading{15pt}} \let\subsubsecfonts = \subsecfonts \def\reducedfonts{% \let\tenrm=\reducedrm \let\tenit=\reducedit \let\tensl=\reducedsl \let\tenbf=\reducedbf \let\tentt=\reducedtt \let\reducedcaps=\reducedsc \let\tensf=\reducedsf \let\teni=\reducedi \let\tensy=\reducedsy \let\tenttsl=\reducedttsl \def\curfontsize{reduced}% \def\lsize{small}\def\lllsize{smaller}% \resetmathfonts \setleading{10.5pt}} \def\smallfonts{% \let\tenrm=\smallrm \let\tenit=\smallit \let\tensl=\smallsl \let\tenbf=\smallbf \let\tentt=\smalltt \let\smallcaps=\smallsc \let\tensf=\smallsf \let\teni=\smalli \let\tensy=\smallsy \let\tenttsl=\smallttsl \def\curfontsize{small}% \def\lsize{smaller}\def\lllsize{smaller}% \resetmathfonts \setleading{10.5pt}} \def\smallerfonts{% \let\tenrm=\smallerrm \let\tenit=\smallerit \let\tensl=\smallersl \let\tenbf=\smallerbf \let\tentt=\smallertt \let\smallcaps=\smallersc \let\tensf=\smallersf \let\teni=\smalleri \let\tensy=\smallersy \let\tenttsl=\smallerttsl \def\curfontsize{smaller}% \def\lsize{smaller}\def\lllsize{smaller}% \resetmathfonts \setleading{9.5pt}} % Set the fonts to use with the @small... environments. \let\smallexamplefonts = \smallfonts % About \smallexamplefonts. If we use \smallfonts (9pt), @smallexample % can fit this many characters: % 8.5x11=86 smallbook=72 a4=90 a5=69 % If we use \scriptfonts (8pt), then we can fit this many characters: % 8.5x11=90+ smallbook=80 a4=90+ a5=77 % For me, subjectively, the few extra characters that fit aren't worth % the additional smallness of 8pt. So I'm making the default 9pt. % % By the way, for comparison, here's what fits with @example (10pt): % 8.5x11=71 smallbook=60 a4=75 a5=58 % % I wish the USA used A4 paper. % --karl, 24jan03. % Set up the default fonts, so we can use them for creating boxes. % \textfonts \rm % Define these so they can be easily changed for other fonts. \def\angleleft{$\langle$} \def\angleright{$\rangle$} % Count depth in font-changes, for error checks \newcount\fontdepth \fontdepth=0 % Fonts for short table of contents. \setfont\shortcontrm\rmshape{12}{1000} \setfont\shortcontbf\bfshape{10}{\magstep1} % no cmb12 \setfont\shortcontsl\slshape{12}{1000} \setfont\shortconttt\ttshape{12}{1000} %% Add scribe-like font environments, plus @l for inline lisp (usually sans %% serif) and @ii for TeX italic % \smartitalic{ARG} outputs arg in italics, followed by an italic correction % unless the following character is such as not to need one. \def\smartitalicx{\ifx\next,\else\ifx\next-\else\ifx\next.\else \ptexslash\fi\fi\fi} \def\smartslanted#1{{\ifusingtt\ttsl\sl #1}\futurelet\next\smartitalicx} \def\smartitalic#1{{\ifusingtt\ttsl\it #1}\futurelet\next\smartitalicx} % like \smartslanted except unconditionally uses \ttsl. % @var is set to this for defun arguments. \def\ttslanted#1{{\ttsl #1}\futurelet\next\smartitalicx} % like \smartslanted except unconditionally use \sl. We never want % ttsl for book titles, do we? \def\cite#1{{\sl #1}\futurelet\next\smartitalicx} \let\i=\smartitalic \let\slanted=\smartslanted \let\var=\smartslanted \let\dfn=\smartslanted \let\emph=\smartitalic % @b, explicit bold. \def\b#1{{\bf #1}} \let\strong=\b % @sansserif, explicit sans. \def\sansserif#1{{\sf #1}} % We can't just use \exhyphenpenalty, because that only has effect at % the end of a paragraph. Restore normal hyphenation at the end of the % group within which \nohyphenation is presumably called. % \def\nohyphenation{\hyphenchar\font = -1 \aftergroup\restorehyphenation} \def\restorehyphenation{\hyphenchar\font = `- } % Set sfcode to normal for the chars that usually have another value. % Can't use plain's \frenchspacing because it uses the `\x notation, and % sometimes \x has an active definition that messes things up. % \catcode`@=11 \def\frenchspacing{% \sfcode\dotChar =\@m \sfcode\questChar=\@m \sfcode\exclamChar=\@m \sfcode\colonChar=\@m \sfcode\semiChar =\@m \sfcode\commaChar =\@m } \catcode`@=\other \def\t#1{% {\tt \rawbackslash \frenchspacing #1}% \null } \def\samp#1{`\tclose{#1}'\null} \setfont\keyrm\rmshape{8}{1000} \font\keysy=cmsy9 \def\key#1{{\keyrm\textfont2=\keysy \leavevmode\hbox{% \raise0.4pt\hbox{\angleleft}\kern-.08em\vtop{% \vbox{\hrule\kern-0.4pt \hbox{\raise0.4pt\hbox{\vphantom{\angleleft}}#1}}% \kern-0.4pt\hrule}% \kern-.06em\raise0.4pt\hbox{\angleright}}}} % The old definition, with no lozenge: %\def\key #1{{\ttsl \nohyphenation \uppercase{#1}}\null} \def\ctrl #1{{\tt \rawbackslash \hat}#1} % @file, @option are the same as @samp. \let\file=\samp \let\option=\samp % @code is a modification of @t, % which makes spaces the same size as normal in the surrounding text. \def\tclose#1{% {% % Change normal interword space to be same as for the current font. \spaceskip = \fontdimen2\font % % Switch to typewriter. \tt % % But `\ ' produces the large typewriter interword space. \def\ {{\spaceskip = 0pt{} }}% % % Turn off hyphenation. \nohyphenation % \rawbackslash \frenchspacing #1% }% \null } % We *must* turn on hyphenation at `-' and `_' in @code. % Otherwise, it is too hard to avoid overfull hboxes % in the Emacs manual, the Library manual, etc. % Unfortunately, TeX uses one parameter (\hyphenchar) to control % both hyphenation at - and hyphenation within words. % We must therefore turn them both off (\tclose does that) % and arrange explicitly to hyphenate at a dash. % -- rms. { \catcode`\-=\active \catcode`\_=\active % \global\def\code{\begingroup \catcode`\-=\active \let-\codedash \catcode`\_=\active \let_\codeunder \codex } } \def\realdash{-} \def\codedash{-\discretionary{}{}{}} \def\codeunder{% % this is all so @math{@code{var_name}+1} can work. In math mode, _ % is "active" (mathcode"8000) and \normalunderscore (or \char95, etc.) % will therefore expand the active definition of _, which is us % (inside @code that is), therefore an endless loop. \ifusingtt{\ifmmode \mathchar"075F % class 0=ordinary, family 7=ttfam, pos 0x5F=_. \else\normalunderscore \fi \discretionary{}{}{}}% {\_}% } \def\codex #1{\tclose{#1}\endgroup} % @kbd is like @code, except that if the argument is just one @key command, % then @kbd has no effect. % @kbdinputstyle -- arg is `distinct' (@kbd uses slanted tty font always), % `example' (@kbd uses ttsl only inside of @example and friends), % or `code' (@kbd uses normal tty font always). \parseargdef\kbdinputstyle{% \def\arg{#1}% \ifx\arg\worddistinct \gdef\kbdexamplefont{\ttsl}\gdef\kbdfont{\ttsl}% \else\ifx\arg\wordexample \gdef\kbdexamplefont{\ttsl}\gdef\kbdfont{\tt}% \else\ifx\arg\wordcode \gdef\kbdexamplefont{\tt}\gdef\kbdfont{\tt}% \else \errhelp = \EMsimple \errmessage{Unknown @kbdinputstyle option `\arg'}% \fi\fi\fi } \def\worddistinct{distinct} \def\wordexample{example} \def\wordcode{code} % Default is `distinct.' \kbdinputstyle distinct \def\xkey{\key} \def\kbdfoo#1#2#3\par{\def\one{#1}\def\three{#3}\def\threex{??}% \ifx\one\xkey\ifx\threex\three \key{#2}% \else{\tclose{\kbdfont\look}}\fi \else{\tclose{\kbdfont\look}}\fi} % For @indicateurl, @env, @command quotes seem unnecessary, so use \code. \let\indicateurl=\code \let\env=\code \let\command=\code % @uref (abbreviation for `urlref') takes an optional (comma-separated) % second argument specifying the text to display and an optional third % arg as text to display instead of (rather than in addition to) the url % itself. First (mandatory) arg is the url. Perhaps eventually put in % a hypertex \special here. % \def\uref#1{\douref #1,,,\finish} \def\douref#1,#2,#3,#4\finish{\begingroup \unsepspaces \pdfurl{#1}% \setbox0 = \hbox{\ignorespaces #3}% \ifdim\wd0 > 0pt \unhbox0 % third arg given, show only that \else \setbox0 = \hbox{\ignorespaces #2}% \ifdim\wd0 > 0pt \ifpdf \unhbox0 % PDF: 2nd arg given, show only it \else \unhbox0\ (\code{#1})% DVI: 2nd arg given, show both it and url \fi \else \code{#1}% only url given, so show it \fi \fi \endlink \endgroup} % @url synonym for @uref, since that's how everyone uses it. % \let\url=\uref % rms does not like angle brackets --karl, 17may97. % So now @email is just like @uref, unless we are pdf. % %\def\email#1{\angleleft{\tt #1}\angleright} \ifpdf \def\email#1{\doemail#1,,\finish} \def\doemail#1,#2,#3\finish{\begingroup \unsepspaces \pdfurl{mailto:#1}% \setbox0 = \hbox{\ignorespaces #2}% \ifdim\wd0>0pt\unhbox0\else\code{#1}\fi \endlink \endgroup} \else \let\email=\uref \fi % Check if we are currently using a typewriter font. Since all the % Computer Modern typewriter fonts have zero interword stretch (and % shrink), and it is reasonable to expect all typewriter fonts to have % this property, we can check that font parameter. % \def\ifmonospace{\ifdim\fontdimen3\font=0pt } % Typeset a dimension, e.g., `in' or `pt'. The only reason for the % argument is to make the input look right: @dmn{pt} instead of @dmn{}pt. % \def\dmn#1{\thinspace #1} \def\kbd#1{\def\look{#1}\expandafter\kbdfoo\look??\par} % @l was never documented to mean ``switch to the Lisp font'', % and it is not used as such in any manual I can find. We need it for % Polish suppressed-l. --karl, 22sep96. %\def\l#1{{\li #1}\null} % Explicit font changes: @r, @sc, undocumented @ii. \def\r#1{{\rm #1}} % roman font \def\sc#1{{\smallcaps#1}} % smallcaps font \def\ii#1{{\it #1}} % italic font % @acronym for "FBI", "NATO", and the like. % We print this one point size smaller, since it's intended for % all-uppercase. % \def\acronym#1{\doacronym #1,,\finish} \def\doacronym#1,#2,#3\finish{% {\selectfonts\lsize #1}% \def\temp{#2}% \ifx\temp\empty \else \space ({\unsepspaces \ignorespaces \temp \unskip})% \fi } % @abbr for "Comput. J." and the like. % No font change, but don't do end-of-sentence spacing. % \def\abbr#1{\doabbr #1,,\finish} \def\doabbr#1,#2,#3\finish{% {\frenchspacing #1}% \def\temp{#2}% \ifx\temp\empty \else \space ({\unsepspaces \ignorespaces \temp \unskip})% \fi } % @pounds{} is a sterling sign, which Knuth put in the CM italic font. % \def\pounds{{\it\$}} % @euro{} comes from a separate font, depending on the current style. % We use the free feym* fonts from the eurosym package by Henrik % Theiling, which support regular, slanted, bold and bold slanted (and % "outlined" (blackboard board, sort of) versions, which we don't need). % It is available from http://www.ctan.org/tex-archive/fonts/eurosym. % % Although only regular is the truly official Euro symbol, we ignore % that. The Euro is designed to be slightly taller than the regular % font height. % % feymr - regular % feymo - slanted % feybr - bold % feybo - bold slanted % % There is no good (free) typewriter version, to my knowledge. % A feymr10 euro is ~7.3pt wide, while a normal cmtt10 char is ~5.25pt wide. % Hmm. % % Also doesn't work in math. Do we need to do math with euro symbols? % Hope not. % % \def\euro{{\eurofont e}} \def\eurofont{% % We set the font at each command, rather than predefining it in % \textfonts and the other font-switching commands, so that % installations which never need the symbold don't have to have the % font installed. % % There is only one designed size (nominal 10pt), so we always scale % that to the current nominal size. % % By the way, simply using "at 1em" works for cmr10 and the like, but % does not work for cmbx10 and other extended/shrunken fonts. % \def\eurosize{\csname\curfontsize nominalsize\endcsname}% % \ifx\curfontstyle\bfstylename % bold: \font\thiseurofont = \ifusingit{feybo10}{feybr10} at \eurosize \else % regular: \font\thiseurofont = \ifusingit{feymo10}{feymr10} at \eurosize \fi \thiseurofont } % @registeredsymbol - R in a circle. The font for the R should really % be smaller yet, but lllsize is the best we can do for now. % Adapted from the plain.tex definition of \copyright. % \def\registeredsymbol{% $^{{\ooalign{\hfil\raise.07ex\hbox{\selectfonts\lllsize R}% \hfil\crcr\Orb}}% }$% } % Laurent Siebenmann reports \Orb undefined with: % Textures 1.7.7 (preloaded format=plain 93.10.14) (68K) 16 APR 2004 02:38 % so we'll define it if necessary. % \ifx\Orb\undefined \def\Orb{\mathhexbox20D} \fi \message{page headings,} \newskip\titlepagetopglue \titlepagetopglue = 1.5in \newskip\titlepagebottomglue \titlepagebottomglue = 2pc % First the title page. Must do @settitle before @titlepage. \newif\ifseenauthor \newif\iffinishedtitlepage % Do an implicit @contents or @shortcontents after @end titlepage if the % user says @setcontentsaftertitlepage or @setshortcontentsaftertitlepage. % \newif\ifsetcontentsaftertitlepage \let\setcontentsaftertitlepage = \setcontentsaftertitlepagetrue \newif\ifsetshortcontentsaftertitlepage \let\setshortcontentsaftertitlepage = \setshortcontentsaftertitlepagetrue \parseargdef\shorttitlepage{\begingroup\hbox{}\vskip 1.5in \chaprm \centerline{#1}% \endgroup\page\hbox{}\page} \envdef\titlepage{% % Open one extra group, as we want to close it in the middle of \Etitlepage. \begingroup \parindent=0pt \textfonts % Leave some space at the very top of the page. \vglue\titlepagetopglue % No rule at page bottom unless we print one at the top with @title. \finishedtitlepagetrue % % Most title ``pages'' are actually two pages long, with space % at the top of the second. We don't want the ragged left on the second. \let\oldpage = \page \def\page{% \iffinishedtitlepage\else \finishtitlepage \fi \let\page = \oldpage \page \null }% } \def\Etitlepage{% \iffinishedtitlepage\else \finishtitlepage \fi % It is important to do the page break before ending the group, % because the headline and footline are only empty inside the group. % If we use the new definition of \page, we always get a blank page % after the title page, which we certainly don't want. \oldpage \endgroup % % Need this before the \...aftertitlepage checks so that if they are % in effect the toc pages will come out with page numbers. \HEADINGSon % % If they want short, they certainly want long too. \ifsetshortcontentsaftertitlepage \shortcontents \contents \global\let\shortcontents = \relax \global\let\contents = \relax \fi % \ifsetcontentsaftertitlepage \contents \global\let\contents = \relax \global\let\shortcontents = \relax \fi } \def\finishtitlepage{% \vskip4pt \hrule height 2pt width \hsize \vskip\titlepagebottomglue \finishedtitlepagetrue } %%% Macros to be used within @titlepage: \let\subtitlerm=\tenrm \def\subtitlefont{\subtitlerm \normalbaselineskip = 13pt \normalbaselines} \def\authorfont{\authorrm \normalbaselineskip = 16pt \normalbaselines \let\tt=\authortt} \parseargdef\title{% \checkenv\titlepage \leftline{\titlefonts\rm #1} % print a rule at the page bottom also. \finishedtitlepagefalse \vskip4pt \hrule height 4pt width \hsize \vskip4pt } \parseargdef\subtitle{% \checkenv\titlepage {\subtitlefont \rightline{#1}}% } % @author should come last, but may come many times. % It can also be used inside @quotation. % \parseargdef\author{% \def\temp{\quotation}% \ifx\thisenv\temp \def\quotationauthor{#1}% printed in \Equotation. \else \checkenv\titlepage \ifseenauthor\else \vskip 0pt plus 1filll \seenauthortrue \fi {\authorfont \leftline{#1}}% \fi } %%% Set up page headings and footings. \let\thispage=\folio \newtoks\evenheadline % headline on even pages \newtoks\oddheadline % headline on odd pages \newtoks\evenfootline % footline on even pages \newtoks\oddfootline % footline on odd pages % Now make TeX use those variables \headline={{\textfonts\rm \ifodd\pageno \the\oddheadline \else \the\evenheadline \fi}} \footline={{\textfonts\rm \ifodd\pageno \the\oddfootline \else \the\evenfootline \fi}\HEADINGShook} \let\HEADINGShook=\relax % Commands to set those variables. % For example, this is what @headings on does % @evenheading @thistitle|@thispage|@thischapter % @oddheading @thischapter|@thispage|@thistitle % @evenfooting @thisfile|| % @oddfooting ||@thisfile \def\evenheading{\parsearg\evenheadingxxx} \def\evenheadingxxx #1{\evenheadingyyy #1\|\|\|\|\finish} \def\evenheadingyyy #1\|#2\|#3\|#4\finish{% \global\evenheadline={\rlap{\centerline{#2}}\line{#1\hfil#3}}} \def\oddheading{\parsearg\oddheadingxxx} \def\oddheadingxxx #1{\oddheadingyyy #1\|\|\|\|\finish} \def\oddheadingyyy #1\|#2\|#3\|#4\finish{% \global\oddheadline={\rlap{\centerline{#2}}\line{#1\hfil#3}}} \parseargdef\everyheading{\oddheadingxxx{#1}\evenheadingxxx{#1}}% \def\evenfooting{\parsearg\evenfootingxxx} \def\evenfootingxxx #1{\evenfootingyyy #1\|\|\|\|\finish} \def\evenfootingyyy #1\|#2\|#3\|#4\finish{% \global\evenfootline={\rlap{\centerline{#2}}\line{#1\hfil#3}}} \def\oddfooting{\parsearg\oddfootingxxx} \def\oddfootingxxx #1{\oddfootingyyy #1\|\|\|\|\finish} \def\oddfootingyyy #1\|#2\|#3\|#4\finish{% \global\oddfootline = {\rlap{\centerline{#2}}\line{#1\hfil#3}}% % % Leave some space for the footline. Hopefully ok to assume % @evenfooting will not be used by itself. \global\advance\pageheight by -\baselineskip \global\advance\vsize by -\baselineskip } \parseargdef\everyfooting{\oddfootingxxx{#1}\evenfootingxxx{#1}} % @headings double turns headings on for double-sided printing. % @headings single turns headings on for single-sided printing. % @headings off turns them off. % @headings on same as @headings double, retained for compatibility. % @headings after turns on double-sided headings after this page. % @headings doubleafter turns on double-sided headings after this page. % @headings singleafter turns on single-sided headings after this page. % By default, they are off at the start of a document, % and turned `on' after @end titlepage. \def\headings #1 {\csname HEADINGS#1\endcsname} \def\HEADINGSoff{% \global\evenheadline={\hfil} \global\evenfootline={\hfil} \global\oddheadline={\hfil} \global\oddfootline={\hfil}} \HEADINGSoff % When we turn headings on, set the page number to 1. % For double-sided printing, put current file name in lower left corner, % chapter name on inside top of right hand pages, document % title on inside top of left hand pages, and page numbers on outside top % edge of all pages. \def\HEADINGSdouble{% \global\pageno=1 \global\evenfootline={\hfil} \global\oddfootline={\hfil} \global\evenheadline={\line{\folio\hfil\thistitle}} \global\oddheadline={\line{\thischapter\hfil\folio}} \global\let\contentsalignmacro = \chapoddpage } \let\contentsalignmacro = \chappager % For single-sided printing, chapter title goes across top left of page, % page number on top right. \def\HEADINGSsingle{% \global\pageno=1 \global\evenfootline={\hfil} \global\oddfootline={\hfil} \global\evenheadline={\line{\thischapter\hfil\folio}} \global\oddheadline={\line{\thischapter\hfil\folio}} \global\let\contentsalignmacro = \chappager } \def\HEADINGSon{\HEADINGSdouble} \def\HEADINGSafter{\let\HEADINGShook=\HEADINGSdoublex} \let\HEADINGSdoubleafter=\HEADINGSafter \def\HEADINGSdoublex{% \global\evenfootline={\hfil} \global\oddfootline={\hfil} \global\evenheadline={\line{\folio\hfil\thistitle}} \global\oddheadline={\line{\thischapter\hfil\folio}} \global\let\contentsalignmacro = \chapoddpage } \def\HEADINGSsingleafter{\let\HEADINGShook=\HEADINGSsinglex} \def\HEADINGSsinglex{% \global\evenfootline={\hfil} \global\oddfootline={\hfil} \global\evenheadline={\line{\thischapter\hfil\folio}} \global\oddheadline={\line{\thischapter\hfil\folio}} \global\let\contentsalignmacro = \chappager } % Subroutines used in generating headings % This produces Day Month Year style of output. % Only define if not already defined, in case a txi-??.tex file has set % up a different format (e.g., txi-cs.tex does this). \ifx\today\undefined \def\today{% \number\day\space \ifcase\month \or\putwordMJan\or\putwordMFeb\or\putwordMMar\or\putwordMApr \or\putwordMMay\or\putwordMJun\or\putwordMJul\or\putwordMAug \or\putwordMSep\or\putwordMOct\or\putwordMNov\or\putwordMDec \fi \space\number\year} \fi % @settitle line... specifies the title of the document, for headings. % It generates no output of its own. \def\thistitle{\putwordNoTitle} \def\settitle{\parsearg{\gdef\thistitle}} \message{tables,} % Tables -- @table, @ftable, @vtable, @item(x). % default indentation of table text \newdimen\tableindent \tableindent=.8in % default indentation of @itemize and @enumerate text \newdimen\itemindent \itemindent=.3in % margin between end of table item and start of table text. \newdimen\itemmargin \itemmargin=.1in % used internally for \itemindent minus \itemmargin \newdimen\itemmax % Note @table, @ftable, and @vtable define @item, @itemx, etc., with % these defs. % They also define \itemindex % to index the item name in whatever manner is desired (perhaps none). \newif\ifitemxneedsnegativevskip \def\itemxpar{\par\ifitemxneedsnegativevskip\nobreak\vskip-\parskip\nobreak\fi} \def\internalBitem{\smallbreak \parsearg\itemzzz} \def\internalBitemx{\itemxpar \parsearg\itemzzz} \def\itemzzz #1{\begingroup % \advance\hsize by -\rightskip \advance\hsize by -\tableindent \setbox0=\hbox{\itemindicate{#1}}% \itemindex{#1}% \nobreak % This prevents a break before @itemx. % % If the item text does not fit in the space we have, put it on a line % by itself, and do not allow a page break either before or after that % line. We do not start a paragraph here because then if the next % command is, e.g., @kindex, the whatsit would get put into the % horizontal list on a line by itself, resulting in extra blank space. \ifdim \wd0>\itemmax % % Make this a paragraph so we get the \parskip glue and wrapping, % but leave it ragged-right. \begingroup \advance\leftskip by-\tableindent \advance\hsize by\tableindent \advance\rightskip by0pt plus1fil \leavevmode\unhbox0\par \endgroup % % We're going to be starting a paragraph, but we don't want the % \parskip glue -- logically it's part of the @item we just started. \nobreak \vskip-\parskip % % Stop a page break at the \parskip glue coming up. However, if % what follows is an environment such as @example, there will be no % \parskip glue; then the negative vskip we just inserted would % cause the example and the item to crash together. So we use this % bizarre value of 10001 as a signal to \aboveenvbreak to insert % \parskip glue after all. Section titles are handled this way also. % \penalty 10001 \endgroup \itemxneedsnegativevskipfalse \else % The item text fits into the space. Start a paragraph, so that the % following text (if any) will end up on the same line. \noindent % Do this with kerns and \unhbox so that if there is a footnote in % the item text, it can migrate to the main vertical list and % eventually be printed. \nobreak\kern-\tableindent \dimen0 = \itemmax \advance\dimen0 by \itemmargin \advance\dimen0 by -\wd0 \unhbox0 \nobreak\kern\dimen0 \endgroup \itemxneedsnegativevskiptrue \fi } \def\item{\errmessage{@item while not in a list environment}} \def\itemx{\errmessage{@itemx while not in a list environment}} % @table, @ftable, @vtable. \envdef\table{% \let\itemindex\gobble \tablecheck{table}% } \envdef\ftable{% \def\itemindex ##1{\doind {fn}{\code{##1}}}% \tablecheck{ftable}% } \envdef\vtable{% \def\itemindex ##1{\doind {vr}{\code{##1}}}% \tablecheck{vtable}% } \def\tablecheck#1{% \ifnum \the\catcode`\^^M=\active \endgroup \errmessage{This command won't work in this context; perhaps the problem is that we are \inenvironment\thisenv}% \def\next{\doignore{#1}}% \else \let\next\tablex \fi \next } \def\tablex#1{% \def\itemindicate{#1}% \parsearg\tabley } \def\tabley#1{% {% \makevalueexpandable \edef\temp{\noexpand\tablez #1\space\space\space}% \expandafter }\temp \endtablez } \def\tablez #1 #2 #3 #4\endtablez{% \aboveenvbreak \ifnum 0#1>0 \advance \leftskip by #1\mil \fi \ifnum 0#2>0 \tableindent=#2\mil \fi \ifnum 0#3>0 \advance \rightskip by #3\mil \fi \itemmax=\tableindent \advance \itemmax by -\itemmargin \advance \leftskip by \tableindent \exdentamount=\tableindent \parindent = 0pt \parskip = \smallskipamount \ifdim \parskip=0pt \parskip=2pt \fi \let\item = \internalBitem \let\itemx = \internalBitemx } \def\Etable{\endgraf\afterenvbreak} \let\Eftable\Etable \let\Evtable\Etable \let\Eitemize\Etable \let\Eenumerate\Etable % This is the counter used by @enumerate, which is really @itemize \newcount \itemno \envdef\itemize{\parsearg\doitemize} \def\doitemize#1{% \aboveenvbreak \itemmax=\itemindent \advance\itemmax by -\itemmargin \advance\leftskip by \itemindent \exdentamount=\itemindent \parindent=0pt \parskip=\smallskipamount \ifdim\parskip=0pt \parskip=2pt \fi \def\itemcontents{#1}% % @itemize with no arg is equivalent to @itemize @bullet. \ifx\itemcontents\empty\def\itemcontents{\bullet}\fi \let\item=\itemizeitem } % Definition of @item while inside @itemize and @enumerate. % \def\itemizeitem{% \advance\itemno by 1 % for enumerations {\let\par=\endgraf \smallbreak}% reasonable place to break {% % If the document has an @itemize directly after a section title, a % \nobreak will be last on the list, and \sectionheading will have % done a \vskip-\parskip. In that case, we don't want to zero % parskip, or the item text will crash with the heading. On the % other hand, when there is normal text preceding the item (as there % usually is), we do want to zero parskip, or there would be too much % space. In that case, we won't have a \nobreak before. At least % that's the theory. \ifnum\lastpenalty<10000 \parskip=0in \fi \noindent \hbox to 0pt{\hss \itemcontents \kern\itemmargin}% \vadjust{\penalty 1200}}% not good to break after first line of item. \flushcr } % \splitoff TOKENS\endmark defines \first to be the first token in % TOKENS, and \rest to be the remainder. % \def\splitoff#1#2\endmark{\def\first{#1}\def\rest{#2}}% % Allow an optional argument of an uppercase letter, lowercase letter, % or number, to specify the first label in the enumerated list. No % argument is the same as `1'. % \envparseargdef\enumerate{\enumeratey #1 \endenumeratey} \def\enumeratey #1 #2\endenumeratey{% % If we were given no argument, pretend we were given `1'. \def\thearg{#1}% \ifx\thearg\empty \def\thearg{1}\fi % % Detect if the argument is a single token. If so, it might be a % letter. Otherwise, the only valid thing it can be is a number. % (We will always have one token, because of the test we just made. % This is a good thing, since \splitoff doesn't work given nothing at % all -- the first parameter is undelimited.) \expandafter\splitoff\thearg\endmark \ifx\rest\empty % Only one token in the argument. It could still be anything. % A ``lowercase letter'' is one whose \lccode is nonzero. % An ``uppercase letter'' is one whose \lccode is both nonzero, and % not equal to itself. % Otherwise, we assume it's a number. % % We need the \relax at the end of the \ifnum lines to stop TeX from % continuing to look for a . % \ifnum\lccode\expandafter`\thearg=0\relax \numericenumerate % a number (we hope) \else % It's a letter. \ifnum\lccode\expandafter`\thearg=\expandafter`\thearg\relax \lowercaseenumerate % lowercase letter \else \uppercaseenumerate % uppercase letter \fi \fi \else % Multiple tokens in the argument. We hope it's a number. \numericenumerate \fi } % An @enumerate whose labels are integers. The starting integer is % given in \thearg. % \def\numericenumerate{% \itemno = \thearg \startenumeration{\the\itemno}% } % The starting (lowercase) letter is in \thearg. \def\lowercaseenumerate{% \itemno = \expandafter`\thearg \startenumeration{% % Be sure we're not beyond the end of the alphabet. \ifnum\itemno=0 \errmessage{No more lowercase letters in @enumerate; get a bigger alphabet}% \fi \char\lccode\itemno }% } % The starting (uppercase) letter is in \thearg. \def\uppercaseenumerate{% \itemno = \expandafter`\thearg \startenumeration{% % Be sure we're not beyond the end of the alphabet. \ifnum\itemno=0 \errmessage{No more uppercase letters in @enumerate; get a bigger alphabet} \fi \char\uccode\itemno }% } % Call \doitemize, adding a period to the first argument and supplying the % common last two arguments. Also subtract one from the initial value in % \itemno, since @item increments \itemno. % \def\startenumeration#1{% \advance\itemno by -1 \doitemize{#1.}\flushcr } % @alphaenumerate and @capsenumerate are abbreviations for giving an arg % to @enumerate. % \def\alphaenumerate{\enumerate{a}} \def\capsenumerate{\enumerate{A}} \def\Ealphaenumerate{\Eenumerate} \def\Ecapsenumerate{\Eenumerate} % @multitable macros % Amy Hendrickson, 8/18/94, 3/6/96 % % @multitable ... @end multitable will make as many columns as desired. % Contents of each column will wrap at width given in preamble. Width % can be specified either with sample text given in a template line, % or in percent of \hsize, the current width of text on page. % Table can continue over pages but will only break between lines. % To make preamble: % % Either define widths of columns in terms of percent of \hsize: % @multitable @columnfractions .25 .3 .45 % @item ... % % Numbers following @columnfractions are the percent of the total % current hsize to be used for each column. You may use as many % columns as desired. % Or use a template: % @multitable {Column 1 template} {Column 2 template} {Column 3 template} % @item ... % using the widest term desired in each column. % Each new table line starts with @item, each subsequent new column % starts with @tab. Empty columns may be produced by supplying @tab's % with nothing between them for as many times as empty columns are needed, % ie, @tab@tab@tab will produce two empty columns. % @item, @tab do not need to be on their own lines, but it will not hurt % if they are. % Sample multitable: % @multitable {Column 1 template} {Column 2 template} {Column 3 template} % @item first col stuff @tab second col stuff @tab third col % @item % first col stuff % @tab % second col stuff % @tab % third col % @item first col stuff @tab second col stuff % @tab Many paragraphs of text may be used in any column. % % They will wrap at the width determined by the template. % @item@tab@tab This will be in third column. % @end multitable % Default dimensions may be reset by user. % @multitableparskip is vertical space between paragraphs in table. % @multitableparindent is paragraph indent in table. % @multitablecolmargin is horizontal space to be left between columns. % @multitablelinespace is space to leave between table items, baseline % to baseline. % 0pt means it depends on current normal line spacing. % \newskip\multitableparskip \newskip\multitableparindent \newdimen\multitablecolspace \newskip\multitablelinespace \multitableparskip=0pt \multitableparindent=6pt \multitablecolspace=12pt \multitablelinespace=0pt % Macros used to set up halign preamble: % \let\endsetuptable\relax \def\xendsetuptable{\endsetuptable} \let\columnfractions\relax \def\xcolumnfractions{\columnfractions} \newif\ifsetpercent % #1 is the @columnfraction, usually a decimal number like .5, but might % be just 1. We just use it, whatever it is. % \def\pickupwholefraction#1 {% \global\advance\colcount by 1 \expandafter\xdef\csname col\the\colcount\endcsname{#1\hsize}% \setuptable } \newcount\colcount \def\setuptable#1{% \def\firstarg{#1}% \ifx\firstarg\xendsetuptable \let\go = \relax \else \ifx\firstarg\xcolumnfractions \global\setpercenttrue \else \ifsetpercent \let\go\pickupwholefraction \else \global\advance\colcount by 1 \setbox0=\hbox{#1\unskip\space}% Add a normal word space as a % separator; typically that is always in the input, anyway. \expandafter\xdef\csname col\the\colcount\endcsname{\the\wd0}% \fi \fi \ifx\go\pickupwholefraction % Put the argument back for the \pickupwholefraction call, so % we'll always have a period there to be parsed. \def\go{\pickupwholefraction#1}% \else \let\go = \setuptable \fi% \fi \go } % multitable-only commands. % % @headitem starts a heading row, which we typeset in bold. % Assignments have to be global since we are inside the implicit group % of an alignment entry. Note that \everycr resets \everytab. \def\headitem{\checkenv\multitable \crcr \global\everytab={\bf}\the\everytab}% % % A \tab used to include \hskip1sp. But then the space in a template % line is not enough. That is bad. So let's go back to just `&' until % we encounter the problem it was intended to solve again. % --karl, nathan@acm.org, 20apr99. \def\tab{\checkenv\multitable &\the\everytab}% % @multitable ... @end multitable definitions: % \newtoks\everytab % insert after every tab. % \envdef\multitable{% \vskip\parskip \startsavinginserts % % @item within a multitable starts a normal row. % We use \def instead of \let so that if one of the multitable entries % contains an @itemize, we don't choke on the \item (seen as \crcr aka % \endtemplate) expanding \doitemize. \def\item{\crcr}% % \tolerance=9500 \hbadness=9500 \setmultitablespacing \parskip=\multitableparskip \parindent=\multitableparindent \overfullrule=0pt \global\colcount=0 % \everycr = {% \noalign{% \global\everytab={}% \global\colcount=0 % Reset the column counter. % Check for saved footnotes, etc. \checkinserts % Keeps underfull box messages off when table breaks over pages. %\filbreak % Maybe so, but it also creates really weird page breaks when the % table breaks over pages. Wouldn't \vfil be better? Wait until the % problem manifests itself, so it can be fixed for real --karl. }% }% % \parsearg\domultitable } \def\domultitable#1{% % To parse everything between @multitable and @item: \setuptable#1 \endsetuptable % % This preamble sets up a generic column definition, which will % be used as many times as user calls for columns. % \vtop will set a single line and will also let text wrap and % continue for many paragraphs if desired. \halign\bgroup &% \global\advance\colcount by 1 \multistrut \vtop{% % Use the current \colcount to find the correct column width: \hsize=\expandafter\csname col\the\colcount\endcsname % % In order to keep entries from bumping into each other % we will add a \leftskip of \multitablecolspace to all columns after % the first one. % % If a template has been used, we will add \multitablecolspace % to the width of each template entry. % % If the user has set preamble in terms of percent of \hsize we will % use that dimension as the width of the column, and the \leftskip % will keep entries from bumping into each other. Table will start at % left margin and final column will justify at right margin. % % Make sure we don't inherit \rightskip from the outer environment. \rightskip=0pt \ifnum\colcount=1 % The first column will be indented with the surrounding text. \advance\hsize by\leftskip \else \ifsetpercent \else % If user has not set preamble in terms of percent of \hsize % we will advance \hsize by \multitablecolspace. \advance\hsize by \multitablecolspace \fi % In either case we will make \leftskip=\multitablecolspace: \leftskip=\multitablecolspace \fi % Ignoring space at the beginning and end avoids an occasional spurious % blank line, when TeX decides to break the line at the space before the % box from the multistrut, so the strut ends up on a line by itself. % For example: % @multitable @columnfractions .11 .89 % @item @code{#} % @tab Legal holiday which is valid in major parts of the whole country. % Is automatically provided with highlighting sequences respectively % marking characters. \noindent\ignorespaces##\unskip\multistrut }\cr } \def\Emultitable{% \crcr \egroup % end the \halign \global\setpercentfalse } \def\setmultitablespacing{% \def\multistrut{\strut}% just use the standard line spacing % % Compute \multitablelinespace (if not defined by user) for use in % \multitableparskip calculation. We used define \multistrut based on % this, but (ironically) that caused the spacing to be off. % See bug-texinfo report from Werner Lemberg, 31 Oct 2004 12:52:20 +0100. \ifdim\multitablelinespace=0pt \setbox0=\vbox{X}\global\multitablelinespace=\the\baselineskip \global\advance\multitablelinespace by-\ht0 \fi %% Test to see if parskip is larger than space between lines of %% table. If not, do nothing. %% If so, set to same dimension as multitablelinespace. \ifdim\multitableparskip>\multitablelinespace \global\multitableparskip=\multitablelinespace \global\advance\multitableparskip-7pt %% to keep parskip somewhat smaller %% than skip between lines in the table. \fi% \ifdim\multitableparskip=0pt \global\multitableparskip=\multitablelinespace \global\advance\multitableparskip-7pt %% to keep parskip somewhat smaller %% than skip between lines in the table. \fi} \message{conditionals,} % @iftex, @ifnotdocbook, @ifnothtml, @ifnotinfo, @ifnotplaintext, % @ifnotxml always succeed. They currently do nothing; we don't % attempt to check whether the conditionals are properly nested. But we % have to remember that they are conditionals, so that @end doesn't % attempt to close an environment group. % \def\makecond#1{% \expandafter\let\csname #1\endcsname = \relax \expandafter\let\csname iscond.#1\endcsname = 1 } \makecond{iftex} \makecond{ifnotdocbook} \makecond{ifnothtml} \makecond{ifnotinfo} \makecond{ifnotplaintext} \makecond{ifnotxml} % Ignore @ignore, @ifhtml, @ifinfo, and the like. % \def\direntry{\doignore{direntry}} \def\documentdescription{\doignore{documentdescription}} \def\docbook{\doignore{docbook}} \def\html{\doignore{html}} \def\ifdocbook{\doignore{ifdocbook}} \def\ifhtml{\doignore{ifhtml}} \def\ifinfo{\doignore{ifinfo}} \def\ifnottex{\doignore{ifnottex}} \def\ifplaintext{\doignore{ifplaintext}} \def\ifxml{\doignore{ifxml}} \def\ignore{\doignore{ignore}} \def\menu{\doignore{menu}} \def\xml{\doignore{xml}} % Ignore text until a line `@end #1', keeping track of nested conditionals. % % A count to remember the depth of nesting. \newcount\doignorecount \def\doignore#1{\begingroup % Scan in ``verbatim'' mode: \catcode`\@ = \other \catcode`\{ = \other \catcode`\} = \other % % Make sure that spaces turn into tokens that match what \doignoretext wants. \spaceisspace % % Count number of #1's that we've seen. \doignorecount = 0 % % Swallow text until we reach the matching `@end #1'. \dodoignore{#1}% } { \catcode`_=11 % We want to use \_STOP_ which cannot appear in texinfo source. \obeylines % % \gdef\dodoignore#1{% % #1 contains the command name as a string, e.g., `ifinfo'. % % Define a command to find the next `@end #1', which must be on a line % by itself. \long\def\doignoretext##1^^M@end #1{\doignoretextyyy##1^^M@#1\_STOP_}% % And this command to find another #1 command, at the beginning of a % line. (Otherwise, we would consider a line `@c @ifset', for % example, to count as an @ifset for nesting.) \long\def\doignoretextyyy##1^^M@#1##2\_STOP_{\doignoreyyy{##2}\_STOP_}% % % And now expand that command. \obeylines % \doignoretext ^^M% }% } \def\doignoreyyy#1{% \def\temp{#1}% \ifx\temp\empty % Nothing found. \let\next\doignoretextzzz \else % Found a nested condition, ... \advance\doignorecount by 1 \let\next\doignoretextyyy % ..., look for another. % If we're here, #1 ends with ^^M\ifinfo (for example). \fi \next #1% the token \_STOP_ is present just after this macro. } % We have to swallow the remaining "\_STOP_". % \def\doignoretextzzz#1{% \ifnum\doignorecount = 0 % We have just found the outermost @end. \let\next\enddoignore \else % Still inside a nested condition. \advance\doignorecount by -1 \let\next\doignoretext % Look for the next @end. \fi \next } % Finish off ignored text. \def\enddoignore{\endgroup\ignorespaces} % @set VAR sets the variable VAR to an empty value. % @set VAR REST-OF-LINE sets VAR to the value REST-OF-LINE. % % Since we want to separate VAR from REST-OF-LINE (which might be % empty), we can't just use \parsearg; we have to insert a space of our % own to delimit the rest of the line, and then take it out again if we % didn't need it. % We rely on the fact that \parsearg sets \catcode`\ =10. % \parseargdef\set{\setyyy#1 \endsetyyy} \def\setyyy#1 #2\endsetyyy{% {% \makevalueexpandable \def\temp{#2}% \edef\next{\gdef\makecsname{SET#1}}% \ifx\temp\empty \next{}% \else \setzzz#2\endsetzzz \fi }% } % Remove the trailing space \setxxx inserted. \def\setzzz#1 \endsetzzz{\next{#1}} % @clear VAR clears (i.e., unsets) the variable VAR. % \parseargdef\clear{% {% \makevalueexpandable \global\expandafter\let\csname SET#1\endcsname=\relax }% } % @value{foo} gets the text saved in variable foo. \def\value{\begingroup\makevalueexpandable\valuexxx} \def\valuexxx#1{\expandablevalue{#1}\endgroup} { \catcode`\- = \active \catcode`\_ = \active % \gdef\makevalueexpandable{% \let\value = \expandablevalue % We don't want these characters active, ... \catcode`\-=\other \catcode`\_=\other % ..., but we might end up with active ones in the argument if % we're called from @code, as @code{@value{foo-bar_}}, though. % So \let them to their normal equivalents. \let-\realdash \let_\normalunderscore } } % We have this subroutine so that we can handle at least some @value's % properly in indexes (we call \makevalueexpandable in \indexdummies). % The command has to be fully expandable (if the variable is set), since % the result winds up in the index file. This means that if the % variable's value contains other Texinfo commands, it's almost certain % it will fail (although perhaps we could fix that with sufficient work % to do a one-level expansion on the result, instead of complete). % \def\expandablevalue#1{% \expandafter\ifx\csname SET#1\endcsname\relax {[No value for ``#1'']}% \message{Variable `#1', used in @value, is not set.}% \else \csname SET#1\endcsname \fi } % @ifset VAR ... @end ifset reads the `...' iff VAR has been defined % with @set. % % To get special treatment of `@end ifset,' call \makeond and the redefine. % \makecond{ifset} \def\ifset{\parsearg{\doifset{\let\next=\ifsetfail}}} \def\doifset#1#2{% {% \makevalueexpandable \let\next=\empty \expandafter\ifx\csname SET#2\endcsname\relax #1% If not set, redefine \next. \fi \expandafter }\next } \def\ifsetfail{\doignore{ifset}} % @ifclear VAR ... @end ifclear reads the `...' iff VAR has never been % defined with @set, or has been undefined with @clear. % % The `\else' inside the `\doifset' parameter is a trick to reuse the % above code: if the variable is not set, do nothing, if it is set, % then redefine \next to \ifclearfail. % \makecond{ifclear} \def\ifclear{\parsearg{\doifset{\else \let\next=\ifclearfail}}} \def\ifclearfail{\doignore{ifclear}} % @dircategory CATEGORY -- specify a category of the dir file % which this file should belong to. Ignore this in TeX. \let\dircategory=\comment % @defininfoenclose. \let\definfoenclose=\comment \message{indexing,} % Index generation facilities % Define \newwrite to be identical to plain tex's \newwrite % except not \outer, so it can be used within macros and \if's. \edef\newwrite{\makecsname{ptexnewwrite}} % \newindex {foo} defines an index named foo. % It automatically defines \fooindex such that % \fooindex ...rest of line... puts an entry in the index foo. % It also defines \fooindfile to be the number of the output channel for % the file that accumulates this index. The file's extension is foo. % The name of an index should be no more than 2 characters long % for the sake of vms. % \def\newindex#1{% \iflinks \expandafter\newwrite \csname#1indfile\endcsname \openout \csname#1indfile\endcsname \jobname.#1 % Open the file \fi \expandafter\xdef\csname#1index\endcsname{% % Define @#1index \noexpand\doindex{#1}} } % @defindex foo == \newindex{foo} % \def\defindex{\parsearg\newindex} % Define @defcodeindex, like @defindex except put all entries in @code. % \def\defcodeindex{\parsearg\newcodeindex} % \def\newcodeindex#1{% \iflinks \expandafter\newwrite \csname#1indfile\endcsname \openout \csname#1indfile\endcsname \jobname.#1 \fi \expandafter\xdef\csname#1index\endcsname{% \noexpand\docodeindex{#1}}% } % @synindex foo bar makes index foo feed into index bar. % Do this instead of @defindex foo if you don't want it as a separate index. % % @syncodeindex foo bar similar, but put all entries made for index foo % inside @code. % \def\synindex#1 #2 {\dosynindex\doindex{#1}{#2}} \def\syncodeindex#1 #2 {\dosynindex\docodeindex{#1}{#2}} % #1 is \doindex or \docodeindex, #2 the index getting redefined (foo), % #3 the target index (bar). \def\dosynindex#1#2#3{% % Only do \closeout if we haven't already done it, else we'll end up % closing the target index. \expandafter \ifx\csname donesynindex#2\endcsname \undefined % The \closeout helps reduce unnecessary open files; the limit on the % Acorn RISC OS is a mere 16 files. \expandafter\closeout\csname#2indfile\endcsname \expandafter\let\csname\donesynindex#2\endcsname = 1 \fi % redefine \fooindfile: \expandafter\let\expandafter\temp\expandafter=\csname#3indfile\endcsname \expandafter\let\csname#2indfile\endcsname=\temp % redefine \fooindex: \expandafter\xdef\csname#2index\endcsname{\noexpand#1{#3}}% } % Define \doindex, the driver for all \fooindex macros. % Argument #1 is generated by the calling \fooindex macro, % and it is "foo", the name of the index. % \doindex just uses \parsearg; it calls \doind for the actual work. % This is because \doind is more useful to call from other macros. % There is also \dosubind {index}{topic}{subtopic} % which makes an entry in a two-level index such as the operation index. \def\doindex#1{\edef\indexname{#1}\parsearg\singleindexer} \def\singleindexer #1{\doind{\indexname}{#1}} % like the previous two, but they put @code around the argument. \def\docodeindex#1{\edef\indexname{#1}\parsearg\singlecodeindexer} \def\singlecodeindexer #1{\doind{\indexname}{\code{#1}}} % Take care of Texinfo commands that can appear in an index entry. % Since there are some commands we want to expand, and others we don't, % we have to laboriously prevent expansion for those that we don't. % \def\indexdummies{% \def\@{@}% change to @@ when we switch to @ as escape char in index files. \def\ {\realbackslash\space }% % Need these in case \tex is in effect and \{ is a \delimiter again. % But can't use \lbracecmd and \rbracecmd because texindex assumes % braces and backslashes are used only as delimiters. \let\{ = \mylbrace \let\} = \myrbrace % % \definedummyword defines \#1 as \realbackslash #1\space, thus % effectively preventing its expansion. This is used only for control % words, not control letters, because the \space would be incorrect % for control characters, but is needed to separate the control word % from whatever follows. % % For control letters, we have \definedummyletter, which omits the % space. % % These can be used both for control words that take an argument and % those that do not. If it is followed by {arg} in the input, then % that will dutifully get written to the index (or wherever). % \def\definedummyword##1{% \expandafter\def\csname ##1\endcsname{\realbackslash ##1\space}% }% \def\definedummyletter##1{% \expandafter\def\csname ##1\endcsname{\realbackslash ##1}% }% \let\definedummyaccent\definedummyletter % % Do the redefinitions. \commondummies } % For the aux file, @ is the escape character. So we want to redefine % everything using @ instead of \realbackslash. When everything uses % @, this will be simpler. % \def\atdummies{% \def\@{@@}% \def\ {@ }% \let\{ = \lbraceatcmd \let\} = \rbraceatcmd % % (See comments in \indexdummies.) \def\definedummyword##1{% \expandafter\def\csname ##1\endcsname{@##1\space}% }% \def\definedummyletter##1{% \expandafter\def\csname ##1\endcsname{@##1}% }% \let\definedummyaccent\definedummyletter % % Do the redefinitions. \commondummies } % Called from \indexdummies and \atdummies. \definedummyword and % \definedummyletter must be defined first. % \def\commondummies{% % \normalturnoffactive % \commondummiesnofonts % \definedummyletter{_}% % % Non-English letters. \definedummyword{AA}% \definedummyword{AE}% \definedummyword{L}% \definedummyword{OE}% \definedummyword{O}% \definedummyword{aa}% \definedummyword{ae}% \definedummyword{l}% \definedummyword{oe}% \definedummyword{o}% \definedummyword{ss}% \definedummyword{exclamdown}% \definedummyword{questiondown}% \definedummyword{ordf}% \definedummyword{ordm}% % % Although these internal commands shouldn't show up, sometimes they do. \definedummyword{bf}% \definedummyword{gtr}% \definedummyword{hat}% \definedummyword{less}% \definedummyword{sf}% \definedummyword{sl}% \definedummyword{tclose}% \definedummyword{tt}% % \definedummyword{LaTeX}% \definedummyword{TeX}% % % Assorted special characters. \definedummyword{bullet}% \definedummyword{comma}% \definedummyword{copyright}% \definedummyword{registeredsymbol}% \definedummyword{dots}% \definedummyword{enddots}% \definedummyword{equiv}% \definedummyword{error}% \definedummyword{euro}% \definedummyword{expansion}% \definedummyword{minus}% \definedummyword{pounds}% \definedummyword{point}% \definedummyword{print}% \definedummyword{result}% % % Handle some cases of @value -- where it does not contain any % (non-fully-expandable) commands. \makevalueexpandable % % Normal spaces, not active ones. \unsepspaces % % No macro expansion. \turnoffmacros } % \commondummiesnofonts: common to \commondummies and \indexnofonts. % % Better have this without active chars. { \catcode`\~=\other \gdef\commondummiesnofonts{% % Control letters and accents. \definedummyletter{!}% \definedummyaccent{"}% \definedummyaccent{'}% \definedummyletter{*}% \definedummyaccent{,}% \definedummyletter{.}% \definedummyletter{/}% \definedummyletter{:}% \definedummyaccent{=}% \definedummyletter{?}% \definedummyaccent{^}% \definedummyaccent{`}% \definedummyaccent{~}% \definedummyword{u}% \definedummyword{v}% \definedummyword{H}% \definedummyword{dotaccent}% \definedummyword{ringaccent}% \definedummyword{tieaccent}% \definedummyword{ubaraccent}% \definedummyword{udotaccent}% \definedummyword{dotless}% % % Texinfo font commands. \definedummyword{b}% \definedummyword{i}% \definedummyword{r}% \definedummyword{sc}% \definedummyword{t}% % % Commands that take arguments. \definedummyword{acronym}% \definedummyword{cite}% \definedummyword{code}% \definedummyword{command}% \definedummyword{dfn}% \definedummyword{emph}% \definedummyword{env}% \definedummyword{file}% \definedummyword{kbd}% \definedummyword{key}% \definedummyword{math}% \definedummyword{option}% \definedummyword{samp}% \definedummyword{strong}% \definedummyword{tie}% \definedummyword{uref}% \definedummyword{url}% \definedummyword{var}% \definedummyword{verb}% \definedummyword{w}% } } % \indexnofonts is used when outputting the strings to sort the index % by, and when constructing control sequence names. It eliminates all % control sequences and just writes whatever the best ASCII sort string % would be for a given command (usually its argument). % \def\indexnofonts{% % Accent commands should become @asis. \def\definedummyaccent##1{% \expandafter\let\csname ##1\endcsname\asis }% % We can just ignore other control letters. \def\definedummyletter##1{% \expandafter\def\csname ##1\endcsname{}% }% % Hopefully, all control words can become @asis. \let\definedummyword\definedummyaccent % \commondummiesnofonts % % Don't no-op \tt, since it isn't a user-level command % and is used in the definitions of the active chars like <, >, |, etc. % Likewise with the other plain tex font commands. %\let\tt=\asis % \def\ { }% \def\@{@}% % how to handle braces? \def\_{\normalunderscore}% % % Non-English letters. \def\AA{AA}% \def\AE{AE}% \def\L{L}% \def\OE{OE}% \def\O{O}% \def\aa{aa}% \def\ae{ae}% \def\l{l}% \def\oe{oe}% \def\o{o}% \def\ss{ss}% \def\exclamdown{!}% \def\questiondown{?}% \def\ordf{a}% \def\ordm{o}% % \def\LaTeX{LaTeX}% \def\TeX{TeX}% % % Assorted special characters. % (The following {} will end up in the sort string, but that's ok.) \def\bullet{bullet}% \def\comma{,}% \def\copyright{copyright}% \def\registeredsymbol{R}% \def\dots{...}% \def\enddots{...}% \def\equiv{==}% \def\error{error}% \def\euro{euro}% \def\expansion{==>}% \def\minus{-}% \def\pounds{pounds}% \def\point{.}% \def\print{-|}% \def\result{=>}% % % Don't write macro names. \emptyusermacros } \let\indexbackslash=0 %overridden during \printindex. \let\SETmarginindex=\relax % put index entries in margin (undocumented)? % Most index entries go through here, but \dosubind is the general case. % #1 is the index name, #2 is the entry text. \def\doind#1#2{\dosubind{#1}{#2}{}} % Workhorse for all \fooindexes. % #1 is name of index, #2 is stuff to put there, #3 is subentry -- % empty if called from \doind, as we usually are (the main exception % is with most defuns, which call us directly). % \def\dosubind#1#2#3{% \iflinks {% % Store the main index entry text (including the third arg). \toks0 = {#2}% % If third arg is present, precede it with a space. \def\thirdarg{#3}% \ifx\thirdarg\empty \else \toks0 = \expandafter{\the\toks0 \space #3}% \fi % \edef\writeto{\csname#1indfile\endcsname}% % \ifvmode \dosubindsanitize \else \dosubindwrite \fi }% \fi } % Write the entry in \toks0 to the index file: % \def\dosubindwrite{% % Put the index entry in the margin if desired. \ifx\SETmarginindex\relax\else \insert\margin{\hbox{\vrule height8pt depth3pt width0pt \the\toks0}}% \fi % % Remember, we are within a group. \indexdummies % Must do this here, since \bf, etc expand at this stage \escapechar=`\\ \def\backslashcurfont{\indexbackslash}% \indexbackslash isn't defined now % so it will be output as is; and it will print as backslash. % % Process the index entry with all font commands turned off, to % get the string to sort by. {\indexnofonts \edef\temp{\the\toks0}% need full expansion \xdef\indexsorttmp{\temp}% }% % % Set up the complete index entry, with both the sort key and % the original text, including any font commands. We write % three arguments to \entry to the .?? file (four in the % subentry case), texindex reduces to two when writing the .??s % sorted result. \edef\temp{% \write\writeto{% \string\entry{\indexsorttmp}{\noexpand\folio}{\the\toks0}}% }% \temp } % Take care of unwanted page breaks: % % If a skip is the last thing on the list now, preserve it % by backing up by \lastskip, doing the \write, then inserting % the skip again. Otherwise, the whatsit generated by the % \write will make \lastskip zero. The result is that sequences % like this: % @end defun % @tindex whatever % @defun ... % will have extra space inserted, because the \medbreak in the % start of the @defun won't see the skip inserted by the @end of % the previous defun. % % But don't do any of this if we're not in vertical mode. We % don't want to do a \vskip and prematurely end a paragraph. % % Avoid page breaks due to these extra skips, too. % % But wait, there is a catch there: % We'll have to check whether \lastskip is zero skip. \ifdim is not % sufficient for this purpose, as it ignores stretch and shrink parts % of the skip. The only way seems to be to check the textual % representation of the skip. % % The following is almost like \def\zeroskipmacro{0.0pt} except that % the ``p'' and ``t'' characters have catcode \other, not 11 (letter). % \edef\zeroskipmacro{\expandafter\the\csname z@skip\endcsname} % % ..., ready, GO: % \def\dosubindsanitize{% % \lastskip and \lastpenalty cannot both be nonzero simultaneously. \skip0 = \lastskip \edef\lastskipmacro{\the\lastskip}% \count255 = \lastpenalty % % If \lastskip is nonzero, that means the last item was a % skip. And since a skip is discardable, that means this % -\skip0 glue we're inserting is preceded by a % non-discardable item, therefore it is not a potential % breakpoint, therefore no \nobreak needed. \ifx\lastskipmacro\zeroskipmacro \else \vskip-\skip0 \fi % \dosubindwrite % \ifx\lastskipmacro\zeroskipmacro % If \lastskip was zero, perhaps the last item was a penalty, and % perhaps it was >=10000, e.g., a \nobreak. In that case, we want % to re-insert the same penalty (values >10000 are used for various % signals); since we just inserted a non-discardable item, any % following glue (such as a \parskip) would be a breakpoint. For example: % % @deffn deffn-whatever % @vindex index-whatever % Description. % would allow a break between the index-whatever whatsit % and the "Description." paragraph. \ifnum\count255>9999 \penalty\count255 \fi \else % On the other hand, if we had a nonzero \lastskip, % this make-up glue would be preceded by a non-discardable item % (the whatsit from the \write), so we must insert a \nobreak. \nobreak\vskip\skip0 \fi } % The index entry written in the file actually looks like % \entry {sortstring}{page}{topic} % or % \entry {sortstring}{page}{topic}{subtopic} % The texindex program reads in these files and writes files % containing these kinds of lines: % \initial {c} % before the first topic whose initial is c % \entry {topic}{pagelist} % for a topic that is used without subtopics % \primary {topic} % for the beginning of a topic that is used with subtopics % \secondary {subtopic}{pagelist} % for each subtopic. % Define the user-accessible indexing commands % @findex, @vindex, @kindex, @cindex. \def\findex {\fnindex} \def\kindex {\kyindex} \def\cindex {\cpindex} \def\vindex {\vrindex} \def\tindex {\tpindex} \def\pindex {\pgindex} \def\cindexsub {\begingroup\obeylines\cindexsub} {\obeylines % \gdef\cindexsub "#1" #2^^M{\endgroup % \dosubind{cp}{#2}{#1}}} % Define the macros used in formatting output of the sorted index material. % @printindex causes a particular index (the ??s file) to get printed. % It does not print any chapter heading (usually an @unnumbered). % \parseargdef\printindex{\begingroup \dobreak \chapheadingskip{10000}% % \smallfonts \rm \tolerance = 9500 \everypar = {}% don't want the \kern\-parindent from indentation suppression. % % See if the index file exists and is nonempty. % Change catcode of @ here so that if the index file contains % \initial {@} % as its first line, TeX doesn't complain about mismatched braces % (because it thinks @} is a control sequence). \catcode`\@ = 11 \openin 1 \jobname.#1s \ifeof 1 % \enddoublecolumns gets confused if there is no text in the index, % and it loses the chapter title and the aux file entries for the % index. The easiest way to prevent this problem is to make sure % there is some text. \putwordIndexNonexistent \else % % If the index file exists but is empty, then \openin leaves \ifeof % false. We have to make TeX try to read something from the file, so % it can discover if there is anything in it. \read 1 to \temp \ifeof 1 \putwordIndexIsEmpty \else % Index files are almost Texinfo source, but we use \ as the escape % character. It would be better to use @, but that's too big a change % to make right now. \def\indexbackslash{\backslashcurfont}% \catcode`\\ = 0 \escapechar = `\\ \begindoublecolumns \input \jobname.#1s \enddoublecolumns \fi \fi \closein 1 \endgroup} % These macros are used by the sorted index file itself. % Change them to control the appearance of the index. \def\initial#1{{% % Some minor font changes for the special characters. \let\tentt=\sectt \let\tt=\sectt \let\sf=\sectt % % Remove any glue we may have, we'll be inserting our own. \removelastskip % % We like breaks before the index initials, so insert a bonus. \nobreak \vskip 0pt plus 3\baselineskip \penalty 0 \vskip 0pt plus -3\baselineskip % % Typeset the initial. Making this add up to a whole number of % baselineskips increases the chance of the dots lining up from column % to column. It still won't often be perfect, because of the stretch % we need before each entry, but it's better. % % No shrink because it confuses \balancecolumns. \vskip 1.67\baselineskip plus .5\baselineskip \leftline{\secbf #1}% % Do our best not to break after the initial. \nobreak \vskip .33\baselineskip plus .1\baselineskip }} % \entry typesets a paragraph consisting of the text (#1), dot leaders, and % then page number (#2) flushed to the right margin. It is used for index % and table of contents entries. The paragraph is indented by \leftskip. % % A straightforward implementation would start like this: % \def\entry#1#2{... % But this frozes the catcodes in the argument, and can cause problems to % @code, which sets - active. This problem was fixed by a kludge--- % ``-'' was active throughout whole index, but this isn't really right. % % The right solution is to prevent \entry from swallowing the whole text. % --kasal, 21nov03 \def\entry{% \begingroup % % Start a new paragraph if necessary, so our assignments below can't % affect previous text. \par % % Do not fill out the last line with white space. \parfillskip = 0in % % No extra space above this paragraph. \parskip = 0in % % Do not prefer a separate line ending with a hyphen to fewer lines. \finalhyphendemerits = 0 % % \hangindent is only relevant when the entry text and page number % don't both fit on one line. In that case, bob suggests starting the % dots pretty far over on the line. Unfortunately, a large % indentation looks wrong when the entry text itself is broken across % lines. So we use a small indentation and put up with long leaders. % % \hangafter is reset to 1 (which is the value we want) at the start % of each paragraph, so we need not do anything with that. \hangindent = 2em % % When the entry text needs to be broken, just fill out the first line % with blank space. \rightskip = 0pt plus1fil % % A bit of stretch before each entry for the benefit of balancing % columns. \vskip 0pt plus1pt % % Swallow the left brace of the text (first parameter): \afterassignment\doentry \let\temp = } \def\doentry{% \bgroup % Instead of the swallowed brace. \noindent \aftergroup\finishentry % And now comes the text of the entry. } \def\finishentry#1{% % #1 is the page number. % % The following is kludged to not output a line of dots in the index if % there are no page numbers. The next person who breaks this will be % cursed by a Unix daemon. \def\tempa{{\rm }}% \def\tempb{#1}% \edef\tempc{\tempa}% \edef\tempd{\tempb}% \ifx\tempc\tempd \ % \else % % If we must, put the page number on a line of its own, and fill out % this line with blank space. (The \hfil is overwhelmed with the % fill leaders glue in \indexdotfill if the page number does fit.) \hfil\penalty50 \null\nobreak\indexdotfill % Have leaders before the page number. % % The `\ ' here is removed by the implicit \unskip that TeX does as % part of (the primitive) \par. Without it, a spurious underfull % \hbox ensues. \ifpdf \pdfgettoks#1.% \ \the\toksA \else \ #1% \fi \fi \par \endgroup } % Like \dotfill except takes at least 1 em. \def\indexdotfill{\cleaders \hbox{$\mathsurround=0pt \mkern1.5mu ${\it .}$ \mkern1.5mu$}\hskip 1em plus 1fill} \def\primary #1{\line{#1\hfil}} \newskip\secondaryindent \secondaryindent=0.5cm \def\secondary#1#2{{% \parfillskip=0in \parskip=0in \hangindent=1in \hangafter=1 \noindent\hskip\secondaryindent\hbox{#1}\indexdotfill \ifpdf \pdfgettoks#2.\ \the\toksA % The page number ends the paragraph. \else #2 \fi \par }} % Define two-column mode, which we use to typeset indexes. % Adapted from the TeXbook, page 416, which is to say, % the manmac.tex format used to print the TeXbook itself. \catcode`\@=11 \newbox\partialpage \newdimen\doublecolumnhsize \def\begindoublecolumns{\begingroup % ended by \enddoublecolumns % Grab any single-column material above us. \output = {% % % Here is a possibility not foreseen in manmac: if we accumulate a % whole lot of material, we might end up calling this \output % routine twice in a row (see the doublecol-lose test, which is % essentially a couple of indexes with @setchapternewpage off). In % that case we just ship out what is in \partialpage with the normal % output routine. Generally, \partialpage will be empty when this % runs and this will be a no-op. See the indexspread.tex test case. \ifvoid\partialpage \else \onepageout{\pagecontents\partialpage}% \fi % \global\setbox\partialpage = \vbox{% % Unvbox the main output page. \unvbox\PAGE \kern-\topskip \kern\baselineskip }% }% \eject % run that output routine to set \partialpage % % Use the double-column output routine for subsequent pages. \output = {\doublecolumnout}% % % Change the page size parameters. We could do this once outside this % routine, in each of @smallbook, @afourpaper, and the default 8.5x11 % format, but then we repeat the same computation. Repeating a couple % of assignments once per index is clearly meaningless for the % execution time, so we may as well do it in one place. % % First we halve the line length, less a little for the gutter between % the columns. We compute the gutter based on the line length, so it % changes automatically with the paper format. The magic constant % below is chosen so that the gutter has the same value (well, +-<1pt) % as it did when we hard-coded it. % % We put the result in a separate register, \doublecolumhsize, so we % can restore it in \pagesofar, after \hsize itself has (potentially) % been clobbered. % \doublecolumnhsize = \hsize \advance\doublecolumnhsize by -.04154\hsize \divide\doublecolumnhsize by 2 \hsize = \doublecolumnhsize % % Double the \vsize as well. (We don't need a separate register here, % since nobody clobbers \vsize.) \vsize = 2\vsize } % The double-column output routine for all double-column pages except % the last. % \def\doublecolumnout{% \splittopskip=\topskip \splitmaxdepth=\maxdepth % Get the available space for the double columns -- the normal % (undoubled) page height minus any material left over from the % previous page. \dimen@ = \vsize \divide\dimen@ by 2 \advance\dimen@ by -\ht\partialpage % % box0 will be the left-hand column, box2 the right. \setbox0=\vsplit255 to\dimen@ \setbox2=\vsplit255 to\dimen@ \onepageout\pagesofar \unvbox255 \penalty\outputpenalty } % % Re-output the contents of the output page -- any previous material, % followed by the two boxes we just split, in box0 and box2. \def\pagesofar{% \unvbox\partialpage % \hsize = \doublecolumnhsize \wd0=\hsize \wd2=\hsize \hbox to\pagewidth{\box0\hfil\box2}% } % % All done with double columns. \def\enddoublecolumns{% \output = {% % Split the last of the double-column material. Leave it on the % current page, no automatic page break. \balancecolumns % % If we end up splitting too much material for the current page, % though, there will be another page break right after this \output % invocation ends. Having called \balancecolumns once, we do not % want to call it again. Therefore, reset \output to its normal % definition right away. (We hope \balancecolumns will never be % called on to balance too much material, but if it is, this makes % the output somewhat more palatable.) \global\output = {\onepageout{\pagecontents\PAGE}}% }% \eject \endgroup % started in \begindoublecolumns % % \pagegoal was set to the doubled \vsize above, since we restarted % the current page. We're now back to normal single-column % typesetting, so reset \pagegoal to the normal \vsize (after the % \endgroup where \vsize got restored). \pagegoal = \vsize } % % Called at the end of the double column material. \def\balancecolumns{% \setbox0 = \vbox{\unvbox255}% like \box255 but more efficient, see p.120. \dimen@ = \ht0 \advance\dimen@ by \topskip \advance\dimen@ by-\baselineskip \divide\dimen@ by 2 % target to split to %debug\message{final 2-column material height=\the\ht0, target=\the\dimen@.}% \splittopskip = \topskip % Loop until we get a decent breakpoint. {% \vbadness = 10000 \loop \global\setbox3 = \copy0 \global\setbox1 = \vsplit3 to \dimen@ \ifdim\ht3>\dimen@ \global\advance\dimen@ by 1pt \repeat }% %debug\message{split to \the\dimen@, column heights: \the\ht1, \the\ht3.}% \setbox0=\vbox to\dimen@{\unvbox1}% \setbox2=\vbox to\dimen@{\unvbox3}% % \pagesofar } \catcode`\@ = \other \message{sectioning,} % Chapters, sections, etc. % \unnumberedno is an oxymoron, of course. But we count the unnumbered % sections so that we can refer to them unambiguously in the pdf % outlines by their "section number". We avoid collisions with chapter % numbers by starting them at 10000. (If a document ever has 10000 % chapters, we're in trouble anyway, I'm sure.) \newcount\unnumberedno \unnumberedno = 10000 \newcount\chapno \newcount\secno \secno=0 \newcount\subsecno \subsecno=0 \newcount\subsubsecno \subsubsecno=0 % This counter is funny since it counts through charcodes of letters A, B, ... \newcount\appendixno \appendixno = `\@ % % \def\appendixletter{\char\the\appendixno} % We do the following ugly conditional instead of the above simple % construct for the sake of pdftex, which needs the actual % letter in the expansion, not just typeset. % \def\appendixletter{% \ifnum\appendixno=`A A% \else\ifnum\appendixno=`B B% \else\ifnum\appendixno=`C C% \else\ifnum\appendixno=`D D% \else\ifnum\appendixno=`E E% \else\ifnum\appendixno=`F F% \else\ifnum\appendixno=`G G% \else\ifnum\appendixno=`H H% \else\ifnum\appendixno=`I I% \else\ifnum\appendixno=`J J% \else\ifnum\appendixno=`K K% \else\ifnum\appendixno=`L L% \else\ifnum\appendixno=`M M% \else\ifnum\appendixno=`N N% \else\ifnum\appendixno=`O O% \else\ifnum\appendixno=`P P% \else\ifnum\appendixno=`Q Q% \else\ifnum\appendixno=`R R% \else\ifnum\appendixno=`S S% \else\ifnum\appendixno=`T T% \else\ifnum\appendixno=`U U% \else\ifnum\appendixno=`V V% \else\ifnum\appendixno=`W W% \else\ifnum\appendixno=`X X% \else\ifnum\appendixno=`Y Y% \else\ifnum\appendixno=`Z Z% % The \the is necessary, despite appearances, because \appendixletter is % expanded while writing the .toc file. \char\appendixno is not % expandable, thus it is written literally, thus all appendixes come out % with the same letter (or @) in the toc without it. \else\char\the\appendixno \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi} % Each @chapter defines this as the name of the chapter. % page headings and footings can use it. @section does likewise. % However, they are not reliable, because we don't use marks. \def\thischapter{} \def\thissection{} \newcount\absseclevel % used to calculate proper heading level \newcount\secbase\secbase=0 % @raisesections/@lowersections modify this count % @raisesections: treat @section as chapter, @subsection as section, etc. \def\raisesections{\global\advance\secbase by -1} \let\up=\raisesections % original BFox name % @lowersections: treat @chapter as section, @section as subsection, etc. \def\lowersections{\global\advance\secbase by 1} \let\down=\lowersections % original BFox name % we only have subsub. \chardef\maxseclevel = 3 % % A numbered section within an unnumbered changes to unnumbered too. % To achive this, remember the "biggest" unnum. sec. we are currently in: \chardef\unmlevel = \maxseclevel % % Trace whether the current chapter is an appendix or not: % \chapheadtype is "N" or "A", unnumbered chapters are ignored. \def\chapheadtype{N} % Choose a heading macro % #1 is heading type % #2 is heading level % #3 is text for heading \def\genhead#1#2#3{% % Compute the abs. sec. level: \absseclevel=#2 \advance\absseclevel by \secbase % Make sure \absseclevel doesn't fall outside the range: \ifnum \absseclevel < 0 \absseclevel = 0 \else \ifnum \absseclevel > 3 \absseclevel = 3 \fi \fi % The heading type: \def\headtype{#1}% \if \headtype U% \ifnum \absseclevel < \unmlevel \chardef\unmlevel = \absseclevel \fi \else % Check for appendix sections: \ifnum \absseclevel = 0 \edef\chapheadtype{\headtype}% \else \if \headtype A\if \chapheadtype N% \errmessage{@appendix... within a non-appendix chapter}% \fi\fi \fi % Check for numbered within unnumbered: \ifnum \absseclevel > \unmlevel \def\headtype{U}% \else \chardef\unmlevel = 3 \fi \fi % Now print the heading: \if \headtype U% \ifcase\absseclevel \unnumberedzzz{#3}% \or \unnumberedseczzz{#3}% \or \unnumberedsubseczzz{#3}% \or \unnumberedsubsubseczzz{#3}% \fi \else \if \headtype A% \ifcase\absseclevel \appendixzzz{#3}% \or \appendixsectionzzz{#3}% \or \appendixsubseczzz{#3}% \or \appendixsubsubseczzz{#3}% \fi \else \ifcase\absseclevel \chapterzzz{#3}% \or \seczzz{#3}% \or \numberedsubseczzz{#3}% \or \numberedsubsubseczzz{#3}% \fi \fi \fi \suppressfirstparagraphindent } % an interface: \def\numhead{\genhead N} \def\apphead{\genhead A} \def\unnmhead{\genhead U} % @chapter, @appendix, @unnumbered. Increment top-level counter, reset % all lower-level sectioning counters to zero. % % Also set \chaplevelprefix, which we prepend to @float sequence numbers % (e.g., figures), q.v. By default (before any chapter), that is empty. \let\chaplevelprefix = \empty % \outer\parseargdef\chapter{\numhead0{#1}} % normally numhead0 calls chapterzzz \def\chapterzzz#1{% % section resetting is \global in case the chapter is in a group, such % as an @include file. \global\secno=0 \global\subsecno=0 \global\subsubsecno=0 \global\advance\chapno by 1 % % Used for \float. \gdef\chaplevelprefix{\the\chapno.}% \resetallfloatnos % \message{\putwordChapter\space \the\chapno}% % % Write the actual heading. \chapmacro{#1}{Ynumbered}{\the\chapno}% % % So @section and the like are numbered underneath this chapter. \global\let\section = \numberedsec \global\let\subsection = \numberedsubsec \global\let\subsubsection = \numberedsubsubsec } \outer\parseargdef\appendix{\apphead0{#1}} % normally apphead0 calls appendixzzz \def\appendixzzz#1{% \global\secno=0 \global\subsecno=0 \global\subsubsecno=0 \global\advance\appendixno by 1 \gdef\chaplevelprefix{\appendixletter.}% \resetallfloatnos % \def\appendixnum{\putwordAppendix\space \appendixletter}% \message{\appendixnum}% % \chapmacro{#1}{Yappendix}{\appendixletter}% % \global\let\section = \appendixsec \global\let\subsection = \appendixsubsec \global\let\subsubsection = \appendixsubsubsec } \outer\parseargdef\unnumbered{\unnmhead0{#1}} % normally unnmhead0 calls unnumberedzzz \def\unnumberedzzz#1{% \global\secno=0 \global\subsecno=0 \global\subsubsecno=0 \global\advance\unnumberedno by 1 % % Since an unnumbered has no number, no prefix for figures. \global\let\chaplevelprefix = \empty \resetallfloatnos % % This used to be simply \message{#1}, but TeX fully expands the % argument to \message. Therefore, if #1 contained @-commands, TeX % expanded them. For example, in `@unnumbered The @cite{Book}', TeX % expanded @cite (which turns out to cause errors because \cite is meant % to be executed, not expanded). % % Anyway, we don't want the fully-expanded definition of @cite to appear % as a result of the \message, we just want `@cite' itself. We use % \the to achieve this: TeX expands \the only once, % simply yielding the contents of . (We also do this for % the toc entries.) \toks0 = {#1}% \message{(\the\toks0)}% % \chapmacro{#1}{Ynothing}{\the\unnumberedno}% % \global\let\section = \unnumberedsec \global\let\subsection = \unnumberedsubsec \global\let\subsubsection = \unnumberedsubsubsec } % @centerchap is like @unnumbered, but the heading is centered. \outer\parseargdef\centerchap{% % Well, we could do the following in a group, but that would break % an assumption that \chapmacro is called at the outermost level. % Thus we are safer this way: --kasal, 24feb04 \let\centerparametersmaybe = \centerparameters \unnmhead0{#1}% \let\centerparametersmaybe = \relax } % @top is like @unnumbered. \let\top\unnumbered % Sections. \outer\parseargdef\numberedsec{\numhead1{#1}} % normally calls seczzz \def\seczzz#1{% \global\subsecno=0 \global\subsubsecno=0 \global\advance\secno by 1 \sectionheading{#1}{sec}{Ynumbered}{\the\chapno.\the\secno}% } \outer\parseargdef\appendixsection{\apphead1{#1}} % normally calls appendixsectionzzz \def\appendixsectionzzz#1{% \global\subsecno=0 \global\subsubsecno=0 \global\advance\secno by 1 \sectionheading{#1}{sec}{Yappendix}{\appendixletter.\the\secno}% } \let\appendixsec\appendixsection \outer\parseargdef\unnumberedsec{\unnmhead1{#1}} % normally calls unnumberedseczzz \def\unnumberedseczzz#1{% \global\subsecno=0 \global\subsubsecno=0 \global\advance\secno by 1 \sectionheading{#1}{sec}{Ynothing}{\the\unnumberedno.\the\secno}% } % Subsections. \outer\parseargdef\numberedsubsec{\numhead2{#1}} % normally calls numberedsubseczzz \def\numberedsubseczzz#1{% \global\subsubsecno=0 \global\advance\subsecno by 1 \sectionheading{#1}{subsec}{Ynumbered}{\the\chapno.\the\secno.\the\subsecno}% } \outer\parseargdef\appendixsubsec{\apphead2{#1}} % normally calls appendixsubseczzz \def\appendixsubseczzz#1{% \global\subsubsecno=0 \global\advance\subsecno by 1 \sectionheading{#1}{subsec}{Yappendix}% {\appendixletter.\the\secno.\the\subsecno}% } \outer\parseargdef\unnumberedsubsec{\unnmhead2{#1}} %normally calls unnumberedsubseczzz \def\unnumberedsubseczzz#1{% \global\subsubsecno=0 \global\advance\subsecno by 1 \sectionheading{#1}{subsec}{Ynothing}% {\the\unnumberedno.\the\secno.\the\subsecno}% } % Subsubsections. \outer\parseargdef\numberedsubsubsec{\numhead3{#1}} % normally numberedsubsubseczzz \def\numberedsubsubseczzz#1{% \global\advance\subsubsecno by 1 \sectionheading{#1}{subsubsec}{Ynumbered}% {\the\chapno.\the\secno.\the\subsecno.\the\subsubsecno}% } \outer\parseargdef\appendixsubsubsec{\apphead3{#1}} % normally appendixsubsubseczzz \def\appendixsubsubseczzz#1{% \global\advance\subsubsecno by 1 \sectionheading{#1}{subsubsec}{Yappendix}% {\appendixletter.\the\secno.\the\subsecno.\the\subsubsecno}% } \outer\parseargdef\unnumberedsubsubsec{\unnmhead3{#1}} %normally unnumberedsubsubseczzz \def\unnumberedsubsubseczzz#1{% \global\advance\subsubsecno by 1 \sectionheading{#1}{subsubsec}{Ynothing}% {\the\unnumberedno.\the\secno.\the\subsecno.\the\subsubsecno}% } % These macros control what the section commands do, according % to what kind of chapter we are in (ordinary, appendix, or unnumbered). % Define them by default for a numbered chapter. \let\section = \numberedsec \let\subsection = \numberedsubsec \let\subsubsection = \numberedsubsubsec % Define @majorheading, @heading and @subheading % NOTE on use of \vbox for chapter headings, section headings, and such: % 1) We use \vbox rather than the earlier \line to permit % overlong headings to fold. % 2) \hyphenpenalty is set to 10000 because hyphenation in a % heading is obnoxious; this forbids it. % 3) Likewise, headings look best if no \parindent is used, and % if justification is not attempted. Hence \raggedright. \def\majorheading{% {\advance\chapheadingskip by 10pt \chapbreak }% \parsearg\chapheadingzzz } \def\chapheading{\chapbreak \parsearg\chapheadingzzz} \def\chapheadingzzz#1{% {\chapfonts \vbox{\hyphenpenalty=10000\tolerance=5000 \parindent=0pt\raggedright \rm #1\hfill}}% \bigskip \par\penalty 200\relax \suppressfirstparagraphindent } % @heading, @subheading, @subsubheading. \parseargdef\heading{\sectionheading{#1}{sec}{Yomitfromtoc}{} \suppressfirstparagraphindent} \parseargdef\subheading{\sectionheading{#1}{subsec}{Yomitfromtoc}{} \suppressfirstparagraphindent} \parseargdef\subsubheading{\sectionheading{#1}{subsubsec}{Yomitfromtoc}{} \suppressfirstparagraphindent} % These macros generate a chapter, section, etc. heading only % (including whitespace, linebreaking, etc. around it), % given all the information in convenient, parsed form. %%% Args are the skip and penalty (usually negative) \def\dobreak#1#2{\par\ifdim\lastskip<#1\removelastskip\penalty#2\vskip#1\fi} %%% Define plain chapter starts, and page on/off switching for it % Parameter controlling skip before chapter headings (if needed) \newskip\chapheadingskip \def\chapbreak{\dobreak \chapheadingskip {-4000}} \def\chappager{\par\vfill\supereject} \def\chapoddpage{\chappager \ifodd\pageno \else \hbox to 0pt{} \chappager\fi} \def\setchapternewpage #1 {\csname CHAPPAG#1\endcsname} \def\CHAPPAGoff{% \global\let\contentsalignmacro = \chappager \global\let\pchapsepmacro=\chapbreak \global\let\pagealignmacro=\chappager} \def\CHAPPAGon{% \global\let\contentsalignmacro = \chappager \global\let\pchapsepmacro=\chappager \global\let\pagealignmacro=\chappager \global\def\HEADINGSon{\HEADINGSsingle}} \def\CHAPPAGodd{% \global\let\contentsalignmacro = \chapoddpage \global\let\pchapsepmacro=\chapoddpage \global\let\pagealignmacro=\chapoddpage \global\def\HEADINGSon{\HEADINGSdouble}} \CHAPPAGon % Chapter opening. % % #1 is the text, #2 is the section type (Ynumbered, Ynothing, % Yappendix, Yomitfromtoc), #3 the chapter number. % % To test against our argument. \def\Ynothingkeyword{Ynothing} \def\Yomitfromtockeyword{Yomitfromtoc} \def\Yappendixkeyword{Yappendix} % \def\chapmacro#1#2#3{% \pchapsepmacro {% \chapfonts \rm % % Have to define \thissection before calling \donoderef, because the % xref code eventually uses it. On the other hand, it has to be called % after \pchapsepmacro, or the headline will change too soon. \gdef\thissection{#1}% \gdef\thischaptername{#1}% % % Only insert the separating space if we have a chapter/appendix % number, and don't print the unnumbered ``number''. \def\temptype{#2}% \ifx\temptype\Ynothingkeyword \setbox0 = \hbox{}% \def\toctype{unnchap}% \def\thischapter{#1}% \else\ifx\temptype\Yomitfromtockeyword \setbox0 = \hbox{}% contents like unnumbered, but no toc entry \def\toctype{omit}% \xdef\thischapter{}% \else\ifx\temptype\Yappendixkeyword \setbox0 = \hbox{\putwordAppendix{} #3\enspace}% \def\toctype{app}% % We don't substitute the actual chapter name into \thischapter % because we don't want its macros evaluated now. And we don't % use \thissection because that changes with each section. % \xdef\thischapter{\putwordAppendix{} \appendixletter: \noexpand\thischaptername}% \else \setbox0 = \hbox{#3\enspace}% \def\toctype{numchap}% \xdef\thischapter{\putwordChapter{} \the\chapno: \noexpand\thischaptername}% \fi\fi\fi % % Write the toc entry for this chapter. Must come before the % \donoderef, because we include the current node name in the toc % entry, and \donoderef resets it to empty. \writetocentry{\toctype}{#1}{#3}% % % For pdftex, we have to write out the node definition (aka, make % the pdfdest) after any page break, but before the actual text has % been typeset. If the destination for the pdf outline is after the % text, then jumping from the outline may wind up with the text not % being visible, for instance under high magnification. \donoderef{#2}% % % Typeset the actual heading. \vbox{\hyphenpenalty=10000 \tolerance=5000 \parindent=0pt \raggedright \hangindent=\wd0 \centerparametersmaybe \unhbox0 #1\par}% }% \nobreak\bigskip % no page break after a chapter title \nobreak } % @centerchap -- centered and unnumbered. \let\centerparametersmaybe = \relax \def\centerparameters{% \advance\rightskip by 3\rightskip \leftskip = \rightskip \parfillskip = 0pt } % I don't think this chapter style is supported any more, so I'm not % updating it with the new noderef stuff. We'll see. --karl, 11aug03. % \def\setchapterstyle #1 {\csname CHAPF#1\endcsname} % \def\unnchfopen #1{% \chapoddpage {\chapfonts \vbox{\hyphenpenalty=10000\tolerance=5000 \parindent=0pt\raggedright \rm #1\hfill}}\bigskip \par\nobreak } \def\chfopen #1#2{\chapoddpage {\chapfonts \vbox to 3in{\vfil \hbox to\hsize{\hfil #2} \hbox to\hsize{\hfil #1} \vfil}}% \par\penalty 5000 % } \def\centerchfopen #1{% \chapoddpage {\chapfonts \vbox{\hyphenpenalty=10000\tolerance=5000 \parindent=0pt \hfill {\rm #1}\hfill}}\bigskip \par\nobreak } \def\CHAPFopen{% \global\let\chapmacro=\chfopen \global\let\centerchapmacro=\centerchfopen} % Section titles. These macros combine the section number parts and % call the generic \sectionheading to do the printing. % \newskip\secheadingskip \def\secheadingbreak{\dobreak \secheadingskip{-1000}} % Subsection titles. \newskip\subsecheadingskip \def\subsecheadingbreak{\dobreak \subsecheadingskip{-500}} % Subsubsection titles. \def\subsubsecheadingskip{\subsecheadingskip} \def\subsubsecheadingbreak{\subsecheadingbreak} % Print any size, any type, section title. % % #1 is the text, #2 is the section level (sec/subsec/subsubsec), #3 is % the section type for xrefs (Ynumbered, Ynothing, Yappendix), #4 is the % section number. % \def\sectionheading#1#2#3#4{% {% % Switch to the right set of fonts. \csname #2fonts\endcsname \rm % % Insert space above the heading. \csname #2headingbreak\endcsname % % Only insert the space after the number if we have a section number. \def\sectionlevel{#2}% \def\temptype{#3}% % \ifx\temptype\Ynothingkeyword \setbox0 = \hbox{}% \def\toctype{unn}% \gdef\thissection{#1}% \else\ifx\temptype\Yomitfromtockeyword % for @headings -- no section number, don't include in toc, % and don't redefine \thissection. \setbox0 = \hbox{}% \def\toctype{omit}% \let\sectionlevel=\empty \else\ifx\temptype\Yappendixkeyword \setbox0 = \hbox{#4\enspace}% \def\toctype{app}% \gdef\thissection{#1}% \else \setbox0 = \hbox{#4\enspace}% \def\toctype{num}% \gdef\thissection{#1}% \fi\fi\fi % % Write the toc entry (before \donoderef). See comments in \chfplain. \writetocentry{\toctype\sectionlevel}{#1}{#4}% % % Write the node reference (= pdf destination for pdftex). % Again, see comments in \chfplain. \donoderef{#3}% % % Output the actual section heading. \vbox{\hyphenpenalty=10000 \tolerance=5000 \parindent=0pt \raggedright \hangindent=\wd0 % zero if no section number \unhbox0 #1}% }% % Add extra space after the heading -- half of whatever came above it. % Don't allow stretch, though. \kern .5 \csname #2headingskip\endcsname % % Do not let the kern be a potential breakpoint, as it would be if it % was followed by glue. \nobreak % % We'll almost certainly start a paragraph next, so don't let that % glue accumulate. (Not a breakpoint because it's preceded by a % discardable item.) \vskip-\parskip % % This is purely so the last item on the list is a known \penalty > % 10000. This is so \startdefun can avoid allowing breakpoints after % section headings. Otherwise, it would insert a valid breakpoint between: % % @section sec-whatever % @deffn def-whatever \penalty 10001 } \message{toc,} % Table of contents. \newwrite\tocfile % Write an entry to the toc file, opening it if necessary. % Called from @chapter, etc. % % Example usage: \writetocentry{sec}{Section Name}{\the\chapno.\the\secno} % We append the current node name (if any) and page number as additional % arguments for the \{chap,sec,...}entry macros which will eventually % read this. The node name is used in the pdf outlines as the % destination to jump to. % % We open the .toc file for writing here instead of at @setfilename (or % any other fixed time) so that @contents can be anywhere in the document. % But if #1 is `omit', then we don't do anything. This is used for the % table of contents chapter openings themselves. % \newif\iftocfileopened \def\omitkeyword{omit}% % \def\writetocentry#1#2#3{% \edef\writetoctype{#1}% \ifx\writetoctype\omitkeyword \else \iftocfileopened\else \immediate\openout\tocfile = \jobname.toc \global\tocfileopenedtrue \fi % \iflinks \toks0 = {#2}% \toks2 = \expandafter{\lastnode}% \edef\temp{\write\tocfile{\realbackslash #1entry{\the\toks0}{#3}% {\the\toks2}{\noexpand\folio}}}% \temp \fi \fi % % Tell \shipout to create a pdf destination on each page, if we're % writing pdf. These are used in the table of contents. We can't % just write one on every page because the title pages are numbered % 1 and 2 (the page numbers aren't printed), and so are the first % two pages of the document. Thus, we'd have two destinations named % `1', and two named `2'. \ifpdf \global\pdfmakepagedesttrue \fi } \newskip\contentsrightmargin \contentsrightmargin=1in \newcount\savepageno \newcount\lastnegativepageno \lastnegativepageno = -1 % Prepare to read what we've written to \tocfile. % \def\startcontents#1{% % If @setchapternewpage on, and @headings double, the contents should % start on an odd page, unlike chapters. Thus, we maintain % \contentsalignmacro in parallel with \pagealignmacro. % From: Torbjorn Granlund \contentsalignmacro \immediate\closeout\tocfile % % Don't need to put `Contents' or `Short Contents' in the headline. % It is abundantly clear what they are. \def\thischapter{}% \chapmacro{#1}{Yomitfromtoc}{}% % \savepageno = \pageno \begingroup % Set up to handle contents files properly. \catcode`\\=0 \catcode`\{=1 \catcode`\}=2 \catcode`\@=11 % We can't do this, because then an actual ^ in a section % title fails, e.g., @chapter ^ -- exponentiation. --karl, 9jul97. %\catcode`\^=7 % to see ^^e4 as \"a etc. juha@piuha.ydi.vtt.fi \raggedbottom % Worry more about breakpoints than the bottom. \advance\hsize by -\contentsrightmargin % Don't use the full line length. % % Roman numerals for page numbers. \ifnum \pageno>0 \global\pageno = \lastnegativepageno \fi } % Normal (long) toc. \def\contents{% \startcontents{\putwordTOC}% \openin 1 \jobname.toc \ifeof 1 \else \input \jobname.toc \fi \vfill \eject \contentsalignmacro % in case @setchapternewpage odd is in effect \ifeof 1 \else \pdfmakeoutlines \fi \closein 1 \endgroup \lastnegativepageno = \pageno \global\pageno = \savepageno } % And just the chapters. \def\summarycontents{% \startcontents{\putwordShortTOC}% % \let\numchapentry = \shortchapentry \let\appentry = \shortchapentry \let\unnchapentry = \shortunnchapentry % We want a true roman here for the page numbers. \secfonts \let\rm=\shortcontrm \let\bf=\shortcontbf \let\sl=\shortcontsl \let\tt=\shortconttt \rm \hyphenpenalty = 10000 \advance\baselineskip by 1pt % Open it up a little. \def\numsecentry##1##2##3##4{} \let\appsecentry = \numsecentry \let\unnsecentry = \numsecentry \let\numsubsecentry = \numsecentry \let\appsubsecentry = \numsecentry \let\unnsubsecentry = \numsecentry \let\numsubsubsecentry = \numsecentry \let\appsubsubsecentry = \numsecentry \let\unnsubsubsecentry = \numsecentry \openin 1 \jobname.toc \ifeof 1 \else \input \jobname.toc \fi \closein 1 \vfill \eject \contentsalignmacro % in case @setchapternewpage odd is in effect \endgroup \lastnegativepageno = \pageno \global\pageno = \savepageno } \let\shortcontents = \summarycontents % Typeset the label for a chapter or appendix for the short contents. % The arg is, e.g., `A' for an appendix, or `3' for a chapter. % \def\shortchaplabel#1{% % This space should be enough, since a single number is .5em, and the % widest letter (M) is 1em, at least in the Computer Modern fonts. % But use \hss just in case. % (This space doesn't include the extra space that gets added after % the label; that gets put in by \shortchapentry above.) % % We'd like to right-justify chapter numbers, but that looks strange % with appendix letters. And right-justifying numbers and % left-justifying letters looks strange when there is less than 10 % chapters. Have to read the whole toc once to know how many chapters % there are before deciding ... \hbox to 1em{#1\hss}% } % These macros generate individual entries in the table of contents. % The first argument is the chapter or section name. % The last argument is the page number. % The arguments in between are the chapter number, section number, ... % Chapters, in the main contents. \def\numchapentry#1#2#3#4{\dochapentry{#2\labelspace#1}{#4}} % % Chapters, in the short toc. % See comments in \dochapentry re vbox and related settings. \def\shortchapentry#1#2#3#4{% \tocentry{\shortchaplabel{#2}\labelspace #1}{\doshortpageno\bgroup#4\egroup}% } % Appendices, in the main contents. % Need the word Appendix, and a fixed-size box. % \def\appendixbox#1{% % We use M since it's probably the widest letter. \setbox0 = \hbox{\putwordAppendix{} M}% \hbox to \wd0{\putwordAppendix{} #1\hss}} % \def\appentry#1#2#3#4{\dochapentry{\appendixbox{#2}\labelspace#1}{#4}} % Unnumbered chapters. \def\unnchapentry#1#2#3#4{\dochapentry{#1}{#4}} \def\shortunnchapentry#1#2#3#4{\tocentry{#1}{\doshortpageno\bgroup#4\egroup}} % Sections. \def\numsecentry#1#2#3#4{\dosecentry{#2\labelspace#1}{#4}} \let\appsecentry=\numsecentry \def\unnsecentry#1#2#3#4{\dosecentry{#1}{#4}} % Subsections. \def\numsubsecentry#1#2#3#4{\dosubsecentry{#2\labelspace#1}{#4}} \let\appsubsecentry=\numsubsecentry \def\unnsubsecentry#1#2#3#4{\dosubsecentry{#1}{#4}} % And subsubsections. \def\numsubsubsecentry#1#2#3#4{\dosubsubsecentry{#2\labelspace#1}{#4}} \let\appsubsubsecentry=\numsubsubsecentry \def\unnsubsubsecentry#1#2#3#4{\dosubsubsecentry{#1}{#4}} % This parameter controls the indentation of the various levels. % Same as \defaultparindent. \newdimen\tocindent \tocindent = 15pt % Now for the actual typesetting. In all these, #1 is the text and #2 is the % page number. % % If the toc has to be broken over pages, we want it to be at chapters % if at all possible; hence the \penalty. \def\dochapentry#1#2{% \penalty-300 \vskip1\baselineskip plus.33\baselineskip minus.25\baselineskip \begingroup \chapentryfonts \tocentry{#1}{\dopageno\bgroup#2\egroup}% \endgroup \nobreak\vskip .25\baselineskip plus.1\baselineskip } \def\dosecentry#1#2{\begingroup \secentryfonts \leftskip=\tocindent \tocentry{#1}{\dopageno\bgroup#2\egroup}% \endgroup} \def\dosubsecentry#1#2{\begingroup \subsecentryfonts \leftskip=2\tocindent \tocentry{#1}{\dopageno\bgroup#2\egroup}% \endgroup} \def\dosubsubsecentry#1#2{\begingroup \subsubsecentryfonts \leftskip=3\tocindent \tocentry{#1}{\dopageno\bgroup#2\egroup}% \endgroup} % We use the same \entry macro as for the index entries. \let\tocentry = \entry % Space between chapter (or whatever) number and the title. \def\labelspace{\hskip1em \relax} \def\dopageno#1{{\rm #1}} \def\doshortpageno#1{{\rm #1}} \def\chapentryfonts{\secfonts \rm} \def\secentryfonts{\textfonts} \def\subsecentryfonts{\textfonts} \def\subsubsecentryfonts{\textfonts} \message{environments,} % @foo ... @end foo. % @point{}, @result{}, @expansion{}, @print{}, @equiv{}. % % Since these characters are used in examples, it should be an even number of % \tt widths. Each \tt character is 1en, so two makes it 1em. % \def\point{$\star$} \def\result{\leavevmode\raise.15ex\hbox to 1em{\hfil$\Rightarrow$\hfil}} \def\expansion{\leavevmode\raise.1ex\hbox to 1em{\hfil$\mapsto$\hfil}} \def\print{\leavevmode\lower.1ex\hbox to 1em{\hfil$\dashv$\hfil}} \def\equiv{\leavevmode\lower.1ex\hbox to 1em{\hfil$\ptexequiv$\hfil}} % The @error{} command. % Adapted from the TeXbook's \boxit. % \newbox\errorbox % {\tentt \global\dimen0 = 3em}% Width of the box. \dimen2 = .55pt % Thickness of rules % The text. (`r' is open on the right, `e' somewhat less so on the left.) \setbox0 = \hbox{\kern-.75pt \tensf error\kern-1.5pt} % \setbox\errorbox=\hbox to \dimen0{\hfil \hsize = \dimen0 \advance\hsize by -5.8pt % Space to left+right. \advance\hsize by -2\dimen2 % Rules. \vbox{% \hrule height\dimen2 \hbox{\vrule width\dimen2 \kern3pt % Space to left of text. \vtop{\kern2.4pt \box0 \kern2.4pt}% Space above/below. \kern3pt\vrule width\dimen2}% Space to right. \hrule height\dimen2} \hfil} % \def\error{\leavevmode\lower.7ex\copy\errorbox} % @tex ... @end tex escapes into raw Tex temporarily. % One exception: @ is still an escape character, so that @end tex works. % But \@ or @@ will get a plain tex @ character. \envdef\tex{% \catcode `\\=0 \catcode `\{=1 \catcode `\}=2 \catcode `\$=3 \catcode `\&=4 \catcode `\#=6 \catcode `\^=7 \catcode `\_=8 \catcode `\~=\active \let~=\tie \catcode `\%=14 \catcode `\+=\other \catcode `\"=\other \catcode `\|=\other \catcode `\<=\other \catcode `\>=\other \escapechar=`\\ % \let\b=\ptexb \let\bullet=\ptexbullet \let\c=\ptexc \let\,=\ptexcomma \let\.=\ptexdot \let\dots=\ptexdots \let\equiv=\ptexequiv \let\!=\ptexexclam \let\i=\ptexi \let\indent=\ptexindent \let\noindent=\ptexnoindent \let\{=\ptexlbrace \let\+=\tabalign \let\}=\ptexrbrace \let\/=\ptexslash \let\*=\ptexstar \let\t=\ptext % \def\endldots{\mathinner{\ldots\ldots\ldots\ldots}}% \def\enddots{\relax\ifmmode\endldots\else$\mathsurround=0pt \endldots\,$\fi}% \def\@{@}% } % There is no need to define \Etex. % Define @lisp ... @end lisp. % @lisp environment forms a group so it can rebind things, % including the definition of @end lisp (which normally is erroneous). % Amount to narrow the margins by for @lisp. \newskip\lispnarrowing \lispnarrowing=0.4in % This is the definition that ^^M gets inside @lisp, @example, and other % such environments. \null is better than a space, since it doesn't % have any width. \def\lisppar{\null\endgraf} % This space is always present above and below environments. \newskip\envskipamount \envskipamount = 0pt % Make spacing and below environment symmetrical. We use \parskip here % to help in doing that, since in @example-like environments \parskip % is reset to zero; thus the \afterenvbreak inserts no space -- but the % start of the next paragraph will insert \parskip. % \def\aboveenvbreak{{% % =10000 instead of <10000 because of a special case in \itemzzz and % \sectionheading, q.v. \ifnum \lastpenalty=10000 \else \advance\envskipamount by \parskip \endgraf \ifdim\lastskip<\envskipamount \removelastskip % it's not a good place to break if the last penalty was \nobreak % or better ... \ifnum\lastpenalty<10000 \penalty-50 \fi \vskip\envskipamount \fi \fi }} \let\afterenvbreak = \aboveenvbreak % \nonarrowing is a flag. If "set", @lisp etc don't narrow margins. \let\nonarrowing=\relax % @cartouche ... @end cartouche: draw rectangle w/rounded corners around % environment contents. \font\circle=lcircle10 \newdimen\circthick \newdimen\cartouter\newdimen\cartinner \newskip\normbskip\newskip\normpskip\newskip\normlskip \circthick=\fontdimen8\circle % \def\ctl{{\circle\char'013\hskip -6pt}}% 6pt from pl file: 1/2charwidth \def\ctr{{\hskip 6pt\circle\char'010}} \def\cbl{{\circle\char'012\hskip -6pt}} \def\cbr{{\hskip 6pt\circle\char'011}} \def\carttop{\hbox to \cartouter{\hskip\lskip \ctl\leaders\hrule height\circthick\hfil\ctr \hskip\rskip}} \def\cartbot{\hbox to \cartouter{\hskip\lskip \cbl\leaders\hrule height\circthick\hfil\cbr \hskip\rskip}} % \newskip\lskip\newskip\rskip \envdef\cartouche{% \ifhmode\par\fi % can't be in the midst of a paragraph. \startsavinginserts \lskip=\leftskip \rskip=\rightskip \leftskip=0pt\rightskip=0pt % we want these *outside*. \cartinner=\hsize \advance\cartinner by-\lskip \advance\cartinner by-\rskip \cartouter=\hsize \advance\cartouter by 18.4pt % allow for 3pt kerns on either % side, and for 6pt waste from % each corner char, and rule thickness \normbskip=\baselineskip \normpskip=\parskip \normlskip=\lineskip % Flag to tell @lisp, etc., not to narrow margin. \let\nonarrowing=\comment \vbox\bgroup \baselineskip=0pt\parskip=0pt\lineskip=0pt \carttop \hbox\bgroup \hskip\lskip \vrule\kern3pt \vbox\bgroup \kern3pt \hsize=\cartinner \baselineskip=\normbskip \lineskip=\normlskip \parskip=\normpskip \vskip -\parskip \comment % For explanation, see the end of \def\group. } \def\Ecartouche{% \ifhmode\par\fi \kern3pt \egroup \kern3pt\vrule \hskip\rskip \egroup \cartbot \egroup \checkinserts } % This macro is called at the beginning of all the @example variants, % inside a group. \def\nonfillstart{% \aboveenvbreak \hfuzz = 12pt % Don't be fussy \sepspaces % Make spaces be word-separators rather than space tokens. \let\par = \lisppar % don't ignore blank lines \obeylines % each line of input is a line of output \parskip = 0pt \parindent = 0pt \emergencystretch = 0pt % don't try to avoid overfull boxes % @cartouche defines \nonarrowing to inhibit narrowing % at next level down. \ifx\nonarrowing\relax \advance \leftskip by \lispnarrowing \exdentamount=\lispnarrowing \fi \let\exdent=\nofillexdent } % If you want all examples etc. small: @set dispenvsize small. % If you want even small examples the full size: @set dispenvsize nosmall. % This affects the following displayed environments: % @example, @display, @format, @lisp % \def\smallword{small} \def\nosmallword{nosmall} \let\SETdispenvsize\relax \def\setnormaldispenv{% \ifx\SETdispenvsize\smallword \smallexamplefonts \rm \fi } \def\setsmalldispenv{% \ifx\SETdispenvsize\nosmallword \else \smallexamplefonts \rm \fi } % We often define two environments, @foo and @smallfoo. % Let's do it by one command: \def\makedispenv #1#2{ \expandafter\envdef\csname#1\endcsname {\setnormaldispenv #2} \expandafter\envdef\csname small#1\endcsname {\setsmalldispenv #2} \expandafter\let\csname E#1\endcsname \afterenvbreak \expandafter\let\csname Esmall#1\endcsname \afterenvbreak } % Define two synonyms: \def\maketwodispenvs #1#2#3{ \makedispenv{#1}{#3} \makedispenv{#2}{#3} } % @lisp: indented, narrowed, typewriter font; @example: same as @lisp. % % @smallexample and @smalllisp: use smaller fonts. % Originally contributed by Pavel@xerox. % \maketwodispenvs {lisp}{example}{% \nonfillstart \tt \let\kbdfont = \kbdexamplefont % Allow @kbd to do something special. \gobble % eat return } % @display/@smalldisplay: same as @lisp except keep current font. % \makedispenv {display}{% \nonfillstart \gobble } % @format/@smallformat: same as @display except don't narrow margins. % \makedispenv{format}{% \let\nonarrowing = t% \nonfillstart \gobble } % @flushleft: same as @format, but doesn't obey \SETdispenvsize. \envdef\flushleft{% \let\nonarrowing = t% \nonfillstart \gobble } \let\Eflushleft = \afterenvbreak % @flushright. % \envdef\flushright{% \let\nonarrowing = t% \nonfillstart \advance\leftskip by 0pt plus 1fill \gobble } \let\Eflushright = \afterenvbreak % @quotation does normal linebreaking (hence we can't use \nonfillstart) % and narrows the margins. We keep \parskip nonzero in general, since % we're doing normal filling. So, when using \aboveenvbreak and % \afterenvbreak, temporarily make \parskip 0. % \envdef\quotation{% {\parskip=0pt \aboveenvbreak}% because \aboveenvbreak inserts \parskip \parindent=0pt % % @cartouche defines \nonarrowing to inhibit narrowing at next level down. \ifx\nonarrowing\relax \advance\leftskip by \lispnarrowing \advance\rightskip by \lispnarrowing \exdentamount = \lispnarrowing \let\nonarrowing = \relax \fi \parsearg\quotationlabel } % We have retained a nonzero parskip for the environment, since we're % doing normal filling. % \def\Equotation{% \par \ifx\quotationauthor\undefined\else % indent a bit. \leftline{\kern 2\leftskip \sl ---\quotationauthor}% \fi {\parskip=0pt \afterenvbreak}% } % If we're given an argument, typeset it in bold with a colon after. \def\quotationlabel#1{% \def\temp{#1}% \ifx\temp\empty \else {\bf #1: }% \fi } % LaTeX-like @verbatim...@end verbatim and @verb{...} % If we want to allow any as delimiter, % we need the curly braces so that makeinfo sees the @verb command, eg: % `@verbx...x' would look like the '@verbx' command. --janneke@gnu.org % % [Knuth]: Donald Ervin Knuth, 1996. The TeXbook. % % [Knuth] p.344; only we need to do the other characters Texinfo sets % active too. Otherwise, they get lost as the first character on a % verbatim line. \def\dospecials{% \do\ \do\\\do\{\do\}\do\$\do\&% \do\#\do\^\do\^^K\do\_\do\^^A\do\%\do\~% \do\<\do\>\do\|\do\@\do+\do\"% } % % [Knuth] p. 380 \def\uncatcodespecials{% \def\do##1{\catcode`##1=\other}\dospecials} % % [Knuth] pp. 380,381,391 % Disable Spanish ligatures ?` and !` of \tt font \begingroup \catcode`\`=\active\gdef`{\relax\lq} \endgroup % % Setup for the @verb command. % % Eight spaces for a tab \begingroup \catcode`\^^I=\active \gdef\tabeightspaces{\catcode`\^^I=\active\def^^I{\ \ \ \ \ \ \ \ }} \endgroup % \def\setupverb{% \tt % easiest (and conventionally used) font for verbatim \def\par{\leavevmode\endgraf}% \catcode`\`=\active \tabeightspaces % Respect line breaks, % print special symbols as themselves, and % make each space count % must do in this order: \obeylines \uncatcodespecials \sepspaces } % Setup for the @verbatim environment % % Real tab expansion \newdimen\tabw \setbox0=\hbox{\tt\space} \tabw=8\wd0 % tab amount % \def\starttabbox{\setbox0=\hbox\bgroup} \begingroup \catcode`\^^I=\active \gdef\tabexpand{% \catcode`\^^I=\active \def^^I{\leavevmode\egroup \dimen0=\wd0 % the width so far, or since the previous tab \divide\dimen0 by\tabw \multiply\dimen0 by\tabw % compute previous multiple of \tabw \advance\dimen0 by\tabw % advance to next multiple of \tabw \wd0=\dimen0 \box0 \starttabbox }% } \endgroup \def\setupverbatim{% \nonfillstart \advance\leftskip by -\defbodyindent % Easiest (and conventionally used) font for verbatim \tt \def\par{\leavevmode\egroup\box0\endgraf}% \catcode`\`=\active \tabexpand % Respect line breaks, % print special symbols as themselves, and % make each space count % must do in this order: \obeylines \uncatcodespecials \sepspaces \everypar{\starttabbox}% } % Do the @verb magic: verbatim text is quoted by unique % delimiter characters. Before first delimiter expect a % right brace, after last delimiter expect closing brace: % % \def\doverb'{'#1'}'{#1} % % [Knuth] p. 382; only eat outer {} \begingroup \catcode`[=1\catcode`]=2\catcode`\{=\other\catcode`\}=\other \gdef\doverb{#1[\def\next##1#1}[##1\endgroup]\next] \endgroup % \def\verb{\begingroup\setupverb\doverb} % % % Do the @verbatim magic: define the macro \doverbatim so that % the (first) argument ends when '@end verbatim' is reached, ie: % % \def\doverbatim#1@end verbatim{#1} % % For Texinfo it's a lot easier than for LaTeX, % because texinfo's \verbatim doesn't stop at '\end{verbatim}': % we need not redefine '\', '{' and '}'. % % Inspired by LaTeX's verbatim command set [latex.ltx] % \begingroup \catcode`\ =\active \obeylines % % ignore everything up to the first ^^M, that's the newline at the end % of the @verbatim input line itself. Otherwise we get an extra blank % line in the output. \xdef\doverbatim#1^^M#2@end verbatim{#2\noexpand\end\gobble verbatim}% % We really want {...\end verbatim} in the body of the macro, but % without the active space; thus we have to use \xdef and \gobble. \endgroup % \envdef\verbatim{% \setupverbatim\doverbatim } \let\Everbatim = \afterenvbreak % @verbatiminclude FILE - insert text of file in verbatim environment. % \def\verbatiminclude{\parseargusing\filenamecatcodes\doverbatiminclude} % \def\doverbatiminclude#1{% {% \makevalueexpandable \setupverbatim \input #1 \afterenvbreak }% } % @copying ... @end copying. % Save the text away for @insertcopying later. % % We save the uninterpreted tokens, rather than creating a box. % Saving the text in a box would be much easier, but then all the % typesetting commands (@smallbook, font changes, etc.) have to be done % beforehand -- and a) we want @copying to be done first in the source % file; b) letting users define the frontmatter in as flexible order as % possible is very desirable. % \def\copying{\checkenv{}\begingroup\scanargctxt\docopying} \def\docopying#1@end copying{\endgroup\def\copyingtext{#1}} % \def\insertcopying{% \begingroup \parindent = 0pt % paragraph indentation looks wrong on title page \scanexp\copyingtext \endgroup } \message{defuns,} % @defun etc. \newskip\defbodyindent \defbodyindent=.4in \newskip\defargsindent \defargsindent=50pt \newskip\deflastargmargin \deflastargmargin=18pt % Start the processing of @deffn: \def\startdefun{% \ifnum\lastpenalty<10000 \medbreak \else % If there are two @def commands in a row, we'll have a \nobreak, % which is there to keep the function description together with its % header. But if there's nothing but headers, we need to allow a % break somewhere. Check specifically for penalty 10002, inserted % by \defargscommonending, instead of 10000, since the sectioning % commands also insert a nobreak penalty, and we don't want to allow % a break between a section heading and a defun. % \ifnum\lastpenalty=10002 \penalty2000 \fi % % Similarly, after a section heading, do not allow a break. % But do insert the glue. \medskip % preceded by discardable penalty, so not a breakpoint \fi % \parindent=0in \advance\leftskip by \defbodyindent \exdentamount=\defbodyindent } \def\dodefunx#1{% % First, check whether we are in the right environment: \checkenv#1% % % As above, allow line break if we have multiple x headers in a row. % It's not a great place, though. \ifnum\lastpenalty=10002 \penalty3000 \fi % % And now, it's time to reuse the body of the original defun: \expandafter\gobbledefun#1% } \def\gobbledefun#1\startdefun{} % \printdefunline \deffnheader{text} % \def\printdefunline#1#2{% \begingroup % call \deffnheader: #1#2 \endheader % common ending: \interlinepenalty = 10000 \advance\rightskip by 0pt plus 1fil \endgraf \nobreak\vskip -\parskip \penalty 10002 % signal to \startdefun and \dodefunx % Some of the @defun-type tags do not enable magic parentheses, % rendering the following check redundant. But we don't optimize. \checkparencounts \endgroup } \def\Edefun{\endgraf\medbreak} % \makedefun{deffn} creates \deffn, \deffnx and \Edeffn; % the only thing remainnig is to define \deffnheader. % \def\makedefun#1{% \expandafter\let\csname E#1\endcsname = \Edefun \edef\temp{\noexpand\domakedefun \makecsname{#1}\makecsname{#1x}\makecsname{#1header}}% \temp } % \domakedefun \deffn \deffnx \deffnheader % % Define \deffn and \deffnx, without parameters. % \deffnheader has to be defined explicitly. % \def\domakedefun#1#2#3{% \envdef#1{% \startdefun \parseargusing\activeparens{\printdefunline#3}% }% \def#2{\dodefunx#1}% \def#3% } %%% Untyped functions: % @deffn category name args \makedefun{deffn}{\deffngeneral{}} % @deffn category class name args \makedefun{defop}#1 {\defopon{#1\ \putwordon}} % \defopon {category on}class name args \def\defopon#1#2 {\deffngeneral{\putwordon\ \code{#2}}{#1\ \code{#2}} } % \deffngeneral {subind}category name args % \def\deffngeneral#1#2 #3 #4\endheader{% % Remember that \dosubind{fn}{foo}{} is equivalent to \doind{fn}{foo}. \dosubind{fn}{\code{#3}}{#1}% \defname{#2}{}{#3}\magicamp\defunargs{#4\unskip}% } %%% Typed functions: % @deftypefn category type name args \makedefun{deftypefn}{\deftypefngeneral{}} % @deftypeop category class type name args \makedefun{deftypeop}#1 {\deftypeopon{#1\ \putwordon}} % \deftypeopon {category on}class type name args \def\deftypeopon#1#2 {\deftypefngeneral{\putwordon\ \code{#2}}{#1\ \code{#2}} } % \deftypefngeneral {subind}category type name args % \def\deftypefngeneral#1#2 #3 #4 #5\endheader{% \dosubind{fn}{\code{#4}}{#1}% \defname{#2}{#3}{#4}\defunargs{#5\unskip}% } %%% Typed variables: % @deftypevr category type var args \makedefun{deftypevr}{\deftypecvgeneral{}} % @deftypecv category class type var args \makedefun{deftypecv}#1 {\deftypecvof{#1\ \putwordof}} % \deftypecvof {category of}class type var args \def\deftypecvof#1#2 {\deftypecvgeneral{\putwordof\ \code{#2}}{#1\ \code{#2}} } % \deftypecvgeneral {subind}category type var args % \def\deftypecvgeneral#1#2 #3 #4 #5\endheader{% \dosubind{vr}{\code{#4}}{#1}% \defname{#2}{#3}{#4}\defunargs{#5\unskip}% } %%% Untyped variables: % @defvr category var args \makedefun{defvr}#1 {\deftypevrheader{#1} {} } % @defcv category class var args \makedefun{defcv}#1 {\defcvof{#1\ \putwordof}} % \defcvof {category of}class var args \def\defcvof#1#2 {\deftypecvof{#1}#2 {} } %%% Type: % @deftp category name args \makedefun{deftp}#1 #2 #3\endheader{% \doind{tp}{\code{#2}}% \defname{#1}{}{#2}\defunargs{#3\unskip}% } % Remaining @defun-like shortcuts: \makedefun{defun}{\deffnheader{\putwordDeffunc} } \makedefun{defmac}{\deffnheader{\putwordDefmac} } \makedefun{defspec}{\deffnheader{\putwordDefspec} } \makedefun{deftypefun}{\deftypefnheader{\putwordDeffunc} } \makedefun{defvar}{\defvrheader{\putwordDefvar} } \makedefun{defopt}{\defvrheader{\putwordDefopt} } \makedefun{deftypevar}{\deftypevrheader{\putwordDefvar} } \makedefun{defmethod}{\defopon\putwordMethodon} \makedefun{deftypemethod}{\deftypeopon\putwordMethodon} \makedefun{defivar}{\defcvof\putwordInstanceVariableof} \makedefun{deftypeivar}{\deftypecvof\putwordInstanceVariableof} % \defname, which formats the name of the @def (not the args). % #1 is the category, such as "Function". % #2 is the return type, if any. % #3 is the function name. % % We are followed by (but not passed) the arguments, if any. % \def\defname#1#2#3{% % Get the values of \leftskip and \rightskip as they were outside the @def... \advance\leftskip by -\defbodyindent % % How we'll format the type name. Putting it in brackets helps % distinguish it from the body text that may end up on the next line % just below it. \def\temp{#1}% \setbox0=\hbox{\kern\deflastargmargin \ifx\temp\empty\else [\rm\temp]\fi} % % Figure out line sizes for the paragraph shape. % The first line needs space for \box0; but if \rightskip is nonzero, % we need only space for the part of \box0 which exceeds it: \dimen0=\hsize \advance\dimen0 by -\wd0 \advance\dimen0 by \rightskip % The continuations: \dimen2=\hsize \advance\dimen2 by -\defargsindent % (plain.tex says that \dimen1 should be used only as global.) \parshape 2 0in \dimen0 \defargsindent \dimen2 % % Put the type name to the right margin. \noindent \hbox to 0pt{% \hfil\box0 \kern-\hsize % \hsize has to be shortened this way: \kern\leftskip % Intentionally do not respect \rightskip, since we need the space. }% % % Allow all lines to be underfull without complaint: \tolerance=10000 \hbadness=10000 \exdentamount=\defbodyindent {% % defun fonts. We use typewriter by default (used to be bold) because: % . we're printing identifiers, they should be in tt in principle. % . in languages with many accents, such as Czech or French, it's % common to leave accents off identifiers. The result looks ok in % tt, but exceedingly strange in rm. % . we don't want -- and --- to be treated as ligatures. % . this still does not fix the ?` and !` ligatures, but so far no % one has made identifiers using them :). \df \tt \def\temp{#2}% return value type \ifx\temp\empty\else \tclose{\temp} \fi #3% output function name }% {\rm\enskip}% hskip 0.5 em of \tenrm % \boldbrax % arguments will be output next, if any. } % Print arguments in slanted roman (not ttsl), inconsistently with using % tt for the name. This is because literal text is sometimes needed in % the argument list (groff manual), and ttsl and tt are not very % distinguishable. Prevent hyphenation at `-' chars. % \def\defunargs#1{% % use sl by default (not ttsl), % tt for the names. \df \sl \hyphenchar\font=0 % % On the other hand, if an argument has two dashes (for instance), we % want a way to get ttsl. Let's try @var for that. \let\var=\ttslanted #1% \sl\hyphenchar\font=45 } % We want ()&[] to print specially on the defun line. % \def\activeparens{% \catcode`\(=\active \catcode`\)=\active \catcode`\[=\active \catcode`\]=\active \catcode`\&=\active } % Make control sequences which act like normal parenthesis chars. \let\lparen = ( \let\rparen = ) % Be sure that we always have a definition for `(', etc. For example, % if the fn name has parens in it, \boldbrax will not be in effect yet, % so TeX would otherwise complain about undefined control sequence. { \activeparens \global\let(=\lparen \global\let)=\rparen \global\let[=\lbrack \global\let]=\rbrack \global\let& = \& \gdef\boldbrax{\let(=\opnr\let)=\clnr\let[=\lbrb\let]=\rbrb} \gdef\magicamp{\let&=\amprm} } \newcount\parencount % If we encounter &foo, then turn on ()-hacking afterwards \newif\ifampseen \def\amprm#1 {\ampseentrue{\bf\ }} \def\parenfont{% \ifampseen % At the first level, print parens in roman, % otherwise use the default font. \ifnum \parencount=1 \rm \fi \else % The \sf parens (in \boldbrax) actually are a little bolder than % the contained text. This is especially needed for [ and ] . \sf \fi } \def\infirstlevel#1{% \ifampseen \ifnum\parencount=1 #1% \fi \fi } \def\bfafterword#1 {#1 \bf} \def\opnr{% \global\advance\parencount by 1 {\parenfont(}% \infirstlevel \bfafterword } \def\clnr{% {\parenfont)}% \infirstlevel \sl \global\advance\parencount by -1 } \newcount\brackcount \def\lbrb{% \global\advance\brackcount by 1 {\bf[}% } \def\rbrb{% {\bf]}% \global\advance\brackcount by -1 } \def\checkparencounts{% \ifnum\parencount=0 \else \badparencount \fi \ifnum\brackcount=0 \else \badbrackcount \fi } \def\badparencount{% \errmessage{Unbalanced parentheses in @def}% \global\parencount=0 } \def\badbrackcount{% \errmessage{Unbalanced square braces in @def}% \global\brackcount=0 } \message{macros,} % @macro. % To do this right we need a feature of e-TeX, \scantokens, % which we arrange to emulate with a temporary file in ordinary TeX. \ifx\eTeXversion\undefined \newwrite\macscribble \def\scantokens#1{% \toks0={#1}% \immediate\openout\macscribble=\jobname.tmp \immediate\write\macscribble{\the\toks0}% \immediate\closeout\macscribble \input \jobname.tmp } \fi \def\scanmacro#1{% \begingroup \newlinechar`\^^M \let\xeatspaces\eatspaces % Undo catcode changes of \startcontents and \doprintindex % When called from @insertcopying or (short)caption, we need active % backslash to get it printed correctly. Previously, we had % \catcode`\\=\other instead. We'll see whether a problem appears % with macro expansion. --kasal, 19aug04 \catcode`\@=0 \catcode`\\=\active \escapechar=`\@ % ... and \example \spaceisspace % % Append \endinput to make sure that TeX does not see the ending newline. % % I've verified that it is necessary both for e-TeX and for ordinary TeX % --kasal, 29nov03 \scantokens{#1\endinput}% \endgroup } \def\scanexp#1{% \edef\temp{\noexpand\scanmacro{#1}}% \temp } \newcount\paramno % Count of parameters \newtoks\macname % Macro name \newif\ifrecursive % Is it recursive? \def\macrolist{} % List of all defined macros in the form % \do\macro1\do\macro2... % Utility routines. % This does \let #1 = #2, with \csnames; that is, % \let \csname#1\endcsname = \csname#2\endcsname % (except of course we have to play expansion games). % \def\cslet#1#2{% \expandafter\let \csname#1\expandafter\endcsname \csname#2\endcsname } % Trim leading and trailing spaces off a string. % Concepts from aro-bend problem 15 (see CTAN). {\catcode`\@=11 \gdef\eatspaces #1{\expandafter\trim@\expandafter{#1 }} \gdef\trim@ #1{\trim@@ @#1 @ #1 @ @@} \gdef\trim@@ #1@ #2@ #3@@{\trim@@@\empty #2 @} \def\unbrace#1{#1} \unbrace{\gdef\trim@@@ #1 } #2@{#1} } % Trim a single trailing ^^M off a string. {\catcode`\^^M=\other \catcode`\Q=3% \gdef\eatcr #1{\eatcra #1Q^^MQ}% \gdef\eatcra#1^^MQ{\eatcrb#1Q}% \gdef\eatcrb#1Q#2Q{#1}% } % Macro bodies are absorbed as an argument in a context where % all characters are catcode 10, 11 or 12, except \ which is active % (as in normal texinfo). It is necessary to change the definition of \. % It's necessary to have hard CRs when the macro is executed. This is % done by making ^^M (\endlinechar) catcode 12 when reading the macro % body, and then making it the \newlinechar in \scanmacro. \def\scanctxt{% \catcode`\"=\other \catcode`\+=\other \catcode`\<=\other \catcode`\>=\other \catcode`\@=\other \catcode`\^=\other \catcode`\_=\other \catcode`\|=\other \catcode`\~=\other } \def\scanargctxt{% \scanctxt \catcode`\\=\other \catcode`\^^M=\other } \def\macrobodyctxt{% \scanctxt \catcode`\{=\other \catcode`\}=\other \catcode`\^^M=\other \usembodybackslash } \def\macroargctxt{% \scanctxt \catcode`\\=\other } % \mbodybackslash is the definition of \ in @macro bodies. % It maps \foo\ => \csname macarg.foo\endcsname => #N % where N is the macro parameter number. % We define \csname macarg.\endcsname to be \realbackslash, so % \\ in macro replacement text gets you a backslash. {\catcode`@=0 @catcode`@\=@active @gdef@usembodybackslash{@let\=@mbodybackslash} @gdef@mbodybackslash#1\{@csname macarg.#1@endcsname} } \expandafter\def\csname macarg.\endcsname{\realbackslash} \def\macro{\recursivefalse\parsearg\macroxxx} \def\rmacro{\recursivetrue\parsearg\macroxxx} \def\macroxxx#1{% \getargs{#1}% now \macname is the macname and \argl the arglist \ifx\argl\empty % no arguments \paramno=0% \else \expandafter\parsemargdef \argl;% \fi \if1\csname ismacro.\the\macname\endcsname \message{Warning: redefining \the\macname}% \else \expandafter\ifx\csname \the\macname\endcsname \relax \else \errmessage{Macro name \the\macname\space already defined}\fi \global\cslet{macsave.\the\macname}{\the\macname}% \global\expandafter\let\csname ismacro.\the\macname\endcsname=1% % Add the macroname to \macrolist \toks0 = \expandafter{\macrolist\do}% \xdef\macrolist{\the\toks0 \expandafter\noexpand\csname\the\macname\endcsname}% \fi \begingroup \macrobodyctxt \ifrecursive \expandafter\parsermacbody \else \expandafter\parsemacbody \fi} \parseargdef\unmacro{% \if1\csname ismacro.#1\endcsname \global\cslet{#1}{macsave.#1}% \global\expandafter\let \csname ismacro.#1\endcsname=0% % Remove the macro name from \macrolist: \begingroup \expandafter\let\csname#1\endcsname \relax \let\do\unmacrodo \xdef\macrolist{\macrolist}% \endgroup \else \errmessage{Macro #1 not defined}% \fi } % Called by \do from \dounmacro on each macro. The idea is to omit any % macro definitions that have been changed to \relax. % \def\unmacrodo#1{% \ifx#1\relax % remove this \else \noexpand\do \noexpand #1% \fi } % This makes use of the obscure feature that if the last token of a % is #, then the preceding argument is delimited by % an opening brace, and that opening brace is not consumed. \def\getargs#1{\getargsxxx#1{}} \def\getargsxxx#1#{\getmacname #1 \relax\getmacargs} \def\getmacname #1 #2\relax{\macname={#1}} \def\getmacargs#1{\def\argl{#1}} % Parse the optional {params} list. Set up \paramno and \paramlist % so \defmacro knows what to do. Define \macarg.blah for each blah % in the params list, to be ##N where N is the position in that list. % That gets used by \mbodybackslash (above). % We need to get `macro parameter char #' into several definitions. % The technique used is stolen from LaTeX: let \hash be something % unexpandable, insert that wherever you need a #, and then redefine % it to # just before using the token list produced. % % The same technique is used to protect \eatspaces till just before % the macro is used. \def\parsemargdef#1;{\paramno=0\def\paramlist{}% \let\hash\relax\let\xeatspaces\relax\parsemargdefxxx#1,;,} \def\parsemargdefxxx#1,{% \if#1;\let\next=\relax \else \let\next=\parsemargdefxxx \advance\paramno by 1% \expandafter\edef\csname macarg.\eatspaces{#1}\endcsname {\xeatspaces{\hash\the\paramno}}% \edef\paramlist{\paramlist\hash\the\paramno,}% \fi\next} % These two commands read recursive and nonrecursive macro bodies. % (They're different since rec and nonrec macros end differently.) \long\def\parsemacbody#1@end macro% {\xdef\temp{\eatcr{#1}}\endgroup\defmacro}% \long\def\parsermacbody#1@end rmacro% {\xdef\temp{\eatcr{#1}}\endgroup\defmacro}% % This defines the macro itself. There are six cases: recursive and % nonrecursive macros of zero, one, and many arguments. % Much magic with \expandafter here. % \xdef is used so that macro definitions will survive the file % they're defined in; @include reads the file inside a group. \def\defmacro{% \let\hash=##% convert placeholders to macro parameter chars \ifrecursive \ifcase\paramno % 0 \expandafter\xdef\csname\the\macname\endcsname{% \noexpand\scanmacro{\temp}}% \or % 1 \expandafter\xdef\csname\the\macname\endcsname{% \bgroup\noexpand\macroargctxt \noexpand\braceorline \expandafter\noexpand\csname\the\macname xxx\endcsname}% \expandafter\xdef\csname\the\macname xxx\endcsname##1{% \egroup\noexpand\scanmacro{\temp}}% \else % many \expandafter\xdef\csname\the\macname\endcsname{% \bgroup\noexpand\macroargctxt \noexpand\csname\the\macname xx\endcsname}% \expandafter\xdef\csname\the\macname xx\endcsname##1{% \expandafter\noexpand\csname\the\macname xxx\endcsname ##1,}% \expandafter\expandafter \expandafter\xdef \expandafter\expandafter \csname\the\macname xxx\endcsname \paramlist{\egroup\noexpand\scanmacro{\temp}}% \fi \else \ifcase\paramno % 0 \expandafter\xdef\csname\the\macname\endcsname{% \noexpand\norecurse{\the\macname}% \noexpand\scanmacro{\temp}\egroup}% \or % 1 \expandafter\xdef\csname\the\macname\endcsname{% \bgroup\noexpand\macroargctxt \noexpand\braceorline \expandafter\noexpand\csname\the\macname xxx\endcsname}% \expandafter\xdef\csname\the\macname xxx\endcsname##1{% \egroup \noexpand\norecurse{\the\macname}% \noexpand\scanmacro{\temp}\egroup}% \else % many \expandafter\xdef\csname\the\macname\endcsname{% \bgroup\noexpand\macroargctxt \expandafter\noexpand\csname\the\macname xx\endcsname}% \expandafter\xdef\csname\the\macname xx\endcsname##1{% \expandafter\noexpand\csname\the\macname xxx\endcsname ##1,}% \expandafter\expandafter \expandafter\xdef \expandafter\expandafter \csname\the\macname xxx\endcsname \paramlist{% \egroup \noexpand\norecurse{\the\macname}% \noexpand\scanmacro{\temp}\egroup}% \fi \fi} \def\norecurse#1{\bgroup\cslet{#1}{macsave.#1}} % \braceorline decides whether the next nonwhitespace character is a % {. If so it reads up to the closing }, if not, it reads the whole % line. Whatever was read is then fed to the next control sequence % as an argument (by \parsebrace or \parsearg) \def\braceorline#1{\let\next=#1\futurelet\nchar\braceorlinexxx} \def\braceorlinexxx{% \ifx\nchar\bgroup\else \expandafter\parsearg \fi \next} % We want to disable all macros during \shipout so that they are not % expanded by \write. \def\turnoffmacros{\begingroup \def\do##1{\let\noexpand##1=\relax}% \edef\next{\macrolist}\expandafter\endgroup\next} % For \indexnofonts, we need to get rid of all macros, leaving only the % arguments (if present). Of course this is not nearly correct, but it % is the best we can do for now. makeinfo does not expand macros in the % argument to @deffn, which ends up writing an index entry, and texindex % isn't prepared for an index sort entry that starts with \. % % Since macro invocations are followed by braces, we can just redefine them % to take a single TeX argument. The case of a macro invocation that % goes to end-of-line is not handled. % \def\emptyusermacros{\begingroup \def\do##1{\let\noexpand##1=\noexpand\asis}% \edef\next{\macrolist}\expandafter\endgroup\next} % @alias. % We need some trickery to remove the optional spaces around the equal % sign. Just make them active and then expand them all to nothing. \def\alias{\parseargusing\obeyspaces\aliasxxx} \def\aliasxxx #1{\aliasyyy#1\relax} \def\aliasyyy #1=#2\relax{% {% \expandafter\let\obeyedspace=\empty \xdef\next{\global\let\makecsname{#1}=\makecsname{#2}}% }% \next } \message{cross references,} \newwrite\auxfile \newif\ifhavexrefs % True if xref values are known. \newif\ifwarnedxrefs % True if we warned once that they aren't known. % @inforef is relatively simple. \def\inforef #1{\inforefzzz #1,,,,**} \def\inforefzzz #1,#2,#3,#4**{\putwordSee{} \putwordInfo{} \putwordfile{} \file{\ignorespaces #3{}}, node \samp{\ignorespaces#1{}}} % @node's only job in TeX is to define \lastnode, which is used in % cross-references. The @node line might or might not have commas, and % might or might not have spaces before the first comma, like: % @node foo , bar , ... % We don't want such trailing spaces in the node name. % \parseargdef\node{\checkenv{}\donode #1 ,\finishnodeparse} % % also remove a trailing comma, in case of something like this: % @node Help-Cross, , , Cross-refs \def\donode#1 ,#2\finishnodeparse{\dodonode #1,\finishnodeparse} \def\dodonode#1,#2\finishnodeparse{\gdef\lastnode{#1}} \let\nwnode=\node \let\lastnode=\empty % Write a cross-reference definition for the current node. #1 is the % type (Ynumbered, Yappendix, Ynothing). % \def\donoderef#1{% \ifx\lastnode\empty\else \setref{\lastnode}{#1}% \global\let\lastnode=\empty \fi } % @anchor{NAME} -- define xref target at arbitrary point. % \newcount\savesfregister % \def\savesf{\relax \ifhmode \savesfregister=\spacefactor \fi} \def\restoresf{\relax \ifhmode \spacefactor=\savesfregister \fi} \def\anchor#1{\savesf \setref{#1}{Ynothing}\restoresf \ignorespaces} % \setref{NAME}{SNT} defines a cross-reference point NAME (a node or an % anchor), which consists of three parts: % 1) NAME-title - the current sectioning name taken from \thissection, % or the anchor name. % 2) NAME-snt - section number and type, passed as the SNT arg, or % empty for anchors. % 3) NAME-pg - the page number. % % This is called from \donoderef, \anchor, and \dofloat. In the case of % floats, there is an additional part, which is not written here: % 4) NAME-lof - the text as it should appear in a @listoffloats. % \def\setref#1#2{% \pdfmkdest{#1}% \iflinks {% \atdummies % preserve commands, but don't expand them \turnoffactive \otherbackslash \edef\writexrdef##1##2{% \write\auxfile{@xrdef{#1-% #1 of \setref, expanded by the \edef ##1}{##2}}% these are parameters of \writexrdef }% \toks0 = \expandafter{\thissection}% \immediate \writexrdef{title}{\the\toks0 }% \immediate \writexrdef{snt}{\csname #2\endcsname}% \Ynumbered etc. \writexrdef{pg}{\folio}% will be written later, during \shipout }% \fi } % @xref, @pxref, and @ref generate cross-references. For \xrefX, #1 is % the node name, #2 the name of the Info cross-reference, #3 the printed % node name, #4 the name of the Info file, #5 the name of the printed % manual. All but the node name can be omitted. % \def\pxref#1{\putwordsee{} \xrefX[#1,,,,,,,]} \def\xref#1{\putwordSee{} \xrefX[#1,,,,,,,]} \def\ref#1{\xrefX[#1,,,,,,,]} \def\xrefX[#1,#2,#3,#4,#5,#6]{\begingroup \unsepspaces \def\printedmanual{\ignorespaces #5}% \def\printedrefname{\ignorespaces #3}% \setbox1=\hbox{\printedmanual\unskip}% \setbox0=\hbox{\printedrefname\unskip}% \ifdim \wd0 = 0pt % No printed node name was explicitly given. \expandafter\ifx\csname SETxref-automatic-section-title\endcsname\relax % Use the node name inside the square brackets. \def\printedrefname{\ignorespaces #1}% \else % Use the actual chapter/section title appear inside % the square brackets. Use the real section title if we have it. \ifdim \wd1 > 0pt % It is in another manual, so we don't have it. \def\printedrefname{\ignorespaces #1}% \else \ifhavexrefs % We know the real title if we have the xref values. \def\printedrefname{\refx{#1-title}{}}% \else % Otherwise just copy the Info node name. \def\printedrefname{\ignorespaces #1}% \fi% \fi \fi \fi % % Make link in pdf output. \ifpdf \leavevmode \getfilename{#4}% {\turnoffactive \otherbackslash \ifnum\filenamelength>0 \startlink attr{/Border [0 0 0]}% goto file{\the\filename.pdf} name{#1}% \else \startlink attr{/Border [0 0 0]}% goto name{\pdfmkpgn{#1}}% \fi }% \linkcolor \fi % % Float references are printed completely differently: "Figure 1.2" % instead of "[somenode], p.3". We distinguish them by the % LABEL-title being set to a magic string. {% % Have to otherify everything special to allow the \csname to % include an _ in the xref name, etc. \indexnofonts \turnoffactive \otherbackslash \expandafter\global\expandafter\let\expandafter\Xthisreftitle \csname XR#1-title\endcsname }% \iffloat\Xthisreftitle % If the user specified the print name (third arg) to the ref, % print it instead of our usual "Figure 1.2". \ifdim\wd0 = 0pt \refx{#1-snt}% \else \printedrefname \fi % % if the user also gave the printed manual name (fifth arg), append % "in MANUALNAME". \ifdim \wd1 > 0pt \space \putwordin{} \cite{\printedmanual}% \fi \else % node/anchor (non-float) references. % % If we use \unhbox0 and \unhbox1 to print the node names, TeX does not % insert empty discretionaries after hyphens, which means that it will % not find a line break at a hyphen in a node names. Since some manuals % are best written with fairly long node names, containing hyphens, this % is a loss. Therefore, we give the text of the node name again, so it % is as if TeX is seeing it for the first time. \ifdim \wd1 > 0pt \putwordsection{} ``\printedrefname'' \putwordin{} \cite{\printedmanual}% \else % _ (for example) has to be the character _ for the purposes of the % control sequence corresponding to the node, but it has to expand % into the usual \leavevmode...\vrule stuff for purposes of % printing. So we \turnoffactive for the \refx-snt, back on for the % printing, back off for the \refx-pg. {\turnoffactive \otherbackslash % Only output a following space if the -snt ref is nonempty; for % @unnumbered and @anchor, it won't be. \setbox2 = \hbox{\ignorespaces \refx{#1-snt}{}}% \ifdim \wd2 > 0pt \refx{#1-snt}\space\fi }% % output the `[mynode]' via a macro so it can be overridden. \xrefprintnodename\printedrefname % % But we always want a comma and a space: ,\space % % output the `page 3'. \turnoffactive \otherbackslash \putwordpage\tie\refx{#1-pg}{}% \fi \fi \endlink \endgroup} % This macro is called from \xrefX for the `[nodename]' part of xref % output. It's a separate macro only so it can be changed more easily, % since square brackets don't work well in some documents. Particularly % one that Bob is working on :). % \def\xrefprintnodename#1{[#1]} % Things referred to by \setref. % \def\Ynothing{} \def\Yomitfromtoc{} \def\Ynumbered{% \ifnum\secno=0 \putwordChapter@tie \the\chapno \else \ifnum\subsecno=0 \putwordSection@tie \the\chapno.\the\secno \else \ifnum\subsubsecno=0 \putwordSection@tie \the\chapno.\the\secno.\the\subsecno \else \putwordSection@tie \the\chapno.\the\secno.\the\subsecno.\the\subsubsecno \fi\fi\fi } \def\Yappendix{% \ifnum\secno=0 \putwordAppendix@tie @char\the\appendixno{}% \else \ifnum\subsecno=0 \putwordSection@tie @char\the\appendixno.\the\secno \else \ifnum\subsubsecno=0 \putwordSection@tie @char\the\appendixno.\the\secno.\the\subsecno \else \putwordSection@tie @char\the\appendixno.\the\secno.\the\subsecno.\the\subsubsecno \fi\fi\fi } % Define \refx{NAME}{SUFFIX} to reference a cross-reference string named NAME. % If its value is nonempty, SUFFIX is output afterward. % \def\refx#1#2{% {% \indexnofonts \otherbackslash \expandafter\global\expandafter\let\expandafter\thisrefX \csname XR#1\endcsname }% \ifx\thisrefX\relax % If not defined, say something at least. \angleleft un\-de\-fined\angleright \iflinks \ifhavexrefs \message{\linenumber Undefined cross reference `#1'.}% \else \ifwarnedxrefs\else \global\warnedxrefstrue \message{Cross reference values unknown; you must run TeX again.}% \fi \fi \fi \else % It's defined, so just use it. \thisrefX \fi #2% Output the suffix in any case. } % This is the macro invoked by entries in the aux file. Usually it's % just a \def (we prepend XR to the control sequence name to avoid % collisions). But if this is a float type, we have more work to do. % \def\xrdef#1#2{% \expandafter\gdef\csname XR#1\endcsname{#2}% remember this xref value. % % Was that xref control sequence that we just defined for a float? \expandafter\iffloat\csname XR#1\endcsname % it was a float, and we have the (safe) float type in \iffloattype. \expandafter\let\expandafter\floatlist \csname floatlist\iffloattype\endcsname % % Is this the first time we've seen this float type? \expandafter\ifx\floatlist\relax \toks0 = {\do}% yes, so just \do \else % had it before, so preserve previous elements in list. \toks0 = \expandafter{\floatlist\do}% \fi % % Remember this xref in the control sequence \floatlistFLOATTYPE, % for later use in \listoffloats. \expandafter\xdef\csname floatlist\iffloattype\endcsname{\the\toks0{#1}}% \fi } % Read the last existing aux file, if any. No error if none exists. % \def\tryauxfile{% \openin 1 \jobname.aux \ifeof 1 \else \readauxfile \global\havexrefstrue \fi \closein 1 } \def\readauxfile{\begingroup \catcode`\^^@=\other \catcode`\^^A=\other \catcode`\^^B=\other \catcode`\^^C=\other \catcode`\^^D=\other \catcode`\^^E=\other \catcode`\^^F=\other \catcode`\^^G=\other \catcode`\^^H=\other \catcode`\^^K=\other \catcode`\^^L=\other \catcode`\^^N=\other \catcode`\^^P=\other \catcode`\^^Q=\other \catcode`\^^R=\other \catcode`\^^S=\other \catcode`\^^T=\other \catcode`\^^U=\other \catcode`\^^V=\other \catcode`\^^W=\other \catcode`\^^X=\other \catcode`\^^Z=\other \catcode`\^^[=\other \catcode`\^^\=\other \catcode`\^^]=\other \catcode`\^^^=\other \catcode`\^^_=\other % It was suggested to set the catcode of ^ to 7, which would allow ^^e4 etc. % in xref tags, i.e., node names. But since ^^e4 notation isn't % supported in the main text, it doesn't seem desirable. Furthermore, % that is not enough: for node names that actually contain a ^ % character, we would end up writing a line like this: 'xrdef {'hat % b-title}{'hat b} and \xrdef does a \csname...\endcsname on the first % argument, and \hat is not an expandable control sequence. It could % all be worked out, but why? Either we support ^^ or we don't. % % The other change necessary for this was to define \auxhat: % \def\auxhat{\def^{'hat }}% extra space so ok if followed by letter % and then to call \auxhat in \setq. % \catcode`\^=\other % % Special characters. Should be turned off anyway, but... \catcode`\~=\other \catcode`\[=\other \catcode`\]=\other \catcode`\"=\other \catcode`\_=\other \catcode`\|=\other \catcode`\<=\other \catcode`\>=\other \catcode`\$=\other \catcode`\#=\other \catcode`\&=\other \catcode`\%=\other \catcode`+=\other % avoid \+ for paranoia even though we've turned it off % % This is to support \ in node names and titles, since the \ % characters end up in a \csname. It's easier than % leaving it active and making its active definition an actual \ % character. What I don't understand is why it works in the *value* % of the xrdef. Seems like it should be a catcode12 \, and that % should not typeset properly. But it works, so I'm moving on for % now. --karl, 15jan04. \catcode`\\=\other % % Make the characters 128-255 be printing characters. {% \count 1=128 \def\loop{% \catcode\count 1=\other \advance\count 1 by 1 \ifnum \count 1<256 \loop \fi }% }% % % @ is our escape character in .aux files, and we need braces. \catcode`\{=1 \catcode`\}=2 \catcode`\@=0 % \input \jobname.aux \endgroup} \message{insertions,} % including footnotes. \newcount \footnoteno % The trailing space in the following definition for supereject is % vital for proper filling; pages come out unaligned when you do a % pagealignmacro call if that space before the closing brace is % removed. (Generally, numeric constants should always be followed by a % space to prevent strange expansion errors.) \def\supereject{\par\penalty -20000\footnoteno =0 } % @footnotestyle is meaningful for info output only. \let\footnotestyle=\comment {\catcode `\@=11 % % Auto-number footnotes. Otherwise like plain. \gdef\footnote{% \let\indent=\ptexindent \let\noindent=\ptexnoindent \global\advance\footnoteno by \@ne \edef\thisfootno{$^{\the\footnoteno}$}% % % In case the footnote comes at the end of a sentence, preserve the % extra spacing after we do the footnote number. \let\@sf\empty \ifhmode\edef\@sf{\spacefactor\the\spacefactor}\ptexslash\fi % % Remove inadvertent blank space before typesetting the footnote number. \unskip \thisfootno\@sf \dofootnote }% % Don't bother with the trickery in plain.tex to not require the % footnote text as a parameter. Our footnotes don't need to be so general. % % Oh yes, they do; otherwise, @ifset (and anything else that uses % \parseargline) fails inside footnotes because the tokens are fixed when % the footnote is read. --karl, 16nov96. % \gdef\dofootnote{% \insert\footins\bgroup % We want to typeset this text as a normal paragraph, even if the % footnote reference occurs in (for example) a display environment. % So reset some parameters. \hsize=\pagewidth \interlinepenalty\interfootnotelinepenalty \splittopskip\ht\strutbox % top baseline for broken footnotes \splitmaxdepth\dp\strutbox \floatingpenalty\@MM \leftskip\z@skip \rightskip\z@skip \spaceskip\z@skip \xspaceskip\z@skip \parindent\defaultparindent % \smallfonts \rm % % Because we use hanging indentation in footnotes, a @noindent appears % to exdent this text, so make it be a no-op. makeinfo does not use % hanging indentation so @noindent can still be needed within footnote % text after an @example or the like (not that this is good style). \let\noindent = \relax % % Hang the footnote text off the number. Use \everypar in case the % footnote extends for more than one paragraph. \everypar = {\hang}% \textindent{\thisfootno}% % % Don't crash into the line above the footnote text. Since this % expands into a box, it must come within the paragraph, lest it % provide a place where TeX can split the footnote. \footstrut \futurelet\next\fo@t } }%end \catcode `\@=11 % In case a @footnote appears in a vbox, save the footnote text and create % the real \insert just after the vbox finished. Otherwise, the insertion % would be lost. % Similarily, if a @footnote appears inside an alignment, save the footnote % text to a box and make the \insert when a row of the table is finished. % And the same can be done for other insert classes. --kasal, 16nov03. % Replace the \insert primitive by a cheating macro. % Deeper inside, just make sure that the saved insertions are not spilled % out prematurely. % \def\startsavinginserts{% \ifx \insert\ptexinsert \let\insert\saveinsert \else \let\checkinserts\relax \fi } % This \insert replacement works for both \insert\footins{foo} and % \insert\footins\bgroup foo\egroup, but it doesn't work for \insert27{foo}. % \def\saveinsert#1{% \edef\next{\noexpand\savetobox \makeSAVEname#1}% \afterassignment\next % swallow the left brace \let\temp = } \def\makeSAVEname#1{\makecsname{SAVE\expandafter\gobble\string#1}} \def\savetobox#1{\global\setbox#1 = \vbox\bgroup \unvbox#1} \def\checksaveins#1{\ifvoid#1\else \placesaveins#1\fi} \def\placesaveins#1{% \ptexinsert \csname\expandafter\gobblesave\string#1\endcsname {\box#1}% } % eat @SAVE -- beware, all of them have catcode \other: { \def\dospecials{\do S\do A\do V\do E} \uncatcodespecials % ;-) \gdef\gobblesave @SAVE{} } % initialization: \def\newsaveins #1{% \edef\next{\noexpand\newsaveinsX \makeSAVEname#1}% \next } \def\newsaveinsX #1{% \csname newbox\endcsname #1% \expandafter\def\expandafter\checkinserts\expandafter{\checkinserts \checksaveins #1}% } % initialize: \let\checkinserts\empty \newsaveins\footins \newsaveins\margin % @image. We use the macros from epsf.tex to support this. % If epsf.tex is not installed and @image is used, we complain. % % Check for and read epsf.tex up front. If we read it only at @image % time, we might be inside a group, and then its definitions would get % undone and the next image would fail. \openin 1 = epsf.tex \ifeof 1 \else % Do not bother showing banner with epsf.tex v2.7k (available in % doc/epsf.tex and on ctan). \def\epsfannounce{\toks0 = }% \input epsf.tex \fi \closein 1 % % We will only complain once about lack of epsf.tex. \newif\ifwarnednoepsf \newhelp\noepsfhelp{epsf.tex must be installed for images to work. It is also included in the Texinfo distribution, or you can get it from ftp://tug.org/tex/epsf.tex.} % \def\image#1{% \ifx\epsfbox\undefined \ifwarnednoepsf \else \errhelp = \noepsfhelp \errmessage{epsf.tex not found, images will be ignored}% \global\warnednoepsftrue \fi \else \imagexxx #1,,,,,\finish \fi } % % Arguments to @image: % #1 is (mandatory) image filename; we tack on .eps extension. % #2 is (optional) width, #3 is (optional) height. % #4 is (ignored optional) html alt text. % #5 is (ignored optional) extension. % #6 is just the usual extra ignored arg for parsing this stuff. \newif\ifimagevmode \def\imagexxx#1,#2,#3,#4,#5,#6\finish{\begingroup \catcode`\^^M = 5 % in case we're inside an example \normalturnoffactive % allow _ et al. in names % If the image is by itself, center it. \ifvmode \imagevmodetrue \nobreak\bigskip % Usually we'll have text after the image which will insert % \parskip glue, so insert it here too to equalize the space % above and below. \nobreak\vskip\parskip \nobreak \line\bgroup\hss \fi % % Output the image. \ifpdf \dopdfimage{#1}{#2}{#3}% \else % \epsfbox itself resets \epsf?size at each figure. \setbox0 = \hbox{\ignorespaces #2}\ifdim\wd0 > 0pt \epsfxsize=#2\relax \fi \setbox0 = \hbox{\ignorespaces #3}\ifdim\wd0 > 0pt \epsfysize=#3\relax \fi \epsfbox{#1.eps}% \fi % \ifimagevmode \hss \egroup \bigbreak \fi % space after the image \endgroup} % @float FLOATTYPE,LABEL,LOC ... @end float for displayed figures, tables, % etc. We don't actually implement floating yet, we always include the % float "here". But it seemed the best name for the future. % \envparseargdef\float{\eatcommaspace\eatcommaspace\dofloat#1, , ,\finish} % There may be a space before second and/or third parameter; delete it. \def\eatcommaspace#1, {#1,} % #1 is the optional FLOATTYPE, the text label for this float, typically % "Figure", "Table", "Example", etc. Can't contain commas. If omitted, % this float will not be numbered and cannot be referred to. % % #2 is the optional xref label. Also must be present for the float to % be referable. % % #3 is the optional positioning argument; for now, it is ignored. It % will somehow specify the positions allowed to float to (here, top, bottom). % % We keep a separate counter for each FLOATTYPE, which we reset at each % chapter-level command. \let\resetallfloatnos=\empty % \def\dofloat#1,#2,#3,#4\finish{% \let\thiscaption=\empty \let\thisshortcaption=\empty % % don't lose footnotes inside @float. % % BEWARE: when the floats start float, we have to issue warning whenever an % insert appears inside a float which could possibly float. --kasal, 26may04 % \startsavinginserts % % We can't be used inside a paragraph. \par % \vtop\bgroup \def\floattype{#1}% \def\floatlabel{#2}% \def\floatloc{#3}% we do nothing with this yet. % \ifx\floattype\empty \let\safefloattype=\empty \else {% % the floattype might have accents or other special characters, % but we need to use it in a control sequence name. \indexnofonts \turnoffactive \xdef\safefloattype{\floattype}% }% \fi % % If label is given but no type, we handle that as the empty type. \ifx\floatlabel\empty \else % We want each FLOATTYPE to be numbered separately (Figure 1, % Table 1, Figure 2, ...). (And if no label, no number.) % \expandafter\getfloatno\csname\safefloattype floatno\endcsname \global\advance\floatno by 1 % {% % This magic value for \thissection is output by \setref as the % XREFLABEL-title value. \xrefX uses it to distinguish float % labels (which have a completely different output format) from % node and anchor labels. And \xrdef uses it to construct the % lists of floats. % \edef\thissection{\floatmagic=\safefloattype}% \setref{\floatlabel}{Yfloat}% }% \fi % % start with \parskip glue, I guess. \vskip\parskip % % Don't suppress indentation if a float happens to start a section. \restorefirstparagraphindent } % we have these possibilities: % @float Foo,lbl & @caption{Cap}: Foo 1.1: Cap % @float Foo,lbl & no caption: Foo 1.1 % @float Foo & @caption{Cap}: Foo: Cap % @float Foo & no caption: Foo % @float ,lbl & Caption{Cap}: 1.1: Cap % @float ,lbl & no caption: 1.1 % @float & @caption{Cap}: Cap % @float & no caption: % \def\Efloat{% \let\floatident = \empty % % In all cases, if we have a float type, it comes first. \ifx\floattype\empty \else \def\floatident{\floattype}\fi % % If we have an xref label, the number comes next. \ifx\floatlabel\empty \else \ifx\floattype\empty \else % if also had float type, need tie first. \appendtomacro\floatident{\tie}% \fi % the number. \appendtomacro\floatident{\chaplevelprefix\the\floatno}% \fi % % Start the printed caption with what we've constructed in % \floatident, but keep it separate; we need \floatident again. \let\captionline = \floatident % \ifx\thiscaption\empty \else \ifx\floatident\empty \else \appendtomacro\captionline{: }% had ident, so need a colon between \fi % % caption text. \appendtomacro\captionline{\scanexp\thiscaption}% \fi % % If we have anything to print, print it, with space before. % Eventually this needs to become an \insert. \ifx\captionline\empty \else \vskip.5\parskip \captionline % % Space below caption. \vskip\parskip \fi % % If have an xref label, write the list of floats info. Do this % after the caption, to avoid chance of it being a breakpoint. \ifx\floatlabel\empty \else % Write the text that goes in the lof to the aux file as % \floatlabel-lof. Besides \floatident, we include the short % caption if specified, else the full caption if specified, else nothing. {% \atdummies \turnoffactive \otherbackslash % since we read the caption text in the macro world, where ^^M % is turned into a normal character, we have to scan it back, so % we don't write the literal three characters "^^M" into the aux file. \scanexp{% \xdef\noexpand\gtemp{% \ifx\thisshortcaption\empty \thiscaption \else \thisshortcaption \fi }% }% \immediate\write\auxfile{@xrdef{\floatlabel-lof}{\floatident \ifx\gtemp\empty \else : \gtemp \fi}}% }% \fi \egroup % end of \vtop % % place the captured inserts % % BEWARE: when the floats start float, we have to issue warning whenever an % insert appears inside a float which could possibly float. --kasal, 26may04 % \checkinserts } % Append the tokens #2 to the definition of macro #1, not expanding either. % \def\appendtomacro#1#2{% \expandafter\def\expandafter#1\expandafter{#1#2}% } % @caption, @shortcaption % \def\caption{\docaption\thiscaption} \def\shortcaption{\docaption\thisshortcaption} \def\docaption{\checkenv\float \bgroup\scanargctxt\defcaption} \def\defcaption#1#2{\egroup \def#1{#2}} % The parameter is the control sequence identifying the counter we are % going to use. Create it if it doesn't exist and assign it to \floatno. \def\getfloatno#1{% \ifx#1\relax % Haven't seen this figure type before. \csname newcount\endcsname #1% % % Remember to reset this floatno at the next chap. \expandafter\gdef\expandafter\resetallfloatnos \expandafter{\resetallfloatnos #1=0 }% \fi \let\floatno#1% } % \setref calls this to get the XREFLABEL-snt value. We want an @xref % to the FLOATLABEL to expand to "Figure 3.1". We call \setref when we % first read the @float command. % \def\Yfloat{\floattype@tie \chaplevelprefix\the\floatno}% % Magic string used for the XREFLABEL-title value, so \xrefX can % distinguish floats from other xref types. \def\floatmagic{!!float!!} % #1 is the control sequence we are passed; we expand into a conditional % which is true if #1 represents a float ref. That is, the magic % \thissection value which we \setref above. % \def\iffloat#1{\expandafter\doiffloat#1==\finish} % % #1 is (maybe) the \floatmagic string. If so, #2 will be the % (safe) float type for this float. We set \iffloattype to #2. % \def\doiffloat#1=#2=#3\finish{% \def\temp{#1}% \def\iffloattype{#2}% \ifx\temp\floatmagic } % @listoffloats FLOATTYPE - print a list of floats like a table of contents. % \parseargdef\listoffloats{% \def\floattype{#1}% floattype {% % the floattype might have accents or other special characters, % but we need to use it in a control sequence name. \indexnofonts \turnoffactive \xdef\safefloattype{\floattype}% }% % % \xrdef saves the floats as a \do-list in \floatlistSAFEFLOATTYPE. \expandafter\ifx\csname floatlist\safefloattype\endcsname \relax \ifhavexrefs % if the user said @listoffloats foo but never @float foo. \message{\linenumber No `\safefloattype' floats to list.}% \fi \else \begingroup \leftskip=\tocindent % indent these entries like a toc \let\do=\listoffloatsdo \csname floatlist\safefloattype\endcsname \endgroup \fi } % This is called on each entry in a list of floats. We're passed the % xref label, in the form LABEL-title, which is how we save it in the % aux file. We strip off the -title and look up \XRLABEL-lof, which % has the text we're supposed to typeset here. % % Figures without xref labels will not be included in the list (since % they won't appear in the aux file). % \def\listoffloatsdo#1{\listoffloatsdoentry#1\finish} \def\listoffloatsdoentry#1-title\finish{{% % Can't fully expand XR#1-lof because it can contain anything. Just % pass the control sequence. On the other hand, XR#1-pg is just the % page number, and we want to fully expand that so we can get a link % in pdf output. \toksA = \expandafter{\csname XR#1-lof\endcsname}% % % use the same \entry macro we use to generate the TOC and index. \edef\writeentry{\noexpand\entry{\the\toksA}{\csname XR#1-pg\endcsname}}% \writeentry }} \message{localization,} % and i18n. % @documentlanguage is usually given very early, just after % @setfilename. If done too late, it may not override everything % properly. Single argument is the language abbreviation. % It would be nice if we could set up a hyphenation file here. % \parseargdef\documentlanguage{% \tex % read txi-??.tex file in plain TeX. % Read the file if it exists. \openin 1 txi-#1.tex \ifeof 1 \errhelp = \nolanghelp \errmessage{Cannot read language file txi-#1.tex}% \else \input txi-#1.tex \fi \closein 1 \endgroup } \newhelp\nolanghelp{The given language definition file cannot be found or is empty. Maybe you need to install it? In the current directory should work if nowhere else does.} % @documentencoding should change something in TeX eventually, most % likely, but for now just recognize it. \let\documentencoding = \comment % Page size parameters. % \newdimen\defaultparindent \defaultparindent = 15pt \chapheadingskip = 15pt plus 4pt minus 2pt \secheadingskip = 12pt plus 3pt minus 2pt \subsecheadingskip = 9pt plus 2pt minus 2pt % Prevent underfull vbox error messages. \vbadness = 10000 % Don't be so finicky about underfull hboxes, either. \hbadness = 2000 % Following George Bush, just get rid of widows and orphans. \widowpenalty=10000 \clubpenalty=10000 % Use TeX 3.0's \emergencystretch to help line breaking, but if we're % using an old version of TeX, don't do anything. We want the amount of % stretch added to depend on the line length, hence the dependence on % \hsize. We call this whenever the paper size is set. % \def\setemergencystretch{% \ifx\emergencystretch\thisisundefined % Allow us to assign to \emergencystretch anyway. \def\emergencystretch{\dimen0}% \else \emergencystretch = .15\hsize \fi } % Parameters in order: 1) textheight; 2) textwidth; 3) voffset; % 4) hoffset; 5) binding offset; 6) topskip; 7) physical page height; 8) % physical page width. % % We also call \setleading{\textleading}, so the caller should define % \textleading. The caller should also set \parskip. % \def\internalpagesizes#1#2#3#4#5#6#7#8{% \voffset = #3\relax \topskip = #6\relax \splittopskip = \topskip % \vsize = #1\relax \advance\vsize by \topskip \outervsize = \vsize \advance\outervsize by 2\topandbottommargin \pageheight = \vsize % \hsize = #2\relax \outerhsize = \hsize \advance\outerhsize by 0.5in \pagewidth = \hsize % \normaloffset = #4\relax \bindingoffset = #5\relax % \ifpdf \pdfpageheight #7\relax \pdfpagewidth #8\relax \fi % \setleading{\textleading} % \parindent = \defaultparindent \setemergencystretch } % @letterpaper (the default). \def\letterpaper{{\globaldefs = 1 \parskip = 3pt plus 2pt minus 1pt \textleading = 13.2pt % % If page is nothing but text, make it come out even. \internalpagesizes{46\baselineskip}{6in}% {\voffset}{.25in}% {\bindingoffset}{36pt}% {11in}{8.5in}% }} % Use @smallbook to reset parameters for 7x9.5 (or so) format. \def\smallbook{{\globaldefs = 1 \parskip = 2pt plus 1pt \textleading = 12pt % \internalpagesizes{7.5in}{5in}% {\voffset}{.25in}% {\bindingoffset}{16pt}% {9.25in}{7in}% % \lispnarrowing = 0.3in \tolerance = 700 \hfuzz = 1pt \contentsrightmargin = 0pt \defbodyindent = .5cm }} % Use @afourpaper to print on European A4 paper. \def\afourpaper{{\globaldefs = 1 \parskip = 3pt plus 2pt minus 1pt \textleading = 13.2pt % % Double-side printing via postscript on Laserjet 4050 % prints double-sided nicely when \bindingoffset=10mm and \hoffset=-6mm. % To change the settings for a different printer or situation, adjust % \normaloffset until the front-side and back-side texts align. Then % do the same for \bindingoffset. You can set these for testing in % your texinfo source file like this: % @tex % \global\normaloffset = -6mm % \global\bindingoffset = 10mm % @end tex \internalpagesizes{51\baselineskip}{160mm} {\voffset}{\hoffset}% {\bindingoffset}{44pt}% {297mm}{210mm}% % \tolerance = 700 \hfuzz = 1pt \contentsrightmargin = 0pt \defbodyindent = 5mm }} % Use @afivepaper to print on European A5 paper. % From romildo@urano.iceb.ufop.br, 2 July 2000. % He also recommends making @example and @lisp be small. \def\afivepaper{{\globaldefs = 1 \parskip = 2pt plus 1pt minus 0.1pt \textleading = 12.5pt % \internalpagesizes{160mm}{120mm}% {\voffset}{\hoffset}% {\bindingoffset}{8pt}% {210mm}{148mm}% % \lispnarrowing = 0.2in \tolerance = 800 \hfuzz = 1.2pt \contentsrightmargin = 0pt \defbodyindent = 2mm \tableindent = 12mm }} % A specific text layout, 24x15cm overall, intended for A4 paper. \def\afourlatex{{\globaldefs = 1 \afourpaper \internalpagesizes{237mm}{150mm}% {\voffset}{4.6mm}% {\bindingoffset}{7mm}% {297mm}{210mm}% % % Must explicitly reset to 0 because we call \afourpaper. \globaldefs = 0 }} % Use @afourwide to print on A4 paper in landscape format. \def\afourwide{{\globaldefs = 1 \afourpaper \internalpagesizes{241mm}{165mm}% {\voffset}{-2.95mm}% {\bindingoffset}{7mm}% {297mm}{210mm}% \globaldefs = 0 }} % @pagesizes TEXTHEIGHT[,TEXTWIDTH] % Perhaps we should allow setting the margins, \topskip, \parskip, % and/or leading, also. Or perhaps we should compute them somehow. % \parseargdef\pagesizes{\pagesizesyyy #1,,\finish} \def\pagesizesyyy#1,#2,#3\finish{{% \setbox0 = \hbox{\ignorespaces #2}\ifdim\wd0 > 0pt \hsize=#2\relax \fi \globaldefs = 1 % \parskip = 3pt plus 2pt minus 1pt \setleading{\textleading}% % \dimen0 = #1 \advance\dimen0 by \voffset % \dimen2 = \hsize \advance\dimen2 by \normaloffset % \internalpagesizes{#1}{\hsize}% {\voffset}{\normaloffset}% {\bindingoffset}{44pt}% {\dimen0}{\dimen2}% }} % Set default to letter. % \letterpaper \message{and turning on texinfo input format.} % Define macros to output various characters with catcode for normal text. \catcode`\"=\other \catcode`\~=\other \catcode`\^=\other \catcode`\_=\other \catcode`\|=\other \catcode`\<=\other \catcode`\>=\other \catcode`\+=\other \catcode`\$=\other \def\normaldoublequote{"} \def\normaltilde{~} \def\normalcaret{^} \def\normalunderscore{_} \def\normalverticalbar{|} \def\normalless{<} \def\normalgreater{>} \def\normalplus{+} \def\normaldollar{$}%$ font-lock fix % This macro is used to make a character print one way in \tt % (where it can probably be output as-is), and another way in other fonts, % where something hairier probably needs to be done. % % #1 is what to print if we are indeed using \tt; #2 is what to print % otherwise. Since all the Computer Modern typewriter fonts have zero % interword stretch (and shrink), and it is reasonable to expect all % typewriter fonts to have this, we can check that font parameter. % \def\ifusingtt#1#2{\ifdim \fontdimen3\font=0pt #1\else #2\fi} % Same as above, but check for italic font. Actually this also catches % non-italic slanted fonts since it is impossible to distinguish them from % italic fonts. But since this is only used by $ and it uses \sl anyway % this is not a problem. \def\ifusingit#1#2{\ifdim \fontdimen1\font>0pt #1\else #2\fi} % Turn off all special characters except @ % (and those which the user can use as if they were ordinary). % Most of these we simply print from the \tt font, but for some, we can % use math or other variants that look better in normal text. \catcode`\"=\active \def\activedoublequote{{\tt\char34}} \let"=\activedoublequote \catcode`\~=\active \def~{{\tt\char126}} \chardef\hat=`\^ \catcode`\^=\active \def^{{\tt \hat}} \catcode`\_=\active \def_{\ifusingtt\normalunderscore\_} % Subroutine for the previous macro. \def\_{\leavevmode \kern.07em \vbox{\hrule width.3em height.1ex}\kern .07em } \catcode`\|=\active \def|{{\tt\char124}} \chardef \less=`\< \catcode`\<=\active \def<{{\tt \less}} \chardef \gtr=`\> \catcode`\>=\active \def>{{\tt \gtr}} \catcode`\+=\active \def+{{\tt \char 43}} \catcode`\$=\active \def${\ifusingit{{\sl\$}}\normaldollar}%$ font-lock fix % If a .fmt file is being used, characters that might appear in a file % name cannot be active until we have parsed the command line. % So turn them off again, and have \everyjob (or @setfilename) turn them on. % \otherifyactive is called near the end of this file. \def\otherifyactive{\catcode`+=\other \catcode`\_=\other} \catcode`\@=0 % \backslashcurfont outputs one backslash character in current font, % as in \char`\\. \global\chardef\backslashcurfont=`\\ \global\let\rawbackslashxx=\backslashcurfont % let existing .??s files work % \rawbackslash defines an active \ to do \backslashcurfont. % \otherbackslash defines an active \ to be a literal `\' character with % catcode other. {\catcode`\\=\active @gdef@rawbackslash{@let\=@backslashcurfont} @gdef@otherbackslash{@let\=@realbackslash} } % \realbackslash is an actual character `\' with catcode other. {\catcode`\\=\other @gdef@realbackslash{\}} % \normalbackslash outputs one backslash in fixed width font. \def\normalbackslash{{\tt\backslashcurfont}} \catcode`\\=\active % Used sometimes to turn off (effectively) the active characters % even after parsing them. @def@turnoffactive{% @let"=@normaldoublequote @let\=@realbackslash @let~=@normaltilde @let^=@normalcaret @let_=@normalunderscore @let|=@normalverticalbar @let<=@normalless @let>=@normalgreater @let+=@normalplus @let$=@normaldollar %$ font-lock fix @unsepspaces } % Same as @turnoffactive except outputs \ as {\tt\char`\\} instead of % the literal character `\'. (Thus, \ is not expandable when this is in % effect.) % @def@normalturnoffactive{@turnoffactive @let\=@normalbackslash} % Make _ and + \other characters, temporarily. % This is canceled by @fixbackslash. @otherifyactive % If a .fmt file is being used, we don't want the `\input texinfo' to show up. % That is what \eatinput is for; after that, the `\' should revert to printing % a backslash. % @gdef@eatinput input texinfo{@fixbackslash} @global@let\ = @eatinput % On the other hand, perhaps the file did not have a `\input texinfo'. Then % the first `\{ in the file would cause an error. This macro tries to fix % that, assuming it is called before the first `\' could plausibly occur. % Also back turn on active characters that might appear in the input % file name, in case not using a pre-dumped format. % @gdef@fixbackslash{% @ifx\@eatinput @let\ = @normalbackslash @fi @catcode`+=@active @catcode`@_=@active } % Say @foo, not \foo, in error messages. @escapechar = `@@ % These look ok in all fonts, so just make them not special. @catcode`@& = @other @catcode`@# = @other @catcode`@% = @other @c Local variables: @c eval: (add-hook 'write-file-hooks 'time-stamp) @c page-delimiter: "^\\\\message" @c time-stamp-start: "def\\\\texinfoversion{" @c time-stamp-format: "%:y-%02m-%02d.%02H" @c time-stamp-end: "}" @c End: @c vim:sw=2: @ignore arch-tag: e1b36e32-c96e-4135-a41a-0b2efa2ea115 @end ignore gsl-1.0.8/doc/gsl_sf.texi0000644000175000017500000036152411201030403013023 0ustar shsh\input texinfo @ifnottex @node Top @top Octave gsl @end ifnottex gsl_sf -*- texinfo -*- @deftypefn {Loadable Function} {} gsl_sf () Octave bindings to the GNU Scientific Library. All GSL functions can be called with by the GSL names within octave. @end deftypefn clausen -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} clausen (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} clausen (@dots{}) The Clausen function is defined by the following integral, Cl_2(x) = - \\int_0^x dt \\log(2 \\sin(t/2)) It is related to the dilogarithm by Cl_2(\\theta) = \\Im Li_2(\\exp(i \\theta)). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn dawson -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} dawson (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} dawson (@dots{}) The Dawson integral is defined by \\exp(-x^2) \\int_0^x dt \\exp(t^2). A table of Dawson integral can be found in Abramowitz & Stegun, Table 7.5. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn debye_1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} debye_1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_1 (@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn debye_2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} debye_2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_2 (@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn debye_3 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} debye_3 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_3 (@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn debye_4 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} debye_4 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_4 (@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn erf_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} erf_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erf_gsl (@dots{}) These routines compute the error function erf(x) = (2/\\sqrt(\\pi)) \\int_0^x dt \\exp(-t^2). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn erfc_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} erfc_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erfc_gsl (@dots{}) These routines compute the complementary error function erfc(x) = 1 - erf(x) = (2/\\sqrt(\\pi)) \\int_x^\\infty \\exp(-t^2). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn log_erfc -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} log_erfc (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} log_erfc (@dots{}) These routines compute the logarithm of the complementary error function \\log(\\erfc(x)). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn erf_Z -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} erf_Z (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erf_Z (@dots{}) These routines compute the Gaussian probability function Z(x) = (1/(2\\pi)) \\exp(-x^2/2). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn erf_Q -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} erf_Q (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erf_Q (@dots{}) These routines compute the upper tail of the Gaussian probability function Q(x) = (1/(2\\pi)) \\int_x^\\infty dt \\exp(-t^2/2). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hazard -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} hazard (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} hazard (@dots{}) The hazard function for the normal distrbution, also known as the inverse Mill\\'s ratio, is defined as h(x) = Z(x)/Q(x) = \\sqrt@{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2)@}. It decreases rapidly as x approaches -\\infty and asymptotes to h(x) \\sim x as x approaches +\\infty. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn expm1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} expm1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expm1 (@dots{}) These routines compute the quantity \\exp(x)-1 using an algorithm that is accurate for small x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn exprel -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} exprel (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} exprel (@dots{}) These routines compute the quantity (\\exp(x)-1)/x using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion (\\exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\dots. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn exprel_2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} exprel_2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} exprel_2 (@dots{}) These routines compute the quantity 2(\\exp(x)-1-x)/x^2 using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion 2(\\exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\dots. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn expint_E1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} expint_E1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_E1 (@dots{}) These routines compute the exponential integral E_1(x), E_1(x) := Re \\int_1^\\infty dt \\exp(-xt)/t. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn expint_E2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} expint_E2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_E2 (@dots{}) These routines compute the second-order exponential integral E_2(x), E_2(x) := \\Re \\int_1^\\infty dt \\exp(-xt)/t^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn expint_Ei -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} expint_Ei (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_Ei (@dots{}) These routines compute the exponential integral E_i(x), Ei(x) := - PV(\\int_@{-x@}^\\infty dt \\exp(-t)/t) where PV denotes the principal value of the integral. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn Shi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} Shi (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Shi (@dots{}) These routines compute the integral Shi(x) = \\int_0^x dt \\sinh(t)/t. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn Chi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} Chi (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Chi (@dots{}) These routines compute the integral Chi(x) := Re[ \\gamma_E + \\log(x) + \\int_0^x dt (\\cosh[t]-1)/t] , where \\gamma_E is the Euler constant. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn expint_3 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} expint_3 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_3 (@dots{}) These routines compute the exponential integral Ei_3(x) = \\int_0^x dt \\exp(-t^3) for x >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn Si -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} Si (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Si (@dots{}) These routines compute the Sine integral Si(x) = \\int_0^x dt \\sin(t)/t. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn Ci -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} Ci (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Ci (@dots{}) These routines compute the Cosine integral Ci(x) = -\\int_x^\\infty dt \\cos(t)/t for x > 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn atanint -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} atanint (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} atanint (@dots{}) These routines compute the Arctangent integral AtanInt(x) = \\int_0^x dt \\arctan(t)/t. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_mhalf -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_mhalf (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_mhalf (@dots{}) These routines compute the complete Fermi-Dirac integral F_@{-1/2@}(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_half -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_half (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_half (@dots{}) These routines compute the complete Fermi-Dirac integral F_@{1/2@}(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_3half -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_3half (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_3half (@dots{}) These routines compute the complete Fermi-Dirac integral F_@{3/2@}(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gamma_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} gamma_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} gamma_gsl (@dots{}) These routines compute the Gamma function \\Gamma(x), subject to x not being a negative integer. The function is computed using the real Lanczos method. The maximum value of x such that \\Gamma(x) is not considered an overflow is given by the macro GSL_SF_GAMMA_XMAX and is 171.0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lngamma_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lngamma_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lngamma_gsl (@dots{}) These routines compute the logarithm of the Gamma function, \\log(\\Gamma(x)), subject to x not a being negative integer. For x<0 the real part of \\log(\\Gamma(x)) is returned, which is equivalent to \\log(|\\Gamma(x)|). The function is computed using the real Lanczos method. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gammastar -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} gammastar (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} gammastar (@dots{}) These routines compute the regulated Gamma Function \\Gamma^*(x) for x > 0. The regulated gamma function is given by, \\Gamma^*(x) = \\Gamma(x)/(\\sqrt@{2\\pi@} x^@{(x-1/2)@} \\exp(-x)) = (1 + (1/12x) + ...) for x \\to \\infty and is a useful suggestion of Temme. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gammainv_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} gammainv_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} gammainv_gsl (@dots{}) These routines compute the reciprocal of the gamma function, 1/\\Gamma(x) using the real Lanczos method. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lambert_W0 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lambert_W0 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lambert_W0 (@dots{}) These compute the principal branch of the Lambert W function, W_0(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@{-1@}(x) to be the other real branch, where W < -1 for x < 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lambert_Wm1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lambert_Wm1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lambert_Wm1 (@dots{}) These compute the secondary real-valued branch of the Lambert W function, W_@{-1@}(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@{-1@}(x) to be the other real branch, where W < -1 for x < 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn log_1plusx -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} log_1plusx (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} log_1plusx (@dots{}) These routines compute \\log(1 + x) for x > -1 using an algorithm that is accurate for small x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn log_1plusx_mx -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} log_1plusx_mx (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} log_1plusx_mx (@dots{}) These routines compute \\log(1 + x) - x for x > -1 using an algorithm that is accurate for small x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn psi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} psi (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi (@dots{}) These routines compute the digamma function \\psi(x) for general x, x \ e 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn psi_1piy -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} psi_1piy (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi_1piy (@dots{}) These routines compute the real part of the digamma function on the line 1+i y, Re[\\psi(1 + i y)]. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn synchrotron_1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} synchrotron_1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} synchrotron_1 (@dots{}) These routines compute the first synchrotron function x \\int_x^\\infty dt K_@{5/3@}(t) for x >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn synchrotron_2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} synchrotron_2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} synchrotron_2 (@dots{}) These routines compute the second synchrotron function x K_@{2/3@}(x) for x >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn transport_2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} transport_2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_2 (@dots{}) These routines compute the transport function J(2,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn transport_3 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} transport_3 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_3 (@dots{}) These routines compute the transport function J(3,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn transport_4 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} transport_4 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_4 (@dots{}) These routines compute the transport function J(4,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn transport_5 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} transport_5 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_5 (@dots{}) These routines compute the transport function J(5,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn sinc_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} sinc_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} sinc_gsl (@dots{}) These routines compute \\sinc(x) = \\sin(\\pi x) / (\\pi x) for any value of x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lnsinh -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lnsinh (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lnsinh (@dots{}) These routines compute \\log(\\sinh(x)) for x > 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lncosh -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lncosh (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lncosh (@dots{}) These routines compute \\log(\\cosh(x)) for any x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn zeta -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} zeta (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} zeta (@dots{}) These routines compute the Riemann zeta function \\zeta(s) for arbitrary s, s \ e 1. The Riemann zeta function is defined by the infinite sum \\zeta(s) = \\sum_@{k=1@}^\\infty k^@{-s@}. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn eta -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} eta (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} eta (@dots{}) These routines compute the eta function \\eta(s) for arbitrary s. The eta function is defined by \\eta(s) = (1-2^@{1-s@}) \\zeta(s). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Jn -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_Jn (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Jn (@dots{}) These routines compute the regular cylindrical Bessel function of order n, J_n(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Yn -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_Yn (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Yn (@dots{}) These routines compute the irregular cylindrical Bessel function of order n, Y_n(x), for x>0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_In -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_In (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_In (@dots{}) These routines compute the regular modified cylindrical Bessel function of order n, I_n(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_In_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_In_scaled (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_In_scaled (@dots{}) These routines compute the scaled regular modified cylindrical Bessel function of order n, \\exp(-|x|) I_n(x) @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Kn -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_Kn (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Kn (@dots{}) These routines compute the irregular modified cylindrical Bessel function of order n, K_n(x), for x > 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Kn_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_Kn_scaled (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Kn_scaled (@dots{}) @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_jl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_jl (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_jl (@dots{}) These routines compute the regular spherical Bessel function of order l, j_l(x), for l >= 0 and x >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_yl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_yl (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_yl (@dots{}) These routines compute the irregular spherical Bessel function of order l, y_l(x), for l >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_il_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_il_scaled (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_il_scaled (@dots{}) These routines compute the scaled regular modified spherical Bessel function of order l, \\exp(-|x|) i_l(x) @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_kl_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_kl_scaled (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_kl_scaled (@dots{}) These routines compute the scaled irregular modified spherical Bessel function of order l, \\exp(x) k_l(x), for x>0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn exprel_n -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} exprel_n (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} exprel_n (@dots{}) These routines compute the N-relative exponential, which is the n-th generalization of the functions gsl_sf_exprel and gsl_sf_exprel2. The N-relative exponential is given by, exprel_N(x) = N!/x^N (\\exp(x) - \\sum_@{k=0@}^@{N-1@} x^k/k!) = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ... = 1F1 (1,1+N,x) @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_int -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_int (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_int (@dots{}) These routines compute the complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/\\Gamma(j+1)) \\int_0^\\infty dt (t^j /(\\exp(t-x)+1)). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn taylorcoeff -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} taylorcoeff (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} taylorcoeff (@dots{}) These routines compute the Taylor coefficient x^n / n! for x >= 0, n >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn legendre_Pl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} legendre_Pl (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_Pl (@dots{}) These functions evaluate the Legendre polynomial P_l(x) for a specific value of l, x subject to l >= 0, |x| <= 1 @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn legendre_Ql -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} legendre_Ql (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_Ql (@dots{}) These routines compute the Legendre function Q_l(x) for x > -1, x != 1 and l >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn psi_n -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} psi_n (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi_n (@dots{}) These routines compute the polygamma function \\psi^@{(m)@}(x) for m >= 0, x > 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Jnu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Jnu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Jnu (@dots{}) These routines compute the regular cylindrical Bessel function of fractional order nu, J_\ u(x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Ynu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Ynu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Ynu (@dots{}) These routines compute the irregular cylindrical Bessel function of fractional order nu, Y_\ u(x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Inu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Inu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Inu (@dots{}) These routines compute the regular modified Bessel function of fractional order nu, I_\ u(x) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Inu_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Inu_scaled (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Inu_scaled (@dots{}) These routines compute the scaled regular modified Bessel function of fractional order nu, \\exp(-|x|)I_\ u(x) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Knu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Knu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Knu (@dots{}) These routines compute the irregular modified Bessel function of fractional order nu, K_\ u(x) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_lnKnu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_lnKnu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_lnKnu (@dots{}) These routines compute the logarithm of the irregular modified Bessel function of fractional order nu, \\ln(K_\ u(x)) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Knu_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Knu_scaled (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Knu_scaled (@dots{}) These routines compute the scaled irregular modified Bessel function of fractional order nu, \\exp(+|x|) K_\ u(x) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn exp_mult -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} exp_mult (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} exp_mult (@dots{}) These routines exponentiate x and multiply by the factor y to return the product y \\exp(x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_inc_0 -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} fermi_dirac_inc_0 (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} fermi_dirac_inc_0 (@dots{}) These routines compute the incomplete Fermi-Dirac integral with an index of zero, F_0(x,b) = \\ln(1 + e^@{b-x@}) - (b-x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn poch -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} poch (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} poch (@dots{}) These routines compute the Pochhammer symbol (a)_x := \\Gamma(a + x)/\\Gamma(a), subject to a and a+x not being negative integers. The Pochhammer symbol is also known as the Apell symbol. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lnpoch -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} lnpoch (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} lnpoch (@dots{}) These routines compute the logarithm of the Pochhammer symbol, \\log((a)_x) = \\log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn pochrel -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} pochrel (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} pochrel (@dots{}) These routines compute the relative Pochhammer symbol ((a,x) - 1)/x where (a,x) = (a)_x := \\Gamma(a + x)/\\Gamma(a). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gamma_inc_Q -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} gamma_inc_Q (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} gamma_inc_Q (@dots{}) These routines compute the normalized incomplete Gamma Function Q(a,x) = 1/\\Gamma(a) \\int_x\\infty dt t^@{a-1@} \\exp(-t) for a > 0, x >= 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gamma_inc_P -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} gamma_inc_P (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} gamma_inc_P (@dots{}) These routines compute the complementary normalized incomplete Gamma Function P(a,x) = 1/\\Gamma(a) \\int_0^x dt t^@{a-1@} \\exp(-t) for a > 0, x >= 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gamma_inc -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} gamma_inc (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} gamma_inc (@dots{}) These functions compute the incomplete Gamma Function the normalization factor included in the previously defined functions: \\Gamma(a,x) = \\int_x\\infty dt t^@{a-1@} \\exp(-t) for a real and x >= 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn beta_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} beta_gsl (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} beta_gsl (@dots{}) These routines compute the Beta Function, B(a,b) = \\Gamma(a)\\Gamma(b)/\\Gamma(a+b) for a > 0, b > 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lnbeta -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} lnbeta (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} lnbeta (@dots{}) These routines compute the logarithm of the Beta Function, \\log(B(a,b)) for a > 0, b > 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hyperg_0F1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} hyperg_0F1 (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} hyperg_0F1 (@dots{}) These routines compute the hypergeometric function 0F1(c,x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn conicalP_half -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} conicalP_half (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_half (@dots{}) These routines compute the irregular Spherical Conical Function P^@{1/2@}_@{-1/2 + i \\lambda@}(x) for x > -1. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn conicalP_mhalf -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} conicalP_mhalf (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_mhalf (@dots{}) These routines compute the regular Spherical Conical Function P^@{-1/2@}_@{-1/2 + i \\lambda@}(x) for x > -1. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn conicalP_0 -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} conicalP_0 (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_0 (@dots{}) These routines compute the conical function P^0_@{-1/2 + i \\lambda@}(x) for x > -1. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn conicalP_1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} conicalP_1 (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_1 (@dots{}) These routines compute the conical function P^1_@{-1/2 + i \\lambda@}(x) for x > -1. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hzeta -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} hzeta (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} hzeta (@dots{}) These routines compute the Hurwitz zeta function \\zeta(s,q) for s > 1, q > 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Ai -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Ai (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai (@dots{}) These routines compute the Airy function Ai(x) with an accuracy specified by mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Bi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Bi (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi (@dots{}) These routines compute the Airy function Bi(x) with an accuracy specified by mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Ai_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Ai_scaled (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai_scaled (@dots{}) These routines compute a scaled version of the Airy function S_A(x) Ai(x). For x>0 the scaling factor S_A(x) is \\exp(+(2/3) x^(3/2)), and is 1 for x<0. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Bi_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Bi_scaled (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi_scaled (@dots{}) These routines compute a scaled version of the Airy function S_B(x) Bi(x). For x>0 the scaling factor S_B(x) is exp(-(2/3) x^(3/2)), and is 1 for x<0. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Ai_deriv -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Ai_deriv (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai_deriv (@dots{}) These routines compute the Airy function derivative Ai'(x) with an accuracy specified by mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Bi_deriv -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Bi_deriv (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi_deriv (@dots{}) These routines compute the Airy function derivative Bi'(x) with an accuracy specified by mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Ai_deriv_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Ai_deriv_scaled (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai_deriv_scaled (@dots{}) These routines compute the derivative of the scaled Airy function S_A(x) Ai(x). The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Bi_deriv_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Bi_deriv_scaled (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi_deriv_scaled (@dots{}) These routines compute the derivative of the scaled Airy function S_B(x) Bi(x). The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn ellint_Kcomp -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} ellint_Kcomp (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} ellint_Kcomp (@dots{}) These routines compute the complete elliptic integral K(k) @tex \beforedisplay $$ \eqalign{ K(k) &= \int_0^{\pi/2} {dt \over \sqrt{(1 - k^2 \sin^2(t))}} \cr } $$ \afterdisplay See also: @end tex @ifinfo @group @example pi --- 2 / | 1 ellint_Kcomp(k) = | ------------------- dt | 2 2 / sqrt(1 - k sin (t)) 0 @end example @end group @end ifinfo @ifhtml @group @example pi --- 2 / | 1 ellint_Kcomp(k) = | ------------------- dt | 2 2 / sqrt(1 - k sin (t)) 0 @end example @end group @end ifhtml @seealso{ellipj, ellipke} The notation used here is based on Carlson, @cite{Numerische Mathematik} 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter @math{m = k^2}. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn ellint_Ecomp -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} ellint_Ecomp (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} ellint_Ecomp (@dots{}) These routines compute the complete elliptic integral E(k) to the accuracy specified by the mode variable mode. @tex \beforedisplay $$ \eqalign{ E(k) &= \int_0^{\pi/2} \sqrt{(1 - k^2 \sin^2(t))} dt \cr } $$ \afterdisplay See also: @end tex @ifinfo @group @example pi --- 2 / | 2 2 ellint_Ecomp(k) = | sqrt(1 - k sin (t)) dt | / 0 @end example @end group @end ifinfo @ifhtml @group @example pi --- 2 / | 2 2 ellint_Ecomp(k) = | sqrt(1 - k sin (t)) dt | / 0 @end example @end group @end ifhtml @seealso{ellipj, ellipke} The notation used here is based on Carlson, @cite{Numerische Mathematik} 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter @math{m = k^2}. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_zero_Ai -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_zero_Ai (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Ai (@dots{}) These routines compute the location of the s-th zero of the Airy function Ai(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_zero_Bi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_zero_Bi (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Bi (@dots{}) These routines compute the location of the s-th zero of the Airy function Bi(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_zero_Ai_deriv -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_zero_Ai_deriv (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Ai_deriv (@dots{}) These routines compute the location of the s-th zero of the Airy function derivative Ai(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_zero_Bi_deriv -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_zero_Bi_deriv (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Bi_deriv (@dots{}) These routines compute the location of the s-th zero of the Airy function derivative Bi(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_zero_J0 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_zero_J0 (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_zero_J0 (@dots{}) These routines compute the location of the s-th positive zero of the Bessel function J_0(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_zero_J1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_zero_J1 (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_zero_J1 (@dots{}) These routines compute the location of the s-th positive zero of the Bessel function J_1(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn psi_1_int -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} psi_1_int (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi_1_int (@dots{}) These routines compute the Trigamma function \\psi(n) for positive integer n. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn zeta_int -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} zeta_int (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} zeta_int (@dots{}) These routines compute the Riemann zeta function \\zeta(n) for integer n, n \ e 1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn eta_int -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} eta_int (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} eta_int (@dots{}) These routines compute the eta function \\eta(n) for integer n. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn legendre_Plm -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} legendre_Plm (@var{n}, @var{m}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_Plm (@dots{}) These routines compute the associated Legendre polynomial P_l^m(x) for m >= 0, l >= m, |x| <= 1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn legendre_sphPlm -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} legendre_sphPlm (@var{n}, @var{m}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_sphPlm (@dots{}) These routines compute the normalized associated Legendre polynomial $\\sqrt@{(2l+1)/(4\\pi)@} \\sqrt@{(l-m)!/(l+m)!@} P_l^m(x)$ suitable for use in spherical harmonics. The parameters must satisfy m >= 0, l >= m, |x| <= 1. Theses routines avoid the overflows that occur for the standard normalization of P_l^m(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hyperg_U -*- texinfo -*- @deftypefn {Loadable Function} {@var{out} =} hyperg_U (@var{x0}, @var{x1}, @var{x2}) @deftypefnx {Loadable Function} {[@var{out}, @var{err}] =} hyperg_U (@dots{}) Secondary Confluent Hypergoemetric U function A&E 13.1.3 All inputs are double as is the output. @var{err} contains an estimate of the absolute error in the value @var{out}.a. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hyperg_1F1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{out} =} hyperg_1F1 (@var{x0}, @var{x1}, @var{x2}) @deftypefnx {Loadable Function} {[@var{out}, @var{err}] =} hyperg_1F1 (@dots{}) Primary Confluent Hypergoemetric U function A&E 13.1.3 All inputs are double as is the output. @var{err} contains an estimate of the absolute error in the value @var{out}.a. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gsl_sf -*- texinfo -*- @deftypefn {Loadable Function} {} gsl_sf () Octave bindings to the GNU Scientific Library. All GSL functions can be called with by the GSL names within octave. @end deftypefn clausen -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} clausen (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} clausen (@dots{}) The Clausen function is defined by the following integral, Cl_2(x) = - \\int_0^x dt \\log(2 \\sin(t/2)) It is related to the dilogarithm by Cl_2(\\theta) = \\Im Li_2(\\exp(i \\theta)). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn dawson -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} dawson (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} dawson (@dots{}) The Dawson integral is defined by \\exp(-x^2) \\int_0^x dt \\exp(t^2). A table of Dawson integral can be found in Abramowitz & Stegun, Table 7.5. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn debye_1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} debye_1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_1 (@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn debye_2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} debye_2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_2 (@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn debye_3 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} debye_3 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_3 (@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn debye_4 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} debye_4 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_4 (@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn erf_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} erf_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erf_gsl (@dots{}) These routines compute the error function erf(x) = (2/\\sqrt(\\pi)) \\int_0^x dt \\exp(-t^2). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn erfc_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} erfc_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erfc_gsl (@dots{}) These routines compute the complementary error function erfc(x) = 1 - erf(x) = (2/\\sqrt(\\pi)) \\int_x^\\infty \\exp(-t^2). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn log_erfc -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} log_erfc (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} log_erfc (@dots{}) These routines compute the logarithm of the complementary error function \\log(\\erfc(x)). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn erf_Z -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} erf_Z (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erf_Z (@dots{}) These routines compute the Gaussian probability function Z(x) = (1/(2\\pi)) \\exp(-x^2/2). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn erf_Q -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} erf_Q (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erf_Q (@dots{}) These routines compute the upper tail of the Gaussian probability function Q(x) = (1/(2\\pi)) \\int_x^\\infty dt \\exp(-t^2/2). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hazard -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} hazard (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} hazard (@dots{}) The hazard function for the normal distrbution, also known as the inverse Mill\\'s ratio, is defined as h(x) = Z(x)/Q(x) = \\sqrt@{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2)@}. It decreases rapidly as x approaches -\\infty and asymptotes to h(x) \\sim x as x approaches +\\infty. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn expm1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} expm1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expm1 (@dots{}) These routines compute the quantity \\exp(x)-1 using an algorithm that is accurate for small x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn exprel -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} exprel (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} exprel (@dots{}) These routines compute the quantity (\\exp(x)-1)/x using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion (\\exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\dots. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn exprel_2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} exprel_2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} exprel_2 (@dots{}) These routines compute the quantity 2(\\exp(x)-1-x)/x^2 using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion 2(\\exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\dots. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn expint_E1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} expint_E1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_E1 (@dots{}) These routines compute the exponential integral E_1(x), E_1(x) := Re \\int_1^\\infty dt \\exp(-xt)/t. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn expint_E2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} expint_E2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_E2 (@dots{}) These routines compute the second-order exponential integral E_2(x), E_2(x) := \\Re \\int_1^\\infty dt \\exp(-xt)/t^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn expint_Ei -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} expint_Ei (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_Ei (@dots{}) These routines compute the exponential integral E_i(x), Ei(x) := - PV(\\int_@{-x@}^\\infty dt \\exp(-t)/t) where PV denotes the principal value of the integral. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn Shi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} Shi (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Shi (@dots{}) These routines compute the integral Shi(x) = \\int_0^x dt \\sinh(t)/t. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn Chi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} Chi (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Chi (@dots{}) These routines compute the integral Chi(x) := Re[ \\gamma_E + \\log(x) + \\int_0^x dt (\\cosh[t]-1)/t] , where \\gamma_E is the Euler constant. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn expint_3 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} expint_3 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_3 (@dots{}) These routines compute the exponential integral Ei_3(x) = \\int_0^x dt \\exp(-t^3) for x >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn Si -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} Si (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Si (@dots{}) These routines compute the Sine integral Si(x) = \\int_0^x dt \\sin(t)/t. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn Ci -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} Ci (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Ci (@dots{}) These routines compute the Cosine integral Ci(x) = -\\int_x^\\infty dt \\cos(t)/t for x > 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn atanint -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} atanint (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} atanint (@dots{}) These routines compute the Arctangent integral AtanInt(x) = \\int_0^x dt \\arctan(t)/t. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_mhalf -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_mhalf (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_mhalf (@dots{}) These routines compute the complete Fermi-Dirac integral F_@{-1/2@}(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_half -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_half (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_half (@dots{}) These routines compute the complete Fermi-Dirac integral F_@{1/2@}(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_3half -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_3half (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_3half (@dots{}) These routines compute the complete Fermi-Dirac integral F_@{3/2@}(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gamma_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} gamma_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} gamma_gsl (@dots{}) These routines compute the Gamma function \\Gamma(x), subject to x not being a negative integer. The function is computed using the real Lanczos method. The maximum value of x such that \\Gamma(x) is not considered an overflow is given by the macro GSL_SF_GAMMA_XMAX and is 171.0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lngamma_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lngamma_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lngamma_gsl (@dots{}) These routines compute the logarithm of the Gamma function, \\log(\\Gamma(x)), subject to x not a being negative integer. For x<0 the real part of \\log(\\Gamma(x)) is returned, which is equivalent to \\log(|\\Gamma(x)|). The function is computed using the real Lanczos method. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gammastar -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} gammastar (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} gammastar (@dots{}) These routines compute the regulated Gamma Function \\Gamma^*(x) for x > 0. The regulated gamma function is given by, \\Gamma^*(x) = \\Gamma(x)/(\\sqrt@{2\\pi@} x^@{(x-1/2)@} \\exp(-x)) = (1 + (1/12x) + ...) for x \\to \\infty and is a useful suggestion of Temme. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gammainv_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} gammainv_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} gammainv_gsl (@dots{}) These routines compute the reciprocal of the gamma function, 1/\\Gamma(x) using the real Lanczos method. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lambert_W0 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lambert_W0 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lambert_W0 (@dots{}) These compute the principal branch of the Lambert W function, W_0(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@{-1@}(x) to be the other real branch, where W < -1 for x < 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lambert_Wm1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lambert_Wm1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lambert_Wm1 (@dots{}) These compute the secondary real-valued branch of the Lambert W function, W_@{-1@}(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@{-1@}(x) to be the other real branch, where W < -1 for x < 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn log_1plusx -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} log_1plusx (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} log_1plusx (@dots{}) These routines compute \\log(1 + x) for x > -1 using an algorithm that is accurate for small x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn log_1plusx_mx -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} log_1plusx_mx (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} log_1plusx_mx (@dots{}) These routines compute \\log(1 + x) - x for x > -1 using an algorithm that is accurate for small x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn psi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} psi (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi (@dots{}) These routines compute the digamma function \\psi(x) for general x, x \ e 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn psi_1piy -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} psi_1piy (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi_1piy (@dots{}) These routines compute the real part of the digamma function on the line 1+i y, Re[\\psi(1 + i y)]. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn synchrotron_1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} synchrotron_1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} synchrotron_1 (@dots{}) These routines compute the first synchrotron function x \\int_x^\\infty dt K_@{5/3@}(t) for x >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn synchrotron_2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} synchrotron_2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} synchrotron_2 (@dots{}) These routines compute the second synchrotron function x K_@{2/3@}(x) for x >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn transport_2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} transport_2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_2 (@dots{}) These routines compute the transport function J(2,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn transport_3 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} transport_3 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_3 (@dots{}) These routines compute the transport function J(3,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn transport_4 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} transport_4 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_4 (@dots{}) These routines compute the transport function J(4,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn transport_5 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} transport_5 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_5 (@dots{}) These routines compute the transport function J(5,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn sinc_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} sinc_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} sinc_gsl (@dots{}) These routines compute \\sinc(x) = \\sin(\\pi x) / (\\pi x) for any value of x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lnsinh -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lnsinh (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lnsinh (@dots{}) These routines compute \\log(\\sinh(x)) for x > 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lncosh -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lncosh (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lncosh (@dots{}) These routines compute \\log(\\cosh(x)) for any x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn zeta -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} zeta (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} zeta (@dots{}) These routines compute the Riemann zeta function \\zeta(s) for arbitrary s, s \ e 1. The Riemann zeta function is defined by the infinite sum \\zeta(s) = \\sum_@{k=1@}^\\infty k^@{-s@}. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn eta -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} eta (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} eta (@dots{}) These routines compute the eta function \\eta(s) for arbitrary s. The eta function is defined by \\eta(s) = (1-2^@{1-s@}) \\zeta(s). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Jn -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_Jn (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Jn (@dots{}) These routines compute the regular cylindrical Bessel function of order n, J_n(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Yn -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_Yn (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Yn (@dots{}) These routines compute the irregular cylindrical Bessel function of order n, Y_n(x), for x>0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_In -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_In (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_In (@dots{}) These routines compute the regular modified cylindrical Bessel function of order n, I_n(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_In_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_In_scaled (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_In_scaled (@dots{}) These routines compute the scaled regular modified cylindrical Bessel function of order n, \\exp(-|x|) I_n(x) @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Kn -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_Kn (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Kn (@dots{}) These routines compute the irregular modified cylindrical Bessel function of order n, K_n(x), for x > 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Kn_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_Kn_scaled (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Kn_scaled (@dots{}) @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_jl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_jl (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_jl (@dots{}) These routines compute the regular spherical Bessel function of order l, j_l(x), for l >= 0 and x >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_yl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_yl (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_yl (@dots{}) These routines compute the irregular spherical Bessel function of order l, y_l(x), for l >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_il_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_il_scaled (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_il_scaled (@dots{}) These routines compute the scaled regular modified spherical Bessel function of order l, \\exp(-|x|) i_l(x) @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_kl_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_kl_scaled (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_kl_scaled (@dots{}) These routines compute the scaled irregular modified spherical Bessel function of order l, \\exp(x) k_l(x), for x>0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn exprel_n -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} exprel_n (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} exprel_n (@dots{}) These routines compute the N-relative exponential, which is the n-th generalization of the functions gsl_sf_exprel and gsl_sf_exprel2. The N-relative exponential is given by, exprel_N(x) = N!/x^N (\\exp(x) - \\sum_@{k=0@}^@{N-1@} x^k/k!) = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ... = 1F1 (1,1+N,x) @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_int -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_int (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_int (@dots{}) These routines compute the complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/\\Gamma(j+1)) \\int_0^\\infty dt (t^j /(\\exp(t-x)+1)). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn taylorcoeff -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} taylorcoeff (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} taylorcoeff (@dots{}) These routines compute the Taylor coefficient x^n / n! for x >= 0, n >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn legendre_Pl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} legendre_Pl (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_Pl (@dots{}) These functions evaluate the Legendre polynomial P_l(x) for a specific value of l, x subject to l >= 0, |x| <= 1 @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn legendre_Ql -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} legendre_Ql (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_Ql (@dots{}) These routines compute the Legendre function Q_l(x) for x > -1, x != 1 and l >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn psi_n -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} psi_n (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi_n (@dots{}) These routines compute the polygamma function \\psi^@{(m)@}(x) for m >= 0, x > 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Jnu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Jnu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Jnu (@dots{}) These routines compute the regular cylindrical Bessel function of fractional order nu, J_\ u(x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Ynu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Ynu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Ynu (@dots{}) These routines compute the irregular cylindrical Bessel function of fractional order nu, Y_\ u(x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Inu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Inu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Inu (@dots{}) These routines compute the regular modified Bessel function of fractional order nu, I_\ u(x) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Inu_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Inu_scaled (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Inu_scaled (@dots{}) These routines compute the scaled regular modified Bessel function of fractional order nu, \\exp(-|x|)I_\ u(x) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Knu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Knu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Knu (@dots{}) These routines compute the irregular modified Bessel function of fractional order nu, K_\ u(x) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_lnKnu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_lnKnu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_lnKnu (@dots{}) These routines compute the logarithm of the irregular modified Bessel function of fractional order nu, \\ln(K_\ u(x)) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Knu_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Knu_scaled (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Knu_scaled (@dots{}) These routines compute the scaled irregular modified Bessel function of fractional order nu, \\exp(+|x|) K_\ u(x) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn exp_mult -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} exp_mult (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} exp_mult (@dots{}) These routines exponentiate x and multiply by the factor y to return the product y \\exp(x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_inc_0 -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} fermi_dirac_inc_0 (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} fermi_dirac_inc_0 (@dots{}) These routines compute the incomplete Fermi-Dirac integral with an index of zero, F_0(x,b) = \\ln(1 + e^@{b-x@}) - (b-x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn poch -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} poch (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} poch (@dots{}) These routines compute the Pochhammer symbol (a)_x := \\Gamma(a + x)/\\Gamma(a), subject to a and a+x not being negative integers. The Pochhammer symbol is also known as the Apell symbol. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lnpoch -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} lnpoch (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} lnpoch (@dots{}) These routines compute the logarithm of the Pochhammer symbol, \\log((a)_x) = \\log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn pochrel -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} pochrel (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} pochrel (@dots{}) These routines compute the relative Pochhammer symbol ((a,x) - 1)/x where (a,x) = (a)_x := \\Gamma(a + x)/\\Gamma(a). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gamma_inc_Q -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} gamma_inc_Q (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} gamma_inc_Q (@dots{}) These routines compute the normalized incomplete Gamma Function Q(a,x) = 1/\\Gamma(a) \\int_x\\infty dt t^@{a-1@} \\exp(-t) for a > 0, x >= 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gamma_inc_P -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} gamma_inc_P (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} gamma_inc_P (@dots{}) These routines compute the complementary normalized incomplete Gamma Function P(a,x) = 1/\\Gamma(a) \\int_0^x dt t^@{a-1@} \\exp(-t) for a > 0, x >= 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gamma_inc -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} gamma_inc (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} gamma_inc (@dots{}) These functions compute the incomplete Gamma Function the normalization factor included in the previously defined functions: \\Gamma(a,x) = \\int_x\\infty dt t^@{a-1@} \\exp(-t) for a real and x >= 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn beta_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} beta_gsl (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} beta_gsl (@dots{}) These routines compute the Beta Function, B(a,b) = \\Gamma(a)\\Gamma(b)/\\Gamma(a+b) for a > 0, b > 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lnbeta -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} lnbeta (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} lnbeta (@dots{}) These routines compute the logarithm of the Beta Function, \\log(B(a,b)) for a > 0, b > 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hyperg_0F1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} hyperg_0F1 (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} hyperg_0F1 (@dots{}) These routines compute the hypergeometric function 0F1(c,x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn conicalP_half -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} conicalP_half (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_half (@dots{}) These routines compute the irregular Spherical Conical Function P^@{1/2@}_@{-1/2 + i \\lambda@}(x) for x > -1. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn conicalP_mhalf -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} conicalP_mhalf (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_mhalf (@dots{}) These routines compute the regular Spherical Conical Function P^@{-1/2@}_@{-1/2 + i \\lambda@}(x) for x > -1. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn conicalP_0 -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} conicalP_0 (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_0 (@dots{}) These routines compute the conical function P^0_@{-1/2 + i \\lambda@}(x) for x > -1. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn conicalP_1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} conicalP_1 (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_1 (@dots{}) These routines compute the conical function P^1_@{-1/2 + i \\lambda@}(x) for x > -1. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hzeta -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} hzeta (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} hzeta (@dots{}) These routines compute the Hurwitz zeta function \\zeta(s,q) for s > 1, q > 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Ai -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Ai (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai (@dots{}) These routines compute the Airy function Ai(x) with an accuracy specified by mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Bi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Bi (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi (@dots{}) These routines compute the Airy function Bi(x) with an accuracy specified by mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Ai_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Ai_scaled (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai_scaled (@dots{}) These routines compute a scaled version of the Airy function S_A(x) Ai(x). For x>0 the scaling factor S_A(x) is \\exp(+(2/3) x^(3/2)), and is 1 for x<0. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Bi_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Bi_scaled (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi_scaled (@dots{}) These routines compute a scaled version of the Airy function S_B(x) Bi(x). For x>0 the scaling factor S_B(x) is exp(-(2/3) x^(3/2)), and is 1 for x<0. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Ai_deriv -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Ai_deriv (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai_deriv (@dots{}) These routines compute the Airy function derivative Ai'(x) with an accuracy specified by mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Bi_deriv -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Bi_deriv (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi_deriv (@dots{}) These routines compute the Airy function derivative Bi'(x) with an accuracy specified by mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Ai_deriv_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Ai_deriv_scaled (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai_deriv_scaled (@dots{}) These routines compute the derivative of the scaled Airy function S_A(x) Ai(x). The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Bi_deriv_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Bi_deriv_scaled (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi_deriv_scaled (@dots{}) These routines compute the derivative of the scaled Airy function S_B(x) Bi(x). The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn ellint_Kcomp -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} ellint_Kcomp (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} ellint_Kcomp (@dots{}) These routines compute the complete elliptic integral K(k) @tex \beforedisplay $$ \eqalign{ K(k) &= \int_0^{\pi/2} {dt \over \sqrt{(1 - k^2 \sin^2(t))}} \cr } $$ \afterdisplay @end tex The notation used here is based on Carlson, @cite{Numerische Mathematik} 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter @math{m = k^2}. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn ellint_Ecomp -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} ellint_Ecomp (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} ellint_Ecomp (@dots{}) These routines compute the complete elliptic integral E(k) to the accuracy specified by the mode variable mode. @tex \beforedisplay $$ \eqalign{ E(k) &= \int_0^{\pi/2} \sqrt{(1 - k^2 \sin^2(t))} dt \cr } $$ \afterdisplay @end tex The notation used here is based on Carlson, @cite{Numerische Mathematik} 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter @math{m = k^2}. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_zero_Ai -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_zero_Ai (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Ai (@dots{}) These routines compute the location of the s-th zero of the Airy function Ai(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_zero_Bi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_zero_Bi (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Bi (@dots{}) These routines compute the location of the s-th zero of the Airy function Bi(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_zero_Ai_deriv -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_zero_Ai_deriv (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Ai_deriv (@dots{}) These routines compute the location of the s-th zero of the Airy function derivative Ai(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_zero_Bi_deriv -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_zero_Bi_deriv (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Bi_deriv (@dots{}) These routines compute the location of the s-th zero of the Airy function derivative Bi(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_zero_J0 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_zero_J0 (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_zero_J0 (@dots{}) These routines compute the location of the s-th positive zero of the Bessel function J_0(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_zero_J1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_zero_J1 (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_zero_J1 (@dots{}) These routines compute the location of the s-th positive zero of the Bessel function J_1(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn psi_1_int -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} psi_1_int (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi_1_int (@dots{}) These routines compute the Trigamma function \\psi(n) for positive integer n. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn zeta_int -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} zeta_int (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} zeta_int (@dots{}) These routines compute the Riemann zeta function \\zeta(n) for integer n, n \ e 1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn eta_int -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} eta_int (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} eta_int (@dots{}) These routines compute the eta function \\eta(n) for integer n. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn legendre_Plm -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} legendre_Plm (@var{n}, @var{m}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_Plm (@dots{}) These routines compute the associated Legendre polynomial P_l^m(x) for m >= 0, l >= m, |x| <= 1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn legendre_sphPlm -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} legendre_sphPlm (@var{n}, @var{m}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_sphPlm (@dots{}) These routines compute the normalized associated Legendre polynomial $\\sqrt@{(2l+1)/(4\\pi)@} \\sqrt@{(l-m)!/(l+m)!@} P_l^m(x)$ suitable for use in spherical harmonics. The parameters must satisfy m >= 0, l >= m, |x| <= 1. Theses routines avoid the overflows that occur for the standard normalization of P_l^m(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hyperg_U -*- texinfo -*- @deftypefn {Loadable Function} {@var{out} =} hyperg_U (@var{x0}, @var{x1}, @var{x2}) @deftypefnx {Loadable Function} {[@var{out}, @var{err}] =} hyperg_U (@dots{}) Secondary Confluent Hypergoemetric U function A&E 13.1.3 All input are double as is the output. @var{err} contains an estimate of the absolute error in the value @var{out}.a. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hyperg_1F1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{out} =} hyperg_1F1 (@var{x0}, @var{x1}, @var{x2}) @deftypefnx {Loadable Function} {[@var{out}, @var{err}] =} hyperg_1F1 (@dots{}) Primary Confluent Hypergoemetric U function A&E 13.1.3 All inputs are double as is the output. @var{err} contains an estimate of the absolute error in the value @var{out}.a. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn @byegsl-1.0.8/doc/mktexi_inc0000755000175000017500000003045511201030403012727 0ustar shsh#!/usr/bin/env perl # # David Bateman Feb 02 2003 # # Extracts the help in texinfo format for particular function for use # in documentation. Based on make_index script from octave_forge. use strict; use File::Find; use File::Basename; use Text::Wrap; use FileHandle; use IPC::Open3; use POSIX ":sys_wait_h"; my $file = shift @ARGV; my $docfile = shift @ARGV; my $indexfile = shift @ARGV; my $line; print("\\input texinfo \n"); print("\@ifnottex \n"); print("\@node Top \n"); print("\@top Octave gsl \n"); print("\@end ifnottex \n"); if ( open(IN,$file) ) { $line = ; my $tex = 0; while ($line) { if ($line =~ /^\@DOCSTRING/) { my $found = 0; my $func = $line; $func =~ s/\@DOCSTRING\(//; $func =~ s/\)[\n\r]+//; my $func0 = $func; my $func1 = $func; $func0 =~ s/,.*$//; $func1 =~ s/^.*,//; if ( open(DOC,$docfile) ) { while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func0$/) { my $desc = ""; my $docline; my $doctex = 0; while (($docline = ) && ($docline !~ /^\037/)) { $docline =~ s/^\s*-[*]- texinfo -[*]-\s*//; if ($docline =~ /\@tex/) { $doctex = 1; } if ($doctex) { $docline =~ s/\\\\/\\/g; } if ($docline =~ /\@end tex/) { $doctex = 0; } $desc .= $docline; } $desc =~ s/$func0/$func1/g; $desc =~ s/\@seealso\{(.*[^}])\}/See also: \1/g; print "$desc", "\n"; $found = 1; last; } } close (DOC); if (! $found) { print "\@emph{Not implemented}\n"; } } else { print STDERR "Could not open file $docfile\n"; exit 1; } } elsif ($line =~ /^\@REFERENCE_SECTION/) { my $secfound = 0; my $sec = $line; $sec =~ s/\@REFERENCE_SECTION\(//; $sec =~ s/\)[\n\r]+//; my @listfunc = (); my $nfunc = 0; my $seccat = 0; if ( open(IND,$indexfile) ) { while () { next unless /^[^ ]/; my $section = $_; $section =~ s/[\n\r]+//; if ($section =~ /^(.*?)\s*>>\s*(.*?)$/) { $section =~ s/.*>>(.*)/\1/; $seccat = 1; } $section =~ s/^ *//; $section =~ s/ *$//; if ($section =~ /^$sec$/) { if ($seccat) { print "\@iftex\n"; print "\@section Functions by Category\n"; # Get the list of categories to index my $firstcat = 1; my $category; while () { last if />>/; if (/^[^ ]/) { if (! $firstcat) { print "\@end table\n"; } else { $firstcat = 0; } $category = $_; $category =~ s/[\n\r]+//; print "\@subsection $category\n"; print "\@table \@asis\n"; } elsif (/^\s+(\S.*\S)\s*=\s*(\S.*\S)\s*$/) { my $func = $1; my $desc = $2; print "\@item $func\n"; print "$desc\n"; print "\n"; } else { if ($firstcat) { print STDERR "Error parsing index file\n"; exit 1; } s/^\s+//; my @funcs = split /\s+/; while ($#funcs >= 0) { my $func = shift @funcs; $func =~ s/^ *//; $func =~ s/[\n\r]+//; push @listfunc, $func; $nfunc = $nfunc + 1; print "\@item $func\n"; print func_summary($func, $docfile); print "\n"; } } } if (! $firstcat) { print "\@end table\n"; } print "\n\@section Functions Alphabetically\n"; print "\@end iftex\n\n"; } else { # Get the list of functions to index my $indline; while (($indline = ) && ($indline =~ /^ /)) { if ($indline =~ /^\s+(\S.*\S)\s*=\s*(\S.*\S)\s*$/) { next; } $indline =~ s/^\s+//; my @funcs = split(/\s+/,$indline); while ($#funcs >= 0) { my $func = shift @funcs; $func =~ s/^ *//; $func =~ s/[\n\r]+//; push @listfunc, $func; $nfunc = $nfunc + 1; } } } $secfound = 1; last; } } close (IND); if (! $secfound) { print STDERR "Did not find section $sec\n"; } } else { print STDERR "Could not open file $indexfile\n"; exit 1; } @listfunc = sort(@listfunc); my @listfunc2 = (); my $indent = 16 - 3; print "\@menu\n"; foreach my $func (@listfunc) { if ( open(DOC,$docfile) ) { my $found = 0; while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func$/) { $found = 1; last; } } close (DOC); if ($found) { push @listfunc2, $func; my $func0 = "${func}::"; my $entry = sprintf("* %-*s %s",$indent,$func0,func_summary($func,$docfile)); print wrap("","\t\t","$entry"), "\n"; } } else { print STDERR "Could not open file $indexfile\n"; exit 1; } } print "\@end menu\n"; my $up = "Function Reference"; my $next; my $prev; my $mfunc = 1; foreach my $func (@listfunc2) { if ($mfunc == $nfunc) { $next = ""; } else { $next = @listfunc2[$mfunc]; $mfunc = $mfunc + 1; } print "\n\@node $func, $next, $prev, $up\n"; if ($seccat) { print "\@subsection $func\n\n"; } else { print "\@section $func\n\n"; } $prev = $func; my $found = 0; my $desc = ""; if ( open(DOC,$docfile) ) { while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func$/) { my $docline; my $doctex = 0; while (($docline = ) && ($docline !~ /^\037/)) { $docline =~ s/^\s*-[*]- texinfo -[*]-\s*//; if ($docline =~ /\@tex/) { $doctex = 1; } if ($doctex) { $docline =~ s/\\\\/\\/g; } if ($docline =~ /\@end tex/) { $doctex = 0; } $desc .= $docline; } $desc =~ s/\@seealso\{(.*[^}])\}/See also: \1/g; print "$desc", "\n"; $found = 1; last; } } close (DOC); if (! $found) { print "\@emph{Not implemented}\n"; } } else { print STDERR "Could not open file $docfile\n"; exit 1; } } } else { if ($line =~ /\@tex/) { $tex = 1; } if ($tex) { $line =~ s/\\\\/\\/g; } print "$line"; if ($line =~ /\@end tex/) { $tex = 0; } } $line = ; } } else { print STDERR "Could not open file $file\n"; exit 1; }; print("\@bye"); sub func_summary { # {{{1 my ($func, # in function name $docfile # in DOCSTRINGS ) = @_; my $desc = ""; my $found = 0; if ( open(DOC,$docfile) ) { while () { next unless /\037/; my $function = $_; $function =~ s/\037//; $function =~ s/[\n\r]+//; if ($function =~ /^$func$/) { my $docline; my $doctex = 0; while (($docline = ) && ($docline !~ /^\037/)) { if ($docline =~ /\@tex/) { $doctex = 1; } if ($doctex) { $docline =~ s/\\\\/\\/g; } if ($docline =~ /\@end tex/) { $doctex = 0; } $desc .= $docline; } $desc =~ s/\@seealso\{(.*[^}])\}/See also: \1/g; $found = 1; last; } } close (DOC); if (! $found) { $desc = "\@emph{Not implemented}"; } } else { print STDERR "Could not open file $docfile\n"; exit 1; } return first_sentence($desc); } # 1}}} sub first_sentence { # {{{1 # grab the first real sentence from the function documentation my ($desc) = @_; my $retval = ''; my $line; my $next; my @lines; my $trace = 0; # $trace = 1 if $desc =~ /Levenberg/; return "" unless defined $desc; if ($desc =~ /^\s*-[*]- texinfo -[*]-/) { # help text contains texinfo. Strip the indicator and run it # through makeinfo. (XXX FIXME XXX this needs to be a function) $desc =~ s/^\s*-[*]- texinfo -[*]-\s*//; my $cmd = "makeinfo --fill-column 1600 --no-warn --no-validate --no-headers --force --ifinfo"; open3(*Writer, *Reader, *Errer, $cmd) or die "Could not run info"; print Writer "\@macro seealso {args}\n\n\@noindent\nSee also: \\args\\.\n\@end macro\n"; print Writer "$desc"; close(Writer); @lines = ; close(Reader); my @err = ; close(Errer); waitpid(-1,&WNOHANG); # Display source and errors, if any if (@err) { my $n = 1; foreach $line ( split(/\n/,$desc) ) { printf "%2d: %s\n",$n++,$line; } print ">>> @err"; } # Print trace showing formatted output # print "\n"; # Skip prototype and blank lines while (1) { return "" unless @lines; $line = shift @lines; next if $line =~ /^\s*-/; next if $line =~ /^\s*$/; last; } } else { # print "\n"; # Skip prototype and blank lines @lines = split(/\n/,$desc); while (1) { return "" if ($#lines < 0); $line = shift @lines; next if $line =~ /^\s*[Uu][Ss][Aa][Gg][Ee]/; # skip " usage " $line =~ s/^\s*\w+\s*://; # chop " blah : " print "strip blah: $line\n" if $trace; $line =~ s/^\s*[Ff]unction\s+//; # chop " function " print "strip function $line\n" if $trace; $line =~ s/^\s*\[.*\]\s*=\s*//; # chop " [a,b] = " print "strip []= $line\n" if $trace; $line =~ s/^\s*\w+\s*=\s*//; # chop " a = " print "strip a= $line\n" if $trace; $line =~ s/^\s*\w+\s*\([^\)]*\)\s*//; # chop " f(x) " print "strip f(x) $line\n" if $trace; $line =~ s/^\s*[;:]\s*//; # chop " ; " print "strip ; $line\n" if $trace; $line =~ s/^\s*[[:upper:]][[:upper:]0-9_]+//; # chop " BLAH" print "strip BLAH $line\n" if $trace; $line =~ s/^\s*\w*\s*[-]+\s+//; # chop " blah --- " print "strip blah --- $line\n" if $trace; $line =~ s/^\s*\w+ *\t\s*//; # chop " blah " print "strip blah $line\n" if $trace; $line =~ s/^\s*\w+\s\s+//; # chop " blah " print "strip blah $line\n" if $trace; # next if $line =~ /^\s*\[/; # skip [a,b] = f(x) # next if $line =~ /^\s*\w+\s*(=|\()/; # skip a = f(x) OR f(x) next if $line =~ /^\s*or\s*$/; # skip blah \n or \n blah next if $line =~ /^\s*$/; # skip blank line next if $line =~ /^\s?!\//; # skip # !/usr/bin/octave # XXX FIXME XXX should be testing for unmatched () in proto # before going to the next line! last; } } # Try to make a complete sentence, including the '.' if ( "$line " !~ /[^.][.]\s/ && $#lines >= 0) { my $next = $lines[0]; $line =~ s/\s*$//; # trim trailing blanks on last $next =~ s/^\s*//; # trim leading blanks on next $line .= " $next" if "$next " =~ /[^.][.]\s/; # ends the sentence } # Tidy up the sentence. chomp $line; # trim trailing newline, if there is one $line =~ s/^\s*//; # trim leading blanks on line $line =~ s/([^.][.])\s.*$/$1/; # trim everything after the sentence print "Skipping:\n$desc---\n" if $line eq ""; # And return it. return $line; } # 1}}} __END__ This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, see . This program is granted to the public domain. THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. gsl-1.0.8/doc/gsl_sf.cc0000644000175000017500000076072011201030403012440 0ustar shsh// *** DO NOT EDIT *** this file is generated by buildgsl_sf.sh /* Copyright (C) 2004 Teemu Ikonen This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, see . */ #include #include #include #include void octave_gsl_errorhandler (const char * reason, const char * file, int line, int gsl_errno) { error("GSL error %d at %s, line %d: %s\n", gsl_errno, file, line, reason); } DEFUN_DLD (gsl_sf, args, nargout, "-*- texinfo -*-\n\ @deftypefn {Loadable Function} {} gsl_sf ()\n\ \n\ Octave bindings to the GNU Scientific Library. All GSL functions can be\n\ called with by the GSL names within octave.\n\ @end deftypefn") { usage("gsl_sf"); return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(clausen, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} clausen (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} clausen (@dots{})\n\ \n\ The Clausen function is defined by the following integral,\n\ \n\ Cl_2(x) = - \\int_0^x dt \\log(2 \\sin(t/2))\n\ \n\ It is related to the dilogarithm by Cl_2(\\theta) = \\Im Li_2(\\exp(i \\theta)).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_clausen (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_clausen_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(dawson, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} dawson (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} dawson (@dots{})\n\ \n\ The Dawson integral is defined by \\exp(-x^2) \\int_0^x dt \\exp(t^2).\n\ A table of Dawson integral can be found in Abramowitz & Stegun, Table 7.5. \n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_dawson (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_dawson_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(debye_1, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} debye_1 (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_1 (@dots{})\n\ \n\ The Debye functions are defined by the integral \n\ \n\ D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)).\n\ \n\ For further information see Abramowitz & Stegun, Section 27.1.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_debye_1 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_debye_1_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(debye_2, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} debye_2 (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_2 (@dots{})\n\ \n\ The Debye functions are defined by the integral\n\ \n\ D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)).\n\ \n\ For further information see Abramowitz & Stegun, Section 27.1.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_debye_2 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_debye_2_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(debye_3, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} debye_3 (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_3 (@dots{})\n\ \n\ The Debye functions are defined by the integral\n\ \n\ D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)).\n\ \n\ For further information see Abramowitz & Stegun, Section 27.1.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_debye_3 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_debye_3_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(debye_4, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} debye_4 (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_4 (@dots{})\n\ \n\ The Debye functions are defined by the integral\n\ \n\ D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)).\n\ \n\ For further information see Abramowitz & Stegun, Section 27.1.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_debye_4 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_debye_4_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(erf_gsl, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} erf_gsl (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erf_gsl (@dots{})\n\ \n\ These routines compute the error function \n\ erf(x) = (2/\\sqrt(\\pi)) \\int_0^x dt \\exp(-t^2).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_erf (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_erf_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(erfc_gsl, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} erfc_gsl (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erfc_gsl (@dots{})\n\ \n\ These routines compute the complementary error function \n\ erfc(x) = 1 - erf(x) = (2/\\sqrt(\\pi)) \\int_x^\\infty \\exp(-t^2).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_erfc (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_erfc_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(log_erfc, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} log_erfc (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} log_erfc (@dots{})\n\ \n\ These routines compute the logarithm of the complementary error\n\ function \\log(\\erfc(x)).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_log_erfc (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_log_erfc_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(erf_Z, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} erf_Z (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erf_Z (@dots{})\n\ \n\ These routines compute the Gaussian probability function \n\ Z(x) = (1/(2\\pi)) \\exp(-x^2/2).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_erf_Z (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_erf_Z_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(erf_Q, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} erf_Q (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erf_Q (@dots{})\n\ \n\ These routines compute the upper tail of the Gaussian probability\n\ function Q(x) = (1/(2\\pi)) \\int_x^\\infty dt \\exp(-t^2/2).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_erf_Q (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_erf_Q_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(hazard, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} hazard (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} hazard (@dots{})\n\ \n\ The hazard function for the normal distrbution, also known as the \n\ inverse Mill\\'s ratio, is defined as \n\ h(x) = Z(x)/Q(x) = \\sqrt@{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2)@}. \n\ It decreases rapidly as x approaches -\\infty and asymptotes to \n\ h(x) \\sim x as x approaches +\\infty.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_hazard (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_hazard_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(expm1, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} expm1 (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expm1 (@dots{})\n\ \n\ These routines compute the quantity \\exp(x)-1 using an algorithm that \n\ is accurate for small x.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_expm1 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_expm1_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(exprel, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} exprel (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} exprel (@dots{})\n\ \n\ These routines compute the quantity (\\exp(x)-1)/x using an algorithm \n\ that is accurate for small x. For small x the algorithm is based on \n\ the expansion (\\exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\dots.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_exprel (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_exprel_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(exprel_2, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} exprel_2 (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} exprel_2 (@dots{})\n\ \n\ These routines compute the quantity 2(\\exp(x)-1-x)/x^2 using an\n\ algorithm that is accurate for small x. For small x the algorithm is \n\ based on the expansion \n\ 2(\\exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\dots.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_exprel_2 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_exprel_2_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(expint_E1, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} expint_E1 (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_E1 (@dots{})\n\ \n\ These routines compute the exponential integral E_1(x),\n\ \n\ E_1(x) := Re \\int_1^\\infty dt \\exp(-xt)/t.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_expint_E1 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_expint_E1_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(expint_E2, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} expint_E2 (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_E2 (@dots{})\n\ \n\ These routines compute the second-order exponential integral E_2(x),\n\ \n\ E_2(x) := \\Re \\int_1^\\infty dt \\exp(-xt)/t^2.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_expint_E2 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_expint_E2_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(expint_Ei, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} expint_Ei (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_Ei (@dots{})\n\ \n\ These routines compute the exponential integral E_i(x),\n\ \n\ Ei(x) := - PV(\\int_@{-x@}^\\infty dt \\exp(-t)/t)\n\ \n\ where PV denotes the principal value of the integral.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_expint_Ei (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_expint_Ei_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(Shi, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} Shi (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Shi (@dots{})\n\ \n\ These routines compute the integral Shi(x) = \\int_0^x dt \\sinh(t)/t.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_Shi (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_Shi_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(Chi, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} Chi (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Chi (@dots{})\n\ \n\ These routines compute the integral \n\ \n\ Chi(x) := Re[ \\gamma_E + \\log(x) + \\int_0^x dt (\\cosh[t]-1)/t] , \n\ \n\ where \\gamma_E is the Euler constant.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_Chi (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_Chi_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(expint_3, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} expint_3 (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_3 (@dots{})\n\ \n\ These routines compute the exponential integral \n\ Ei_3(x) = \\int_0^x dt \\exp(-t^3) for x >= 0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_expint_3 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_expint_3_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(Si, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} Si (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Si (@dots{})\n\ \n\ These routines compute the Sine integral Si(x) = \\int_0^x dt \\sin(t)/t.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_Si (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_Si_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(Ci, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} Ci (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Ci (@dots{})\n\ \n\ These routines compute the Cosine integral \n\ Ci(x) = -\\int_x^\\infty dt \\cos(t)/t for x > 0. \n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_Ci (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_Ci_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(atanint, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} atanint (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} atanint (@dots{})\n\ \n\ These routines compute the Arctangent integral \n\ AtanInt(x) = \\int_0^x dt \\arctan(t)/t. \n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_atanint (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_atanint_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(fermi_dirac_mhalf, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_mhalf (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_mhalf (@dots{})\n\ \n\ These routines compute the complete Fermi-Dirac integral F_@{-1/2@}(x).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_fermi_dirac_mhalf (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_fermi_dirac_mhalf_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(fermi_dirac_half, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_half (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_half (@dots{})\n\ \n\ These routines compute the complete Fermi-Dirac integral F_@{1/2@}(x).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_fermi_dirac_half (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_fermi_dirac_half_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(fermi_dirac_3half, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_3half (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_3half (@dots{})\n\ \n\ These routines compute the complete Fermi-Dirac integral F_@{3/2@}(x).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_fermi_dirac_3half (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_fermi_dirac_3half_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(gamma_gsl, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} gamma_gsl (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} gamma_gsl (@dots{})\n\ \n\ These routines compute the Gamma function \\Gamma(x), subject to x not \n\ being a negative integer. The function is computed using the real \n\ Lanczos method. The maximum value of x such that \\Gamma(x) is not \n\ considered an overflow is given by the macro GSL_SF_GAMMA_XMAX and is 171.0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_gamma (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_gamma_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(lngamma_gsl, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} lngamma_gsl (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lngamma_gsl (@dots{})\n\ \n\ These routines compute the logarithm of the Gamma function, \n\ \\log(\\Gamma(x)), subject to x not a being negative integer. \n\ For x<0 the real part of \\log(\\Gamma(x)) is returned, which is \n\ equivalent to \\log(|\\Gamma(x)|). The function is computed using \n\ the real Lanczos method.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_lngamma (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_lngamma_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(gammastar, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} gammastar (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} gammastar (@dots{})\n\ \n\ These routines compute the regulated Gamma Function \\Gamma^*(x) \n\ for x > 0. The regulated gamma function is given by,\n\ \n\ \\Gamma^*(x) = \\Gamma(x)/(\\sqrt@{2\\pi@} x^@{(x-1/2)@} \\exp(-x))\n\ = (1 + (1/12x) + ...) for x \\to \\infty\n\ \n\ and is a useful suggestion of Temme. \n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_gammastar (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_gammastar_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(gammainv_gsl, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} gammainv_gsl (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} gammainv_gsl (@dots{})\n\ \n\ These routines compute the reciprocal of the gamma function, 1/\\Gamma(x) using the real Lanczos method.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_gammainv (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_gammainv_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(lambert_W0, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} lambert_W0 (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lambert_W0 (@dots{})\n\ \n\ These compute the principal branch of the Lambert W function, W_0(x).\n\ \n\ Lambert\\'s W functions, W(x), are defined to be solutions of the\n\ equation W(x) \\exp(W(x)) = x. This function has multiple branches \n\ for x < 0; however, it has only two real-valued branches. \n\ We define W_0(x) to be the principal branch, where W > -1 for x < 0, \n\ and W_@{-1@}(x) to be the other real branch, where W < -1 for x < 0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_lambert_W0 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_lambert_W0_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(lambert_Wm1, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} lambert_Wm1 (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lambert_Wm1 (@dots{})\n\ \n\ These compute the secondary real-valued branch of the Lambert \n\ W function, W_@{-1@}(x).\n\ \n\ Lambert\\'s W functions, W(x), are defined to be solutions of the\n\ equation W(x) \\exp(W(x)) = x. This function has multiple branches \n\ for x < 0; however, it has only two real-valued branches. \n\ We define W_0(x) to be the principal branch, where W > -1 for x < 0, \n\ and W_@{-1@}(x) to be the other real branch, where W < -1 for x < 0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_lambert_Wm1 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_lambert_Wm1_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(log_1plusx, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} log_1plusx (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} log_1plusx (@dots{})\n\ \n\ These routines compute \\log(1 + x) for x > -1 using an algorithm that\n\ is accurate for small x.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_log_1plusx (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_log_1plusx_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(log_1plusx_mx, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} log_1plusx_mx (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} log_1plusx_mx (@dots{})\n\ \n\ These routines compute \\log(1 + x) - x for x > -1 using an algorithm \n\ that is accurate for small x.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_log_1plusx_mx (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_log_1plusx_mx_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(psi, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} psi (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi (@dots{})\n\ \n\ These routines compute the digamma function \\psi(x) for general x, \n\ x \\ne 0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_psi (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_psi_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(psi_1piy, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} psi_1piy (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi_1piy (@dots{})\n\ \n\ These routines compute the real part of the digamma function on \n\ the line 1+i y, Re[\\psi(1 + i y)].\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_psi_1piy (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_psi_1piy_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(synchrotron_1, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} synchrotron_1 (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} synchrotron_1 (@dots{})\n\ \n\ These routines compute the first synchrotron function \n\ x \\int_x^\\infty dt K_@{5/3@}(t) for x >= 0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_synchrotron_1 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_synchrotron_1_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(synchrotron_2, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} synchrotron_2 (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} synchrotron_2 (@dots{})\n\ \n\ These routines compute the second synchrotron function \n\ x K_@{2/3@}(x) for x >= 0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_synchrotron_2 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_synchrotron_2_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(transport_2, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} transport_2 (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_2 (@dots{})\n\ \n\ These routines compute the transport function J(2,x).\n\ \n\ The transport functions J(n,x) are defined by the integral\n\ representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_transport_2 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_transport_2_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(transport_3, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} transport_3 (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_3 (@dots{})\n\ \n\ These routines compute the transport function J(3,x).\n\ \n\ The transport functions J(n,x) are defined by the integral\n\ representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_transport_3 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_transport_3_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(transport_4, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} transport_4 (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_4 (@dots{})\n\ \n\ These routines compute the transport function J(4,x).\n\ \n\ The transport functions J(n,x) are defined by the integral\n\ representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_transport_4 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_transport_4_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(transport_5, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} transport_5 (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_5 (@dots{})\n\ \n\ These routines compute the transport function J(5,x).\n\ \n\ The transport functions J(n,x) are defined by the integral\n\ representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_transport_5 (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_transport_5_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(sinc_gsl, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} sinc_gsl (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} sinc_gsl (@dots{})\n\ \n\ These routines compute \\sinc(x) = \\sin(\\pi x) / (\\pi x) for any value of x.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_sinc (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_sinc_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(lnsinh, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} lnsinh (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lnsinh (@dots{})\n\ \n\ These routines compute \\log(\\sinh(x)) for x > 0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_lnsinh (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_lnsinh_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(lncosh, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} lncosh (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lncosh (@dots{})\n\ \n\ These routines compute \\log(\\cosh(x)) for any x.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_lncosh (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_lncosh_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(zeta, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} zeta (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} zeta (@dots{})\n\ \n\ These routines compute the Riemann zeta function \\zeta(s) for \n\ arbitrary s, s \\ne 1.\n\ \n\ The Riemann zeta function is defined by the infinite sum \n\ \\zeta(s) = \\sum_@{k=1@}^\\infty k^@{-s@}. \n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_zeta (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_zeta_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(eta, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} eta (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} eta (@dots{})\n\ \n\ These routines compute the eta function \\eta(s) for arbitrary s.\n\ \n\ The eta function is defined by \\eta(s) = (1-2^@{1-s@}) \\zeta(s).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_eta (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_eta_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_Jn, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} bessel_Jn (@var{n}, @var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Jn (@dots{})\n\ \n\ These routines compute the regular cylindrical Bessel function of\n\ order n, J_n(x).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Jn (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Jn_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Jn (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Jn_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Jn (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Jn_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_Yn, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} bessel_Yn (@var{n}, @var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Yn (@dots{})\n\ \n\ These routines compute the irregular cylindrical Bessel function of \n\ order n, Y_n(x), for x>0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Yn (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Yn_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Yn (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Yn_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Yn (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Yn_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_In, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} bessel_In (@var{n}, @var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_In (@dots{})\n\ \n\ These routines compute the regular modified cylindrical Bessel\n\ function of order n, I_n(x).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_In (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_In_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_In (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_In_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_In (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_In_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_In_scaled, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} bessel_In_scaled (@var{n}, @var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_In_scaled (@dots{})\n\ \n\ These routines compute the scaled regular modified cylindrical Bessel\n\ function of order n, \\exp(-|x|) I_n(x)\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_In_scaled (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_In_scaled_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_In_scaled (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_In_scaled_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_In_scaled (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_In_scaled_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_Kn, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} bessel_Kn (@var{n}, @var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Kn (@dots{})\n\ \n\ These routines compute the irregular modified cylindrical Bessel\n\ function of order n, K_n(x), for x > 0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Kn (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Kn_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Kn (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Kn_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Kn (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Kn_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_Kn_scaled, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} bessel_Kn_scaled (@var{n}, @var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Kn_scaled (@dots{})\n\ \n\ \n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Kn_scaled (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Kn_scaled_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Kn_scaled (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Kn_scaled_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Kn_scaled (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Kn_scaled_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_jl, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} bessel_jl (@var{n}, @var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_jl (@dots{})\n\ \n\ These routines compute the regular spherical Bessel function of \n\ order l, j_l(x), for l >= 0 and x >= 0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_jl (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_jl_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_jl (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_jl_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_jl (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_jl_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_yl, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} bessel_yl (@var{n}, @var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_yl (@dots{})\n\ \n\ These routines compute the irregular spherical Bessel function of\n\ order l, y_l(x), for l >= 0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_yl (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_yl_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_yl (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_yl_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_yl (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_yl_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_il_scaled, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} bessel_il_scaled (@var{n}, @var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_il_scaled (@dots{})\n\ \n\ These routines compute the scaled regular modified spherical Bessel\n\ function of order l, \\exp(-|x|) i_l(x)\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_il_scaled (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_il_scaled_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_il_scaled (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_il_scaled_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_il_scaled (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_il_scaled_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_kl_scaled, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} bessel_kl_scaled (@var{n}, @var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_kl_scaled (@dots{})\n\ \n\ These routines compute the scaled irregular modified spherical Bessel\n\ function of order l, \\exp(x) k_l(x), for x>0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_kl_scaled (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_kl_scaled_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_kl_scaled (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_kl_scaled_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_kl_scaled (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_kl_scaled_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(exprel_n, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} exprel_n (@var{n}, @var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} exprel_n (@dots{})\n\ \n\ These routines compute the N-relative exponential, which is the n-th\n\ generalization of the functions gsl_sf_exprel and gsl_sf_exprel2. The\n\ N-relative exponential is given by,\n\ \n\ exprel_N(x) = N!/x^N (\\exp(x) - \\sum_@{k=0@}^@{N-1@} x^k/k!)\n\ = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ...\n\ = 1F1 (1,1+N,x)\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_exprel_n (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_exprel_n_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_exprel_n (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_exprel_n_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_exprel_n (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_exprel_n_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(fermi_dirac_int, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_int (@var{n}, @var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_int (@dots{})\n\ \n\ These routines compute the complete Fermi-Dirac integral with an\n\ integer index of j, F_j(x) = (1/\\Gamma(j+1)) \\int_0^\\infty dt (t^j\n\ /(\\exp(t-x)+1)).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_fermi_dirac_int (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_fermi_dirac_int_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_fermi_dirac_int (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_fermi_dirac_int_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_fermi_dirac_int (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_fermi_dirac_int_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(taylorcoeff, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} taylorcoeff (@var{n}, @var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} taylorcoeff (@dots{})\n\ \n\ These routines compute the Taylor coefficient x^n / n! \n\ for x >= 0, n >= 0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_taylorcoeff (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_taylorcoeff_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_taylorcoeff (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_taylorcoeff_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_taylorcoeff (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_taylorcoeff_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(legendre_Pl, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} legendre_Pl (@var{n}, @var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_Pl (@dots{})\n\ \n\ These functions evaluate the Legendre polynomial P_l(x) for a specific\n\ value of l, x subject to l >= 0, |x| <= 1\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_Pl (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_Pl_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_Pl (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_Pl_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_Pl (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_Pl_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(legendre_Ql, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} legendre_Ql (@var{n}, @var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_Ql (@dots{})\n\ \n\ These routines compute the Legendre function Q_l(x) for x > -1, x != 1\n\ and l >= 0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_Ql (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_Ql_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_Ql (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_Ql_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_Ql (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_Ql_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(psi_n, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} psi_n (@var{n}, @var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi_n (@dots{})\n\ \n\ These routines compute the polygamma function \\psi^@{(m)@}(x) \n\ for m >= 0, x > 0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_psi_n (static_cast(n.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_psi_n_e (static_cast(n.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_psi_n (nint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_psi_n_e (nint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_psi_n (static_cast(n.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_psi_n_e (static_cast(n.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_Jnu, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} bessel_Jnu (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Jnu (@dots{})\n\ \n\ These routines compute the regular cylindrical Bessel function of\n\ fractional order nu, J_\\nu(x).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Jnu (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Jnu_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Jnu (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Jnu_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Jnu (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Jnu_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_Ynu, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} bessel_Ynu (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Ynu (@dots{})\n\ \n\ These routines compute the irregular cylindrical Bessel function of\n\ fractional order nu, Y_\\nu(x).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Ynu (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Ynu_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Ynu (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Ynu_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Ynu (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Ynu_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_Inu, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} bessel_Inu (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Inu (@dots{})\n\ \n\ These routines compute the regular modified Bessel function of\n\ fractional order nu, I_\\nu(x) for x>0, \\nu>0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Inu (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Inu_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Inu (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Inu_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Inu (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Inu_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_Inu_scaled, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} bessel_Inu_scaled (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Inu_scaled (@dots{})\n\ \n\ These routines compute the scaled regular modified Bessel function of\n\ fractional order nu, \\exp(-|x|)I_\\nu(x) for x>0, \\nu>0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Inu_scaled (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Inu_scaled_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Inu_scaled (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Inu_scaled_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Inu_scaled (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Inu_scaled_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_Knu, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} bessel_Knu (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Knu (@dots{})\n\ \n\ These routines compute the irregular modified Bessel function of\n\ fractional order nu, K_\\nu(x) for x>0, \\nu>0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Knu (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Knu_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Knu (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Knu_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Knu (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Knu_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_lnKnu, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} bessel_lnKnu (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_lnKnu (@dots{})\n\ \n\ These routines compute the logarithm of the irregular modified Bessel\n\ function of fractional order nu, \\ln(K_\\nu(x)) for x>0, \\nu>0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_lnKnu (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_lnKnu_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_lnKnu (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_lnKnu_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_lnKnu (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_lnKnu_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_Knu_scaled, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} bessel_Knu_scaled (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Knu_scaled (@dots{})\n\ \n\ These routines compute the scaled irregular modified Bessel function\n\ of fractional order nu, \\exp(+|x|) K_\\nu(x) for x>0, \\nu>0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Knu_scaled (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Knu_scaled_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Knu_scaled (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Knu_scaled_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_bessel_Knu_scaled (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_bessel_Knu_scaled_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(exp_mult, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} exp_mult (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} exp_mult (@dots{})\n\ \n\ These routines exponentiate x and multiply by the factor y to return\n\ the product y \\exp(x).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_exp_mult (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_exp_mult_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_exp_mult (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_exp_mult_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_exp_mult (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_exp_mult_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(fermi_dirac_inc_0, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} fermi_dirac_inc_0 (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} fermi_dirac_inc_0 (@dots{})\n\ \n\ These routines compute the incomplete Fermi-Dirac integral with an\n\ index of zero, F_0(x,b) = \\ln(1 + e^@{b-x@}) - (b-x).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_fermi_dirac_inc_0 (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_fermi_dirac_inc_0_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_fermi_dirac_inc_0 (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_fermi_dirac_inc_0_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_fermi_dirac_inc_0 (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_fermi_dirac_inc_0_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(poch, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} poch (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} poch (@dots{})\n\ \n\ These routines compute the Pochhammer symbol \n\ \n\ (a)_x := \\Gamma(a + x)/\\Gamma(a), \n\ \n\ subject to a and a+x not being negative integers. The Pochhammer\n\ symbol is also known as the Apell symbol.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_poch (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_poch_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_poch (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_poch_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_poch (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_poch_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(lnpoch, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} lnpoch (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} lnpoch (@dots{})\n\ \n\ These routines compute the logarithm of the Pochhammer symbol,\n\ \\log((a)_x) = \\log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_lnpoch (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_lnpoch_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_lnpoch (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_lnpoch_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_lnpoch (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_lnpoch_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(pochrel, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} pochrel (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} pochrel (@dots{})\n\ \n\ These routines compute the relative Pochhammer symbol ((a,x) - 1)/x\n\ where (a,x) = (a)_x := \\Gamma(a + x)/\\Gamma(a).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_pochrel (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_pochrel_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_pochrel (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_pochrel_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_pochrel (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_pochrel_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(gamma_inc_Q, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} gamma_inc_Q (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} gamma_inc_Q (@dots{})\n\ \n\ These routines compute the normalized incomplete Gamma Function \n\ Q(a,x) = 1/\\Gamma(a) \\int_x\\infty dt t^@{a-1@} \\exp(-t) for a > 0, x >= 0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_gamma_inc_Q (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_gamma_inc_Q_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_gamma_inc_Q (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_gamma_inc_Q_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_gamma_inc_Q (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_gamma_inc_Q_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(gamma_inc_P, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} gamma_inc_P (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} gamma_inc_P (@dots{})\n\ \n\ These routines compute the complementary normalized incomplete Gamma\n\ Function P(a,x) = 1/\\Gamma(a) \\int_0^x dt t^@{a-1@} \\exp(-t) \n\ for a > 0, x >= 0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_gamma_inc_P (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_gamma_inc_P_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_gamma_inc_P (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_gamma_inc_P_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_gamma_inc_P (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_gamma_inc_P_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(gamma_inc, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} gamma_inc (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} gamma_inc (@dots{})\n\ \n\ These functions compute the incomplete Gamma Function the\n\ normalization factor included in the previously defined functions:\n\ \\Gamma(a,x) = \\int_x\\infty dt t^@{a-1@} \\exp(-t) for a real and x >= 0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_gamma_inc (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_gamma_inc_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_gamma_inc (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_gamma_inc_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_gamma_inc (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_gamma_inc_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(beta_gsl, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} beta_gsl (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} beta_gsl (@dots{})\n\ \n\ These routines compute the Beta Function, \n\ B(a,b) = \\Gamma(a)\\Gamma(b)/\\Gamma(a+b) for a > 0, b > 0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_beta (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_beta_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_beta (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_beta_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_beta (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_beta_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(lnbeta, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} lnbeta (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} lnbeta (@dots{})\n\ \n\ These routines compute the logarithm of the Beta Function,\n\ \\log(B(a,b)) for a > 0, b > 0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_lnbeta (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_lnbeta_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_lnbeta (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_lnbeta_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_lnbeta (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_lnbeta_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(hyperg_0F1, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} hyperg_0F1 (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} hyperg_0F1 (@dots{})\n\ \n\ These routines compute the hypergeometric function 0F1(c,x).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_hyperg_0F1 (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_0F1_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_hyperg_0F1 (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_0F1_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_hyperg_0F1 (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_0F1_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(conicalP_half, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} conicalP_half (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_half (@dots{})\n\ \n\ These routines compute the irregular Spherical Conical Function\n\ P^@{1/2@}_@{-1/2 + i \\lambda@}(x) for x > -1.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_half (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_half_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_half (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_half_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_half (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_half_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(conicalP_mhalf, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} conicalP_mhalf (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_mhalf (@dots{})\n\ \n\ These routines compute the regular Spherical Conical Function\n\ P^@{-1/2@}_@{-1/2 + i \\lambda@}(x) for x > -1.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_mhalf (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_mhalf_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_mhalf (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_mhalf_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_mhalf (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_mhalf_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(conicalP_0, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} conicalP_0 (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_0 (@dots{})\n\ \n\ These routines compute the conical function P^0_@{-1/2 + i \\lambda@}(x)\n\ for x > -1.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_0 (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_0_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_0 (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_0_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_0 (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_0_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(conicalP_1, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} conicalP_1 (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_1 (@dots{})\n\ \n\ These routines compute the conical function P^1_@{-1/2 + i \\lambda@}(x)\n\ for x > -1.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_1 (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_1_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_1 (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_1_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_conicalP_1 (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_conicalP_1_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(hzeta, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} hzeta (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} hzeta (@dots{})\n\ \n\ These routines compute the Hurwitz zeta function \\zeta(s,q) \n\ for s > 1, q > 0.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_hzeta (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hzeta_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_hzeta (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hzeta_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_hzeta (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hzeta_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_Ai, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} airy_Ai (@var{x}, @var{mode})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai (@dots{})\n\ \n\ These routines compute the Airy function Ai(x) with an accuracy\n\ specified by mode.\n\ \n\ The second argument @var{mode} must be an integer corresponding to\n\ \n\ @table @asis\n\ @item 0 = GSL_PREC_DOUBLE\n\ Double-precision, a relative accuracy of approximately @code{2 * 10^-16}.\n\ @item 1 = GSL_PREC_SINGLE\n\ Single-precision, a relative accuracy of approximately @code{10^-7}.\n\ @item 2 = GSL_PREC_APPROX\n\ Approximate values, a relative accuracy of approximately @code{5 * 10^-4}.\n\ @end table\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } if(!args(1).is_scalar_type()) { error("The mode must be scalar."); print_usage (); return octave_value(); } int mode = static_cast((args(1).array_value())(0)); if(mode < 0) mode = 0; else if(mode > 2) mode = 2; NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_Ai (x.xelem(i), mode); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_Ai_e (x.xelem(i), mode, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_Bi, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} airy_Bi (@var{x}, @var{mode})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi (@dots{})\n\ \n\ These routines compute the Airy function Bi(x) with an accuracy\n\ specified by mode.\n\ \n\ The second argument @var{mode} must be an integer corresponding to\n\ \n\ @table @asis\n\ @item 0 = GSL_PREC_DOUBLE\n\ Double-precision, a relative accuracy of approximately @code{2 * 10^-16}.\n\ @item 1 = GSL_PREC_SINGLE\n\ Single-precision, a relative accuracy of approximately @code{10^-7}.\n\ @item 2 = GSL_PREC_APPROX\n\ Approximate values, a relative accuracy of approximately @code{5 * 10^-4}.\n\ @end table\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } if(!args(1).is_scalar_type()) { error("The mode must be scalar."); print_usage (); return octave_value(); } int mode = static_cast((args(1).array_value())(0)); if(mode < 0) mode = 0; else if(mode > 2) mode = 2; NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_Bi (x.xelem(i), mode); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_Bi_e (x.xelem(i), mode, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_Ai_scaled, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} airy_Ai_scaled (@var{x}, @var{mode})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai_scaled (@dots{})\n\ \n\ These routines compute a scaled version of the Airy function \n\ S_A(x) Ai(x). For x>0 the scaling factor S_A(x) is \\exp(+(2/3) x^(3/2)), and\n\ is 1 for x<0.\n\ \n\ The second argument @var{mode} must be an integer corresponding to\n\ \n\ @table @asis\n\ @item 0 = GSL_PREC_DOUBLE\n\ Double-precision, a relative accuracy of approximately @code{2 * 10^-16}.\n\ @item 1 = GSL_PREC_SINGLE\n\ Single-precision, a relative accuracy of approximately @code{10^-7}.\n\ @item 2 = GSL_PREC_APPROX\n\ Approximate values, a relative accuracy of approximately @code{5 * 10^-4}.\n\ @end table\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } if(!args(1).is_scalar_type()) { error("The mode must be scalar."); print_usage (); return octave_value(); } int mode = static_cast((args(1).array_value())(0)); if(mode < 0) mode = 0; else if(mode > 2) mode = 2; NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_Ai_scaled (x.xelem(i), mode); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_Ai_scaled_e (x.xelem(i), mode, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_Bi_scaled, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} airy_Bi_scaled (@var{x}, @var{mode})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi_scaled (@dots{})\n\ \n\ These routines compute a scaled version of the Airy function \n\ S_B(x) Bi(x). For x>0 the scaling factor S_B(x) is exp(-(2/3) x^(3/2)), and\n\ is 1 for x<0.\n\ \n\ The second argument @var{mode} must be an integer corresponding to\n\ \n\ @table @asis\n\ @item 0 = GSL_PREC_DOUBLE\n\ Double-precision, a relative accuracy of approximately @code{2 * 10^-16}.\n\ @item 1 = GSL_PREC_SINGLE\n\ Single-precision, a relative accuracy of approximately @code{10^-7}.\n\ @item 2 = GSL_PREC_APPROX\n\ Approximate values, a relative accuracy of approximately @code{5 * 10^-4}.\n\ @end table\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } if(!args(1).is_scalar_type()) { error("The mode must be scalar."); print_usage (); return octave_value(); } int mode = static_cast((args(1).array_value())(0)); if(mode < 0) mode = 0; else if(mode > 2) mode = 2; NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_Bi_scaled (x.xelem(i), mode); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_Bi_scaled_e (x.xelem(i), mode, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_Ai_deriv, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} airy_Ai_deriv (@var{x}, @var{mode})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai_deriv (@dots{})\n\ \n\ These routines compute the Airy function derivative Ai'(x) with an\n\ accuracy specified by mode.\n\ \n\ The second argument @var{mode} must be an integer corresponding to\n\ \n\ @table @asis\n\ @item 0 = GSL_PREC_DOUBLE\n\ Double-precision, a relative accuracy of approximately @code{2 * 10^-16}.\n\ @item 1 = GSL_PREC_SINGLE\n\ Single-precision, a relative accuracy of approximately @code{10^-7}.\n\ @item 2 = GSL_PREC_APPROX\n\ Approximate values, a relative accuracy of approximately @code{5 * 10^-4}.\n\ @end table\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } if(!args(1).is_scalar_type()) { error("The mode must be scalar."); print_usage (); return octave_value(); } int mode = static_cast((args(1).array_value())(0)); if(mode < 0) mode = 0; else if(mode > 2) mode = 2; NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_Ai_deriv (x.xelem(i), mode); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_Ai_deriv_e (x.xelem(i), mode, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_Bi_deriv, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} airy_Bi_deriv (@var{x}, @var{mode})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi_deriv (@dots{})\n\ \n\ These routines compute the Airy function derivative Bi'(x) with an\n\ accuracy specified by mode.\n\ \n\ The second argument @var{mode} must be an integer corresponding to\n\ \n\ @table @asis\n\ @item 0 = GSL_PREC_DOUBLE\n\ Double-precision, a relative accuracy of approximately @code{2 * 10^-16}.\n\ @item 1 = GSL_PREC_SINGLE\n\ Single-precision, a relative accuracy of approximately @code{10^-7}.\n\ @item 2 = GSL_PREC_APPROX\n\ Approximate values, a relative accuracy of approximately @code{5 * 10^-4}.\n\ @end table\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } if(!args(1).is_scalar_type()) { error("The mode must be scalar."); print_usage (); return octave_value(); } int mode = static_cast((args(1).array_value())(0)); if(mode < 0) mode = 0; else if(mode > 2) mode = 2; NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_Bi_deriv (x.xelem(i), mode); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_Bi_deriv_e (x.xelem(i), mode, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_Ai_deriv_scaled, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} airy_Ai_deriv_scaled (@var{x}, @var{mode})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai_deriv_scaled (@dots{})\n\ \n\ These routines compute the derivative of the scaled Airy function\n\ S_A(x) Ai(x).\n\ \n\ The second argument @var{mode} must be an integer corresponding to\n\ \n\ @table @asis\n\ @item 0 = GSL_PREC_DOUBLE\n\ Double-precision, a relative accuracy of approximately @code{2 * 10^-16}.\n\ @item 1 = GSL_PREC_SINGLE\n\ Single-precision, a relative accuracy of approximately @code{10^-7}.\n\ @item 2 = GSL_PREC_APPROX\n\ Approximate values, a relative accuracy of approximately @code{5 * 10^-4}.\n\ @end table\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } if(!args(1).is_scalar_type()) { error("The mode must be scalar."); print_usage (); return octave_value(); } int mode = static_cast((args(1).array_value())(0)); if(mode < 0) mode = 0; else if(mode > 2) mode = 2; NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_Ai_deriv_scaled (x.xelem(i), mode); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_Ai_deriv_scaled_e (x.xelem(i), mode, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_Bi_deriv_scaled, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} airy_Bi_deriv_scaled (@var{x}, @var{mode})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi_deriv_scaled (@dots{})\n\ \n\ These routines compute the derivative of the scaled Airy function\n\ S_B(x) Bi(x).\n\ \n\ The second argument @var{mode} must be an integer corresponding to\n\ \n\ @table @asis\n\ @item 0 = GSL_PREC_DOUBLE\n\ Double-precision, a relative accuracy of approximately @code{2 * 10^-16}.\n\ @item 1 = GSL_PREC_SINGLE\n\ Single-precision, a relative accuracy of approximately @code{10^-7}.\n\ @item 2 = GSL_PREC_APPROX\n\ Approximate values, a relative accuracy of approximately @code{5 * 10^-4}.\n\ @end table\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } if(!args(1).is_scalar_type()) { error("The mode must be scalar."); print_usage (); return octave_value(); } int mode = static_cast((args(1).array_value())(0)); if(mode < 0) mode = 0; else if(mode > 2) mode = 2; NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_Bi_deriv_scaled (x.xelem(i), mode); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_Bi_deriv_scaled_e (x.xelem(i), mode, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(ellint_Kcomp, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} ellint_Kcomp (@var{x}, @var{mode})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} ellint_Kcomp (@dots{})\n\ \n\ These routines compute the complete elliptic integral K(k) \n\ @tex\n\ \\beforedisplay\n\ $$\n\ \\eqalign{\n\ K(k) &= \\int_0^{\\pi/2} {dt \\over \\sqrt{(1 - k^2 \\sin^2(t))}} \\cr\n\ }\n\ $$\n\ \\afterdisplay\n\ See also:\n\ @end tex\n\ @ifinfo\n\ @group\n\ @example\n\ pi\n\ ---\n\ 2\n\ /\n\ | 1\n\ ellint_Kcomp(k) = | ------------------- dt\n\ | 2 2\n\ / sqrt(1 - k sin (t))\n\ 0\n\ \n\ @end example\n\ @end group\n\ @end ifinfo\n\ @ifhtml\n\ @group\n\ @example\n\ pi\n\ ---\n\ 2\n\ /\n\ | 1\n\ ellint_Kcomp(k) = | ------------------- dt\n\ | 2 2\n\ / sqrt(1 - k sin (t))\n\ 0\n\ \n\ @end example\n\ @end group\n\ @end ifhtml\n\ \n\ @seealso{ellipj, ellipke}\n\ \n\ The notation used here is based on Carlson, @cite{Numerische\n\ Mathematik} 33 (1979) and differs slightly from that used by\n\ Abramowitz & Stegun, where the functions are given in terms of the\n\ parameter @math{m = k^2}.\n\ \n\ \n\ The second argument @var{mode} must be an integer corresponding to\n\ \n\ @table @asis\n\ @item 0 = GSL_PREC_DOUBLE\n\ Double-precision, a relative accuracy of approximately @code{2 * 10^-16}.\n\ @item 1 = GSL_PREC_SINGLE\n\ Single-precision, a relative accuracy of approximately @code{10^-7}.\n\ @item 2 = GSL_PREC_APPROX\n\ Approximate values, a relative accuracy of approximately @code{5 * 10^-4}.\n\ @end table\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } if(!args(1).is_scalar_type()) { error("The mode must be scalar."); print_usage (); return octave_value(); } int mode = static_cast((args(1).array_value())(0)); if(mode < 0) mode = 0; else if(mode > 2) mode = 2; NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_ellint_Kcomp (x.xelem(i), mode); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_ellint_Kcomp_e (x.xelem(i), mode, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(ellint_Ecomp, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} ellint_Ecomp (@var{x}, @var{mode})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} ellint_Ecomp (@dots{})\n\ \n\ These routines compute the complete elliptic integral E(k) to the\n\ accuracy specified by the mode variable mode.\n\ \n\ @tex\n\ \\beforedisplay\n\ $$\n\ \\eqalign{\n\ E(k) &= \\int_0^{\\pi/2} \\sqrt{(1 - k^2 \\sin^2(t))} dt \\cr\n\ }\n\ $$\n\ \\afterdisplay\n\ See also: \n\ \n\ @end tex\n\ @ifinfo\n\ @group\n\ @example\n\ pi\n\ ---\n\ 2\n\ /\n\ | 2 2\n\ ellint_Ecomp(k) = | sqrt(1 - k sin (t)) dt\n\ |\n\ /\n\ 0\n\ \n\ @end example\n\ @end group\n\ @end ifinfo\n\ @ifhtml\n\ @group\n\ @example\n\ pi\n\ ---\n\ 2\n\ /\n\ | 2 2\n\ ellint_Ecomp(k) = | sqrt(1 - k sin (t)) dt\n\ |\n\ /\n\ 0\n\ \n\ @end example\n\ @end group\n\ @end ifhtml\n\ \n\ @seealso{ellipj, ellipke}\n\ \n\ The notation used here is based on Carlson, @cite{Numerische\n\ Mathematik} 33 (1979) and differs slightly from that used by\n\ Abramowitz & Stegun, where the functions are given in terms of the\n\ parameter @math{m = k^2}.\n\ \n\ The second argument @var{mode} must be an integer corresponding to\n\ \n\ @table @asis\n\ @item 0 = GSL_PREC_DOUBLE\n\ Double-precision, a relative accuracy of approximately @code{2 * 10^-16}.\n\ @item 1 = GSL_PREC_SINGLE\n\ Single-precision, a relative accuracy of approximately @code{10^-7}.\n\ @item 2 = GSL_PREC_APPROX\n\ Approximate values, a relative accuracy of approximately @code{5 * 10^-4}.\n\ @end table\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } if(!args(1).is_scalar_type()) { error("The mode must be scalar."); print_usage (); return octave_value(); } int mode = static_cast((args(1).array_value())(0)); if(mode < 0) mode = 0; else if(mode > 2) mode = 2; NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_ellint_Ecomp (x.xelem(i), mode); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_ellint_Ecomp_e (x.xelem(i), mode, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_zero_Ai, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} airy_zero_Ai (@var{n})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Ai (@dots{})\n\ \n\ These routines compute the location of the s-th zero of the Airy\n\ function Ai(x).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_zero_Ai (static_cast(x.xelem(i))); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_zero_Ai_e (static_cast(x.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value_list(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_zero_Bi, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} airy_zero_Bi (@var{n})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Bi (@dots{})\n\ \n\ These routines compute the location of the s-th zero of the Airy\n\ function Bi(x).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_zero_Bi (static_cast(x.xelem(i))); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_zero_Bi_e (static_cast(x.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value_list(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_zero_Ai_deriv, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} airy_zero_Ai_deriv (@var{n})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Ai_deriv (@dots{})\n\ \n\ These routines compute the location of the s-th zero of the Airy\n\ function derivative Ai(x).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_zero_Ai_deriv (static_cast(x.xelem(i))); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_zero_Ai_deriv_e (static_cast(x.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value_list(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(airy_zero_Bi_deriv, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} airy_zero_Bi_deriv (@var{n})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Bi_deriv (@dots{})\n\ \n\ These routines compute the location of the s-th zero of the Airy\n\ function derivative Bi(x).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_airy_zero_Bi_deriv (static_cast(x.xelem(i))); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_airy_zero_Bi_deriv_e (static_cast(x.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value_list(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_zero_J0, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} bessel_zero_J0 (@var{n})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_zero_J0 (@dots{})\n\ \n\ These routines compute the location of the s-th positive zero of the\n\ Bessel function J_0(x).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_bessel_zero_J0 (static_cast(x.xelem(i))); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_bessel_zero_J0_e (static_cast(x.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value_list(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(bessel_zero_J1, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} bessel_zero_J1 (@var{n})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_zero_J1 (@dots{})\n\ \n\ These routines compute the location of the s-th positive zero of the\n\ Bessel function J_1(x).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_bessel_zero_J1 (static_cast(x.xelem(i))); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_bessel_zero_J1_e (static_cast(x.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value_list(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(psi_1_int, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} psi_1_int (@var{n})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi_1_int (@dots{})\n\ \n\ These routines compute the Trigamma function \\psi(n) for positive\n\ integer n.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_psi_1_int (static_cast(x.xelem(i))); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_psi_1_int_e (static_cast(x.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value_list(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(zeta_int, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} zeta_int (@var{n})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} zeta_int (@dots{})\n\ \n\ These routines compute the Riemann zeta function \\zeta(n) for \n\ integer n, n \\ne 1.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_zeta_int (static_cast(x.xelem(i))); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_zeta_int_e (static_cast(x.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value_list(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(eta_int, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} eta_int (@var{n})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} eta_int (@dots{})\n\ \n\ These routines compute the eta function \\eta(n) for integer n.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = gsl_sf_eta_int (static_cast(x.xelem(i))); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { gsl_sf_eta_int_e (static_cast(x.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value_list(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(legendre_Plm, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} legendre_Plm (@var{n}, @var{m}, @var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_Plm (@dots{})\n\ \n\ These routines compute the associated Legendre polynomial P_l^m(x) \n\ for m >= 0, l >= m, |x| <= 1.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 3) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type() || !args(2).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray m = args(1).array_value(); if(n.length() != m.length()) { error("Two first arguments must have the same size."); print_usage (); return octave_value(); } NDArray x = args(2).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_Plm (static_cast(n.xelem(i)), static_cast(m.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_Plm_e (static_cast(n.xelem(i)), static_cast(m.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); int mint = static_cast(m.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_Plm (nint, mint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_Plm_e (nint, mint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_Plm (static_cast(n.xelem(i)), static_cast(m.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_Plm_e (static_cast(n.xelem(i)), static_cast(m.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("The two first and the third argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(legendre_sphPlm, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} legendre_sphPlm (@var{n}, @var{m}, @var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_sphPlm (@dots{})\n\ \n\ These routines compute the normalized associated Legendre polynomial\n\ $\\sqrt@{(2l+1)/(4\\pi)@} \\sqrt@{(l-m)!/(l+m)!@} P_l^m(x)$ suitable for use\n\ in spherical harmonics. The parameters must satisfy m >= 0, l >= m,\n\ |x| <= 1. Theses routines avoid the overflows that occur for the\n\ standard normalization of P_l^m(x).\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 3) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type() || !args(2).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray m = args(1).array_value(); if(n.length() != m.length()) { error("Two first arguments must have the same size."); print_usage (); return octave_value(); } NDArray x = args(2).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_sphPlm (static_cast(n.xelem(i)), static_cast(m.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_sphPlm_e (static_cast(n.xelem(i)), static_cast(m.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); int mint = static_cast(m.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_sphPlm (nint, mint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_sphPlm_e (nint, mint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_legendre_sphPlm (static_cast(n.xelem(i)), static_cast(m.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_legendre_sphPlm_e (static_cast(n.xelem(i)), static_cast(m.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("The two first and the third argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(hyperg_U, args, nargout, " -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{out} =} hyperg_U (@var{x0}, @var{x1}, @var{x2})\n\ @deftypefnx {Loadable Function} {[@var{out}, @var{err}] =} hyperg_U (@dots{})\n\ \n\ Secondary Confluent Hypergoemetric U function A&E 13.1.3 \n\ All inputs are double as is the output.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{out}.a.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") // // // Generated R. Rogers 4/21/2008 // Version 1 Expanded to three argument input and added maintainence hints // { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); // Check number of arguments here if((args.length() != 3 )|| (nargout > 2)) { print_usage (); return octave_value(); } // Check argument types here if(!args(0).is_real_type() || !args(1).is_real_type()|| !args(2).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here // Generate internal variables NDArray x0 = args(0).array_value(); NDArray x1 = args(1).array_value(); NDArray x2 = args(2).array_value(); // // Case one; all inputs the same length A A A if((x0.length() == x1.length() )&& (x0.length()==x2.length())) { dv = x0.dims(); NDArray out(dv); int len = x0.length(); // One output argument if(nargout < 2) { for(i = 0; i < len; i++) { out.xelem(i) = gsl_sf_hyperg_U (x0.xelem(i), x1.xelem(i),x2.xelem(i)); } return octave_value(out); // Two arguments } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_U_e (x0.xelem(i), x1.xelem(i), x2.xelem(i), &result); out.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(out); return retval; } // // Now we start on having only one array and two scalars, A S S } else if(( x0.length() != 1)&& (x1.length() == 1) && (x2.length()==1)) { dv = x0.dims(); NDArray out(dv); int len = x0.length(); // int x1_int = static_cast(x1.xelem(0)); // int x2_int = static_cast(x2.xelem(0)); double x1_real = x1.xelem(0); double x2_real = x2.xelem(0); // One output argument if(nargout < 2) { for(i = 0; i < len; i++) { out.xelem(i) = gsl_sf_hyperg_U (x0.xelem(i),x1_real,x2_real); } return octave_value(out); // Two output argument } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_U_e (x0.xelem(i),x1_real,x2_real, &result); out.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(out); return retval; } // S A S input form } else if((x0.length() == 1)&& ( x1.length() != 1) && (x2.length()==1)) { dv = x1.dims(); NDArray out(dv); int len = x1.length(); // int x0_int = static_cast(x0.xelem(0)); // int x2_int = static_cast(x2.xelem(0)); double x0_real = x0.xelem(0); double x2_real = x2.xelem(0); // One output argument if(nargout < 2) { for(i = 0; i < len; i++) { out.xelem(i) = gsl_sf_hyperg_U (x0_real,x1.xelem(i),x2_real); } return octave_value(out); // Two output argument } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_U_e (x0_real,x1.xelem(i),x2_real, &result); out.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(out); return retval; } // S S A input form } else if((x0.length() == 1)&& ( x1.length() == 1) && ( x2.length()!=1)) { dv = x2.dims(); NDArray out(dv); int len = x2.length(); // int x0_int = static_cast(x0.xelem(0)); // int x1_int = static_cast(x1.xelem(0)); double x0_real = x0.xelem(0); double x1_real = x1.xelem(0); // One output argument if(nargout < 2) { for(i = 0; i < len; i++) { out.xelem(i) = gsl_sf_hyperg_U (x0_real,x1_real,x2.xelem(i)); } return octave_value(out); // Two output argument } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_U_e (x0_real,x1_real,x2.xelem(i), &result); out.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(out); return retval; } } else { error("First, second, and third argument must either have the same size, or two of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ DEFUN_DLD(hyperg_1F1, args, nargout, " -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{out} =} hyperg_1F1 (@var{x0}, @var{x1}, @var{x2})\n\ @deftypefnx {Loadable Function} {[@var{out}, @var{err}] =} hyperg_1F1 (@dots{})\n\ \n\ Primary Confluent Hypergoemetric U function A&E 13.1.3 \n\ All inputs are double as is the output.\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{out}.a.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") // // // Generated R. Rogers 4/21/2008 // Version 1 Expanded to three argument input and added maintainence hints // { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); // Check number of arguments here if((args.length() != 3 )|| (nargout > 2)) { print_usage (); return octave_value(); } // Check argument types here if(!args(0).is_real_type() || !args(1).is_real_type()|| !args(2).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here // Generate internal variables NDArray x0 = args(0).array_value(); NDArray x1 = args(1).array_value(); NDArray x2 = args(2).array_value(); // // Case one; all inputs the same length A A A if((x0.length() == x1.length() )&& (x0.length()==x2.length())) { dv = x0.dims(); NDArray out(dv); int len = x0.length(); // One output argument if(nargout < 2) { for(i = 0; i < len; i++) { out.xelem(i) = gsl_sf_hyperg_1F1 (x0.xelem(i), x1.xelem(i),x2.xelem(i)); } return octave_value(out); // Two arguments } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_1F1_e (x0.xelem(i), x1.xelem(i), x2.xelem(i), &result); out.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(out); return retval; } // // Now we start on having only one array and two scalars, A S S } else if(( x0.length() != 1)&& (x1.length() == 1) && (x2.length()==1)) { dv = x0.dims(); NDArray out(dv); int len = x0.length(); // int x1_int = static_cast(x1.xelem(0)); // int x2_int = static_cast(x2.xelem(0)); double x1_real = x1.xelem(0); double x2_real = x2.xelem(0); // One output argument if(nargout < 2) { for(i = 0; i < len; i++) { out.xelem(i) = gsl_sf_hyperg_1F1 (x0.xelem(i),x1_real,x2_real); } return octave_value(out); // Two output argument } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_1F1_e (x0.xelem(i),x1_real,x2_real, &result); out.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(out); return retval; } // S A S input form } else if((x0.length() == 1)&& ( x1.length() != 1) && (x2.length()==1)) { dv = x1.dims(); NDArray out(dv); int len = x1.length(); // int x0_int = static_cast(x0.xelem(0)); // int x2_int = static_cast(x2.xelem(0)); double x0_real = x0.xelem(0); double x2_real = x2.xelem(0); // One output argument if(nargout < 2) { for(i = 0; i < len; i++) { out.xelem(i) = gsl_sf_hyperg_1F1 (x0_real,x1.xelem(i),x2_real); } return octave_value(out); // Two output argument } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_1F1_e (x0_real,x1.xelem(i),x2_real, &result); out.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(out); return retval; } // S S A input form } else if((x0.length() == 1)&& ( x1.length() == 1) && ( x2.length()!=1)) { dv = x2.dims(); NDArray out(dv); int len = x2.length(); // int x0_int = static_cast(x0.xelem(0)); // int x1_int = static_cast(x1.xelem(0)); double x0_real = x0.xelem(0); double x1_real = x1.xelem(0); // One output argument if(nargout < 2) { for(i = 0; i < len; i++) { out.xelem(i) = gsl_sf_hyperg_1F1 (x0_real,x1_real,x2.xelem(i)); } return octave_value(out); // Two output argument } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_hyperg_1F1_e (x0_real,x1_real,x2.xelem(i), &result); out.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(out); return retval; } } else { error("First, second, and third argument must either have the same size, or two of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ gsl-1.0.8/doc/gsl_sf_a.ps0000644000175000017500000115100211201030403012761 0ustar shsh%!PS-Adobe-2.0 %%Creator: dvips(k) 5.95a Copyright 2005 Radical Eye Software %%Title: gsl_sf.dvi %%Pages: 51 %%PageOrder: Ascend %%BoundingBox: 0 0 595 842 %%DocumentFonts: CMR10 CMTT10 CMSS10 CMSLTT10 CMSL10 CMMI10 CMEX10 CMMI7 %%+ CMR7 CMSY10 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -o gsl_sf_a.ps gsl_sf.dvi %DVIPSParameters: dpi=600 %DVIPSSource: TeX output 2008.06.18:1758 %%BeginProcSet: tex.pro 0 0 %! 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All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put readonly def /FontBBox{-29 -960 1116 775}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /zero put dup 50 /two put readonly def /FontBBox{-27 -250 1122 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 25 /pi put dup 61 /slash put readonly def /FontBBox{0 -250 1171 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 90 /integraldisplay put dup 113 /radicalBig put readonly def /FontBBox{-24 -2960 1454 772}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 69 /E put dup 75 /K put dup 100 /d put dup 107 /k put dup 109 /m put dup 116 /t put readonly def /FontBBox{-32 -250 1048 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E394A533A081C36D456A09920001A3D2199583EB9B84B4DEE08E3D12939E321 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTT10 %!PS-AdobeFont-1.1: CMTT10 1.00B %%CreationDate: 1992 Apr 26 10:42:42 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTT10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def /FontName /CMTT10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 42 /asterisk put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 58 /colon put dup 60 /less put dup 61 /equal put dup 62 /greater put dup 65 /A put dup 66 /B put dup 67 /C put dup 69 /E put dup 70 /F put dup 73 /I put dup 74 /J put dup 75 /K put dup 80 /P put dup 81 /Q put dup 83 /S put dup 85 /U put dup 87 /W put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 93 /bracketright put dup 94 /asciicircum put dup 95 /underscore put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /braceleft put dup 124 /bar put dup 125 /braceright put readonly def /FontBBox{-4 -235 731 800}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F00F963068B8232429ED8B7CF6A3D879A2D19 38DD5C4467F9DD8C5D1A2000B3A6BF2F25629BAEC199AE8BD4BA6ED9BBF7DABF 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSL10 %!PS-AdobeFont-1.1: CMSL10 1.0 %%CreationDate: 1991 Aug 20 16:40:20 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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cleartomark %%EndFont %%BeginFont: CMSLTT10 %!PS-AdobeFont-1.1: CMSLTT10 1.0 %%CreationDate: 1991 Aug 20 16:41:43 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSLTT10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -9.46 def /isFixedPitch true def end readonly def /FontName /CMSLTT10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /zero put dup 49 /one put dup 50 /two put dup 100 /d put dup 101 /e put dup 109 /m put dup 110 /n put dup 111 /o put dup 114 /r put dup 116 /t put dup 117 /u put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-20 -233 617 696}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSS10 %!PS-AdobeFont-1.1: CMSS10 1.0 %%CreationDate: 1991 Aug 20 17:33:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSS10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put readonly def /FontBBox{-61 -250 999 759}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 31 /Oslash put dup 33 /exclam put dup 36 /dollar put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 55 /seven put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 93 /bracketright put dup 95 /dotaccent put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-251 -250 1009 969}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont TeXDict begin 39139632 55387786 1000 600 600 (gsl_sf.dvi) @start /Fa 255[71{}1 90.9091 /CMSY10 rf /Fb 205[33 1[33 48[{}2 58.1154 /CMR7 rf /Fc 194[34 35[39 25[{}2 58.1154 /CMMI7 rf /Fd 142[83 22[46 90[{}2 83.022 /CMEX10 rf /Fe 139[33 6[80 1[47 6[47 24[77 5[67 69[{}6 90.9091 /CMMI10 rf /Ff 130[48 48 48 3[48 1[48 48 48 48 1[48 48 48 1[48 3[48 48 48 48 3[48 2[48 31[48 1[48 1[48 2[48 48 48 48 1[48 48 48 48 48 48 2[48 42[{}32 90.9091 /CMTT10 rf /Fg 133[40 48 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b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 1163 42 84 v 390 1252 a Fk(for)30 b(do)s(cumen)m(tation.)275 1467 y(\037b)s(essel_il_scaled)h(-*-)h(texinfo)f(-*-)2960 1682 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(bessel_il_scaled)d Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 1791 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_il_scaled)d Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 1901 y Fk(These)26 b(routines)g(compute)h(the)f(scaled)h(regular)g(mo)s(di\014ed)e (spherical)i(Bessel)g(function)f(of)g(order)390 2011 y(l,)31 b(exp\(-)p Ff(|)p Fk(x)p Ff(|)p Fk(\))f(i_l\(x\))390 2160 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 2310 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o 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b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g (Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 929 42 84 v 390 1019 a Fk(for)30 b(do)s(cumen)m(tation.)275 1215 y(\037ta)m(ylorco)s(e\013)i(-*-)f(texinfo)g(-*-)2960 1412 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(taylorcoeff)c Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 1522 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(taylorcoeff)c Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 1631 y Fk(These)30 b(routines)g(compute)h(the)g(T)-8 b(a)m(ylor)31 b(co)s(e\016cien)m(t)h (x)p Ff(^)p Fk(n)e(/)h(n!)40 b(for)30 b(x)g Ff(>)p Fk(=)g(0,)h(n)f Ff(>)p Fk(=)g(0.)390 1772 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate) i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 1913 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 1933 V 390 2022 a 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Fi(\))2960 4736 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_il_scaled)d Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 4845 y Fk(These)26 b(routines)g(compute)h(the)f(scaled)h(regular)g(mo)s(di\014ed)e (spherical)i(Bessel)g(function)f(of)g(order)390 4955 y(l,)31 b(exp\(-)p Ff(|)p Fk(x)p Ff(|)p Fk(\))f(i_l\(x\))390 5093 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 5230 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o (re/g)o(sl/)p 3977 5251 V 390 5340 a Fk(for)30 b(do)s(cumen)m(tation.)p eop end %%Page: 39 39 TeXDict begin 39 38 bop 275 299 a Fk(\037b)s(essel_kl_scaled)31 b(-*-)g(texinfo)g(-*-)2960 482 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(bessel_kl_scaled)d Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 591 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p 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Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 3087 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(fermi_dirac_int)d Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 3197 y Fk(These)27 b(routines)h(compute)g(the)f(complete)i(F)-8 b(ermi-Dirac)30 b(in)m(tegral)f(with)f(an)f(in)m(teger)i(index)e(of)h(j,)390 3306 y(F_j\(x\))j(=)f(\(1/Gamma\(j+1\)\))k(in)m(t_0)p Ff(^)p Fk(inft)m(y)d(dt)g(\(t)p Ff(^)p Fk(j)f(/\(exp\(t-x\)+1\)\).)390 3440 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 3574 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o (re/g)o(sl/)p 3977 3595 V 390 3684 a Fk(for)30 b(do)s(cumen)m(tation.) 275 3867 y(\037ta)m(ylorco)s(e\013)i(-*-)f(texinfo)g(-*-)2960 4049 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(taylorcoeff)c Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 4159 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(taylorcoeff)c Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 4268 y Fk(These)30 b(routines)g(compute)h(the)g(T)-8 b(a)m(ylor)31 b(co)s(e\016cien)m(t)h (x)p Ff(^)p Fk(n)e(/)h(n!)40 b(for)30 b(x)g Ff(>)p Fk(=)g(0,)h(n)f Ff(>)p Fk(=)g(0.)390 4402 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate) i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 4536 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 4557 V 390 4646 a Fk(for)30 b(do)s(cumen)m(tation.)275 4829 y(\037legendre_Pl)g(-*-)i(texinfo)f(-*-)2960 5011 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(legendre_Pl)c Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 5121 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(legendre_Pl)c Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 5230 y Fk(These)36 b(functions)f(ev)-5 b(aluate)38 b(the)e(Legendre)f(p)s(olynomial)i(P_l\(x\))g(for)e(a)h(sp) s(eci\014c)g(v)-5 b(alue)36 b(of)g(l,)i(x)390 5340 y(sub)5 b(ject)30 b(to)h(l)g Ff(>)p Fk(=)f(0,)h Ff(|)p Fk(x)p Ff(|)e(<)p Fk(=)h(1)p eop end %%Page: 40 40 TeXDict begin 40 39 bop 390 299 a Fg(err)36 b Fk(con)m(tains)c(an)e (estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 434 y(This)19 b(function)h(is)h(from)f(the) g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 454 42 84 v 390 543 a Fk(for)30 b(do)s(cumen)m(tation.)275 729 y(\037legendre_Ql)g(-*-)i(texinfo)f(-*-)2960 914 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(legendre_Ql)c Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 1024 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(legendre_Ql)c Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 1133 y Fk(These)30 b(routines)g (compute)h(the)g(Legendre)f(function)g(Q_l\(x\))h(for)f(x)h Ff(>)f Fk(-1,)h(x)f(!=)h(1)f(and)g(l)h Ff(>)p Fk(=)e(0.)390 1268 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 1403 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o (re/g)o(sl/)p 3977 1424 V 390 1513 a Fk(for)30 b(do)s(cumen)m(tation.) 275 1698 y(\037psi_n)f(-*-)i(texinfo)g(-*-)2960 1884 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(psi_n)47 b Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 1993 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(psi_n)47 b Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 2103 y Fk(These)30 b(routines)g(compute)h(the)g(p)s(olygamma)g(function)f(psi)p Ff(^{)p Fk(\(m\))p Ff(})p Fk(\(x\))g(for)g(m)g Ff(>)p Fk(=)g(0,)h(x)f Ff(>)g Fk(0.)390 2238 y Fg(err)36 b Fk(con)m(tains)c (an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 2373 y(This)19 b(function)h(is)h(from)f (the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 2393 V 390 2482 a Fk(for)30 b(do)s(cumen)m(tation.)275 2668 y(\037b)s(essel_Jn)m(u)f(-*-)i(texinfo)g(-*-)2960 2853 y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53 b(bessel_Jnu)48 b Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b Fi(\))2960 2963 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_Jnu)48 b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 3072 y Fk(These)28 b(routines)f(compute)h(the)g(regular)g(cylindrical)h(Bessel)f(function) g(of)g(fractional)h(order)e(n)m(u,)390 3182 y(J_u\(x\).)390 3317 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(z)p Fk(.)390 3452 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o (re/g)o(sl/)p 3977 3472 V 390 3561 a Fk(for)30 b(do)s(cumen)m(tation.) 275 3747 y(\037b)s(essel_Yn)m(u)f(-*-)j(texinfo)f(-*-)2960 3932 y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53 b(bessel_Ynu)48 b Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b Fi(\))2960 4042 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_Ynu)48 b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 4151 y Fk(These)37 b(routines)f(compute)h(the)g(irregular)g(cylindrical)h(Bessel)g (function)e(of)h(fractional)h(order)390 4261 y(n)m(u,)30 b(Y_u\(x\).)390 4396 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of) f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(z)p Fk(.)390 4531 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 4551 V 390 4641 a Fk(for)30 b(do)s(cumen)m(tation.)275 4826 y(\037b)s(essel_In)m(u)f(-*-)i(texinfo)g(-*-)2960 5011 y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53 b(bessel_Inu)48 b Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b Fi(\))2960 5121 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_Inu)48 b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 5230 y Fk(These)34 b(routines)g(compute)h(the)f(regular)g(mo)s(di\014ed)f(Bessel)j (function)e(of)g(fractional)i(order)d(n)m(u,)390 5340 y(I_u\(x\))e(for)f(x)p Ff(>)p Fk(0,)g(u)p Ff(>)p Fk(0.)p eop end %%Page: 41 41 TeXDict begin 41 40 bop 390 299 a Fg(err)36 b Fk(con)m(tains)c(an)e (estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(z)p Fk(.)390 445 y(This)19 b(function)h(is)h(from)f(the) g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 465 42 84 v 390 554 a Fk(for)30 b(do)s(cumen)m(tation.)275 762 y(\037b)s(essel_In)m(u_scaled)g(-*-)h(texinfo)g(-*-)2960 969 y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53 b(bessel_Inu_scaled)d 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b(airy_Ai_deriv)c Fi(\()p Fh(x)p Fg(,)31 b Fh(mode)12 b Fi(\))2960 4454 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(airy_Ai_deriv)c Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 4564 y Fk(These)24 b(routines)f (compute)h(the)h(Airy)e(function)h(deriv)-5 b(ativ)m(e)25 b(Ai'\(x\))g(with)f(an)g(accuracy)h(sp)s(eci\014ed)390 4674 y(b)m(y)30 b(mo)s(de.)390 4807 y(The)g(second)g(argumen)m(t)h Fg(mo)s(de)k Fk(m)m(ust)30 b(b)s(e)g(an)g(in)m(teger)i(corresp)s (onding)e(to)390 4964 y(0)h(=)f(GSL_PREC_DOUBLE)870 5073 y(Double-precision,)i(a)e(relativ)m(e)j(accuracy)e(of)g(appro)m (ximately)h Ff(2)e(*)g(10^-16)p Fk(.)390 5230 y(1)h(=)f (GSL_PREC_SINGLE)870 5340 y(Single-precision,)h(a)g(relativ)m(e)i (accuracy)e(of)g(appro)m(ximately)h Ff(10^-7)p Fk(.)p eop end %%Page: 47 47 TeXDict begin 47 46 bop 390 299 a Fk(2)31 b(=)f(GSL_PREC_APPR)m(O)m(X) 870 408 y(Appro)m(ximate)h(v)-5 b(alues,)31 b(a)g(relativ)m(e)h (accuracy)g(of)e(appro)m(ximately)i 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y(0)h(=)f(GSL_PREC_DOUBLE)870 2038 y(Double-precision,)i(a)e(relativ)m(e)j(accuracy)e(of)g(appro)m (ximately)h Ff(2)e(*)g(10^-16)p Fk(.)390 2211 y(1)h(=)f (GSL_PREC_SINGLE)870 2321 y(Single-precision,)h(a)g(relativ)m(e)i (accuracy)e(of)g(appro)m(ximately)h Ff(10^-7)p Fk(.)390 2494 y(2)f(=)f(GSL_PREC_APPR)m(O)m(X)870 2604 y(Appro)m(ximate)h(v)-5 b(alues,)31 b(a)g(relativ)m(e)h(accuracy)g(of)e(appro)m(ximately)i Ff(5)e(*)g(10^-4)p Fk(.)390 2784 y Fg(err)36 b Fk(con)m(tains)c(an)e (estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 2932 y(This)19 b(function)h(is)h(from)f (the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 2953 V 390 3042 a Fk(for)30 b(do)s(cumen)m(tation.)275 3254 y(\037airy_Ai_deriv_scaled)i(-*-)f(texinfo)g(-*-)2960 3466 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(airy_Ai_deriv_scaled)e Fi(\()p Fh(x)p Fg(,)31 b Fh(mode)12 b Fi(\))2960 3576 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(airy_Ai_deriv_scaled)e Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 3686 y Fk(These)30 b(routines)g(compute)h(the)g (deriv)-5 b(ativ)m(e)32 b(of)e(the)h(scaled)g(Airy)f(function)g (S_A\(x\))h(Ai\(x\).)390 3834 y(The)f(second)g(argumen)m(t)h Fg(mo)s(de)k Fk(m)m(ust)30 b(b)s(e)g(an)g(in)m(teger)i(corresp)s (onding)e(to)390 4014 y(0)h(=)f(GSL_PREC_DOUBLE)870 4124 y(Double-precision,)i(a)e(relativ)m(e)j(accuracy)e(of)g(appro)m (ximately)h Ff(2)e(*)g(10^-16)p Fk(.)390 4297 y(1)h(=)f (GSL_PREC_SINGLE)870 4407 y(Single-precision,)h(a)g(relativ)m(e)i (accuracy)e(of)g(appro)m(ximately)h Ff(10^-7)p Fk(.)390 4580 y(2)f(=)f(GSL_PREC_APPR)m(O)m(X)870 4690 y(Appro)m(ximate)h(v)-5 b(alues,)31 b(a)g(relativ)m(e)h(accuracy)g(of)e(appro)m(ximately)i Ff(5)e(*)g(10^-4)p Fk(.)390 4870 y Fg(err)36 b Fk(con)m(tains)c(an)e (estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 5018 y(This)19 b(function)h(is)h(from)f (the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 5038 V 390 5128 a Fk(for)30 b(do)s(cumen)m(tation.)275 5340 y(\037airy_Bi_deriv_scaled)i(-*-)f(texinfo)g(-*-)p eop end %%Page: 48 48 TeXDict begin 48 47 bop 2960 299 a Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(airy_Bi_deriv_scaled)e Fi(\()p Fh(x)p Fg(,)31 b Fh(mode)12 b Fi(\))2960 408 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(airy_Bi_deriv_scaled)e Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 518 y Fk(These)30 b(routines)g(compute)h(the)g(deriv)-5 b(ativ)m(e)32 b(of)e(the)h (scaled)g(Airy)f(function)g(S_B\(x\))h(Bi\(x\).)390 653 y(The)f(second)g(argumen)m(t)h Fg(mo)s(de)k Fk(m)m(ust)30 b(b)s(e)g(an)g(in)m(teger)i(corresp)s(onding)e(to)390 813 y(0)h(=)f(GSL_PREC_DOUBLE)870 923 y(Double-precision,)i(a)e (relativ)m(e)j(accuracy)e(of)g(appro)m(ximately)h Ff(2)e(*)g(10^-16)p Fk(.)390 1083 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b(second)g(argumen)m(t)h Fg(mo)s(de)k Fk(m)m(ust)30 b(b)s(e)g(an)g(in)m(teger)i(corresp)s (onding)e(to)390 1213 y(0)h(=)f(GSL_PREC_DOUBLE)870 1322 y(Double-precision,)i(a)e(relativ)m(e)j(accuracy)e(of)g(appro)m (ximately)h Ff(2)e(*)g(10^-16)p Fk(.)390 1485 y(1)h(=)f (GSL_PREC_SINGLE)870 1594 y(Single-precision,)h(a)g(relativ)m(e)i (accuracy)e(of)g(appro)m(ximately)h Ff(10^-7)p Fk(.)390 1757 y(2)f(=)f(GSL_PREC_APPR)m(O)m(X)870 1866 y(Appro)m(ximate)h(v)-5 b(alues,)31 b(a)g(relativ)m(e)h(accuracy)g(of)e(appro)m(ximately)i Ff(5)e(*)g(10^-4)p Fk(.)390 2030 y Fg(err)36 b Fk(con)m(tains)c(an)e (estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 2168 y(This)19 b(function)h(is)h(from)f (the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 2188 42 84 v 390 2277 a Fk(for)30 b(do)s(cumen)m(tation.)275 2468 y(\037airy_zero_Ai)i(-*-)f(texinfo)g(-*-)2960 2658 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 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b(routines)g(compute)h(the)g(lo)s (cation)h(of)e(the)h(s-th)f(zero)h(of)g(the)f(Airy)h(function)f (Bi\(x\).)390 3999 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f (the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 4136 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 4157 V 390 4246 a Fk(for)30 b(do)s(cumen)m(tation.)275 4436 y(\037airy_zero_Ai_deriv)i(-*-)f(texinfo)g(-*-)2960 4627 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(airy_zero_Ai_deriv)e Fi(\()p Fh(n)12 b Fi(\))2960 4736 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(airy_zero_Ai_deriv)e Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 4846 y Fk(These)33 b(routines)f(compute)h(the)g(lo)s(cation)i(of)e(the)g(s-th)g(zero)g(of) g(the)g(Airy)g(function)f(deriv)-5 b(ativ)m(e)390 4955 y(Ai\(x\).)390 5093 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f (the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 5230 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 5251 V 390 5340 a Fk(for)30 b(do)s(cumen)m(tation.)p eop end %%Page: 50 50 TeXDict begin 50 49 bop 275 299 a Fk(\037airy_zero_Bi_deriv)32 b(-*-)f(texinfo)g(-*-)2960 488 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(airy_zero_Bi_deriv)e Fi(\()p Fh(n)12 b Fi(\))2960 597 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(airy_zero_Bi_deriv) e Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 707 y Fk(These)33 b(routines)f(compute)h(the)g(lo)s(cation)i(of)e(the)g(s-th)g(zero)g(of) g(the)g(Airy)g(function)f(deriv)-5 b(ativ)m(e)390 817 y(Bi\(x\).)390 953 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f (the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 1090 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 1110 42 84 v 390 1200 a Fk(for)30 b(do)s(cumen)m(tation.)275 1389 y(\037b)s(essel_zero_J0)h(-*-)g(texinfo)g(-*-)2960 1578 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(bessel_zero_J0)c Fi(\()p Fh(n)12 b Fi(\))2960 1687 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_zero_J0)d Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 1797 y Fk(These)34 b(routines)g(compute)g(the)g(lo)s(cation)i(of)e(the)g(s-th)g(p)s (ositiv)m(e)h(zero)g(of)f(the)g(Bessel)h(function)390 1906 y(J_0\(x\).)390 2043 y Fg(err)h Fk(con)m(tains)c(an)e(estimate)i (of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 2180 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 2200 V 390 2290 a Fk(for)30 b(do)s(cumen)m(tation.)275 2479 y(\037b)s(essel_zero_J1)h(-*-)g(texinfo)g(-*-)2960 2667 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(bessel_zero_J1)c Fi(\()p Fh(n)12 b Fi(\))2960 2777 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_zero_J1)d Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 2887 y Fk(These)34 b(routines)g(compute)g(the)g(lo)s(cation)i(of)e(the)g(s-th)g(p)s (ositiv)m(e)h(zero)g(of)f(the)g(Bessel)h(function)390 2996 y(J_1\(x\).)390 3133 y Fg(err)h Fk(con)m(tains)c(an)e(estimate)i (of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 3270 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 3290 V 390 3379 a Fk(for)30 b(do)s(cumen)m(tation.)275 3568 y(\037psi_1_in)m(t)h(-*-)g(texinfo)g(-*-)2960 3757 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(psi_1_int)48 b Fi(\()p Fh(n)12 b Fi(\))2960 3867 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(psi_1_int)48 b Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 3977 y Fk(These)30 b(routines)g(compute)h(the)g(T)-8 b(rigamma)31 b(function)f(psi\(n\))g(for)g(p)s(ositiv)m(e)h(in)m(teger) h(n.)390 4113 y Fg(err)k Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 4250 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o (re/g)o(sl/)p 3977 4270 V 390 4360 a Fk(for)30 b(do)s(cumen)m(tation.) 275 4549 y(\037zeta_in)m(t)i(-*-)f(texinfo)g(-*-)2960 4738 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(zeta_int)48 b Fi(\()p Fh(n)12 b Fi(\))2960 4847 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(zeta_int)48 b Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 4957 y Fk(These)30 b(routines)g(compute)h(the)g(Riemann)f(zeta)i(function)e(zeta\(n\))i (for)e(in)m(teger)i(n,)e(n)g(e)g(1.)390 5094 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g (the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 5230 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 5251 V 390 5340 a Fk(for)30 b(do)s(cumen)m(tation.)p eop end %%Page: 51 51 TeXDict begin 51 50 bop 275 299 a Fk(\037eta_in)m(t)32 b(-*-)f(texinfo)g(-*-)2960 459 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(eta_int)47 b Fi(\()p Fh(n)12 b Fi(\))2960 569 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(eta_int)47 b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 678 y Fk(These)30 b(routines)g(compute)h(the)g(eta)g(function)f(eta\(n\))i(for)e(in)m (teger)i(n.)390 805 y Fg(err)k Fk(con)m(tains)c(an)e(estimate)i(of)f (the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 931 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h (Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff (http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 951 42 84 v 390 1041 a Fk(for)30 b(do)s(cumen)m(tation.)275 1201 y(\037legendre_Plm)g(-*-)i(texinfo)f(-*-)2960 1361 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(legendre_Plm)c Fi(\()p Fh(n)p Fg(,)31 b Fh(m)p Fg(,)g Fh(x)12 b Fi(\))2960 1471 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(legendre_Plm)c Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 1580 y Fk(These)32 b(routines)g(compute)h(the)g(asso)s(ciated)g(Legendre)g(p)s(olynomial)f (P_l)p Ff(^)p Fk(m\(x\))h(for)f(m)h Ff(>)p Fk(=)e(0,)j(l)390 1690 y Ff(>)p Fk(=)c(m,)g Ff(|)p Fk(x)p Ff(|)g(<)p Fk(=)g(1.)390 1816 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 1943 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o (re/g)o(sl/)p 3977 1963 V 390 2052 a Fk(for)30 b(do)s(cumen)m(tation.) 275 2212 y(\037legendre_sphPlm)f(-*-)i(texinfo)g(-*-)2960 2373 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53 b(legendre_sphPlm)d Fi(\()p Fh(n)p Fg(,)31 b Fh(m)p Fg(,)g Fh(x)12 b Fi(\))2960 2482 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(legendre_sphPlm)d Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 2592 y Fk(These)101 b(routines)g(compute)g(the)g (normalized)h(asso)s(ciated)h(Legendre)e(p)s(olynomial)390 2701 y($sqrt)p Ff({)p Fk(\(2l+1\)/\(4pi\))p Ff(})61 b Fk(sqrt)p Ff({)p Fk(\(l-m\)!/\(l+m\)!)p Ff(})f Fk(P_l)p Ff(^)p Fk(m\(x\)$)g(suitable)f(for)f(use)g(in)h(spherical)390 2811 y(harmonics.)40 b(The)28 b(parameters)i(m)m(ust)e(satisfy)i(m)e Ff(>)p Fk(=)g(0,)i(l)f Ff(>)p Fk(=)f(m,)i Ff(|)p Fk(x)p Ff(|)e(<)p Fk(=)g(1.)41 b(Theses)28 b(routines)390 2921 y(a)m(v)m(oid)k(the)e(o)m(v)m(er\015o)m(ws)i(that)f(o)s(ccur)f(for)g (the)h(standard)f(normalization)i(of)e(P_l)p Ff(^)p Fk(m\(x\).)390 3047 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g (absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 3173 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m (ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o (re/g)o(sl/)p 3977 3194 V 390 3283 a Fk(for)30 b(do)s(cumen)m(tation.) 275 3443 y(\037h)m(yp)s(erg_U)f(-*-)j(texinfo)f(-*-)2960 3603 y([Loadable)g(F)-8 b(unction])-3599 b Fh(out)65 b Fj(=)52 b(hyperg_U)c Fi(\()p Fh(x0)p Fg(,)32 b Fh(x1)p Fg(,)f Fh(x2)12 b Fi(\))2960 3713 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(out)p Fj(,)54 b Fh(err)12 b Fj(])53 b(=)f(hyperg_U)c Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 3823 y Fk(Secondary)28 b(Con\015uen)m(t)g(Hyp)s(ergo)s (emetric)h(U)g(function)f(A&E)g(13.1.3)i(All)f(input)f(are)h(double)f (as)390 3932 y(is)i(the)h(output.)390 4059 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g (the)g(v)-5 b(alue)31 b Fg(out)p Fk(.a.)390 4185 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 4205 V 390 4295 a Fk(for)30 b(do)s(cumen)m(tation.)275 4455 y(\037h)m(yp)s(erg_1F1)h(-*-)g(texinfo)g(-*-)2960 4615 y([Loadable)g(F)-8 b(unction])-3599 b Fh(out)65 b Fj(=)52 b(hyperg_1F1)d Fi(\()p Fh(x0)p Fg(,)31 b Fh(x1)p Fg(,)h Fh(x2)12 b Fi(\))2960 4725 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(out)p Fj(,)54 b Fh(err)12 b Fj(])53 b(=)f(hyperg_1F1)d Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 4834 y Fk(Primary)32 b(Con\015uen)m(t)f(Hyp)s(ergo)s (emetric)j(U)e(function)g(A&E)g(13.1.3)j(All)e(inputs)e(are)i(double)f (as)390 4944 y(is)e(the)h(output.)390 5070 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g (the)g(v)-5 b(alue)31 b Fg(out)p Fk(.a.)390 5197 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 5217 V 390 5306 a Fk(for)30 b(do)s(cumen)m(tation.)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF gsl-1.0.8/doc/gsl_sf.dvi0000644000175000017500000045545411201030403012642 0ustar shsh÷ƒ’À;è TeX output 2008.06.20:1545‹ÿÿÿÿŸòŽ ƒ3* ý ÌÖ‘!Gó2Kñ`y ó3 cmr10Ýgsl_sf–¦f-*-“texinfo“-*-Ž©íD’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gó=ßêto“the˜GNU–W)Scien²!ti c˜Library‘ÿe.‘ÃzAll˜GSL“functions˜can–W=bMÞe˜called“withŽ¡‘.ùœbš²!y–¦fthe“GSL“names“within“oMÞcta˜v˜e.ŽŸíE‘!Gclausen–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gó>ßêÝ=‘¦f0.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸC‘!GSi–¦f-*-“texinfo“-*-ŽŸC’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉSi‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“Si‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“Sine“inš²!tegral“Si(x)“=“in˜t_0Þ^Ýx“dt“sin(t)/t.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ»$‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸC‘!GCi–¦f-*-“texinfo“-*-ŽŽŒ‹/BŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉCi‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“Ci‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Qroutines›Qcompute“the“Cosine“in²!tegral˜Ci(x)“=“-in•²!t_xÞ^Ýinft“y˜dt–Qcos(t)/t“for“x˜Þ>“Ý0.Ž¤ä’‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž© 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤•ñ‘!Gatanin²!t–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉatanint‘yšâ(éx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“atanint‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–@routines“compute“the“Arctangenš²!t“in˜tegral‘@A˜tanIn˜t(x)“=“in˜t_0Þ^Ýx“dt“arctan(t)/t.Ž¤ä’‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤•ñ‘!Gfermi_dirac_mhalf–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉfermi_dirac_mhalf‘yšâ(éx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“fermi_dirac_mhalf‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“complete“F‘ÿeermi-Dirac“in²!tegral“F_Þ{Ý-1/2Þ}Ý(x).Ž¤ä’‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤•ñ‘!Gfermi_dirac_half–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉfermi_dirac_half‘yšâ(éx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“fermi_dirac_half‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“complete“F‘ÿeermi-Dirac“in²!tegral“F_Þ{Ý1/2Þ}Ý(x).Ž¤ä’‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤•ñ‘!Gfermi_dirac_3half–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉfermi_dirac_3half‘yšâ(éx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“fermi_dirac_3half‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“complete“F‘ÿeermi-Dirac“in²!tegral“F_Þ{Ý3/2Þ}Ý(x).Ž¤ä’‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ•ñ‘!Ggamma_gsl–¦f-*-“texinfo“-*-ŽŽŒ‹9|ŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉgamma_gsl‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“gamma_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–garoutines›gbcompute“the“Gamma“function˜Gamma(x),‘— sub‘›»ject“to“x“not˜bMÞeing“aŽ¡‘.ùœnegativ•²!e›¿in“teger.‘ çThe˜function–¾is˜computed˜using˜the“real˜Lanczos˜methoMÞd.‘ çTheŽ¡‘.ùœmaxim²!um–]v‘ÿdDalue›\of“x˜suc²!h“that˜Gamma(x)“is“not˜considered“an˜o•²!v“er o“w‘]is˜giv“en‘]b“yŽ¡‘.ùœthe–¦fmacro“GSL_SF_GAMMA_XMAX“and“is“171.0.Ž©¹™‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ¹š‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ?ÿ‘!Glngamma_gsl–¦f-*-“texinfo“-*-ŽŸ@’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlngamma_gsl‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“lngamma_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–gžroutines“compute›gthe“logarithm“of“the“Gamma˜function,‘t-log(Gamma(x)),‘t,sub-Ž¡‘.ùœject–£¾to“x›£½not“a“bMÞeing“negativ•²!e˜in“teger.‘ÕåF‘ÿeor˜xÞ<Ý0–£¾the“real“part˜of“log(Gamma(x))“isŽ¡‘.ùœreturned,‘rwhic•²!h›ðÖis‘ðÕequiv‘ÿdDalen“t˜to˜log(Þ|ÝGamma(x)Þ|Ý).‘½-The‘ðÕfunction˜is˜computed˜usingŽ¡‘.ùœthe–¦freal“Lanczos“methoMÞd.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ¹š‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ?ÿ‘!Ggammastar–¦f-*-“texinfo“-*-ŽŸ@’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉgammastar‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“gammastar‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–oÙroutines›oÚcompute“the“regulated“Gamma˜F‘ÿeunction“GammaÞ^Ý*(x)“for“x˜Þ>“Ý0.‘Ë®TheŽ¡‘.ùœregulated–¦fgamma“function“is“givš²!en“b˜y‘ÿe,Ž¦‘.ùœGammaÞ^Ý*(x)–ƒ<=›ƒ;Gamma(x)/(sqrtÞ{Ý2piÞ}“ÝxÞ^{Ý(x-1/2)Þ}“Ýexp(-x))“=˜(1“+“(1/12x)˜+“...)Ž¡‘.ùœfor–¦fx“to“inft²!yŽŸ¹š‘.ùœand–¦fis“a“useful“suggestion“of“T‘ÿeemme.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤@‘!Ggammain²!v_gsl–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉgammainv_gsl‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“gammainv_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¤5routines›¤4compute“the˜reciproMÞcal“of˜the“gamma“function,‘ã§1/Gamma(x)“usingŽ¡‘.ùœthe–¦freal“Lanczos“methoMÞd.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ@‘!Glam²!bMÞert_W0–¦f-*-“texinfo“-*-ŽŽŒ‹DñŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlambert_W0‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“lambert_W0‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦fcompute“the“principal“brancš²!h“of“the“Lam˜bMÞert“W“function,“W_0(x).Ž©¹™‘.ùœLam²!bMÞert's›Œ³W‘Œ6functions,–FW(x),“are˜de ned˜to˜bMÞe˜solutions‘Œ´of˜the˜equation˜W(x)Ž¡‘.ùœexp(W(x))–b£=“x.‘ “This“function“has‘b¢mš²!ultiple“branc˜hes“for“x‘b¢Þ<“Ý0;‘@Áho˜w˜ev˜er,‘ѱit“hasŽ¡‘.ùœonly›ct•²!w“o˜real-v‘ÿdDalued˜branc“hes.‘3ÓW‘ÿee˜de ne˜W_0(x)˜to˜bMÞe‘bthe˜principal˜branc“h,‘4âwhereŽ¡‘.ùœW‘}!Þ>–}+Ý-1“for“x“Þ<“Ý0,›…jand“W_Þ{Ý-1Þ}Ý(x)“to“bMÞe“the“other“real“branc²!h,˜where“W‘}!Þ<“Ý-1“for“x“Þ<“Ý0.ŽŸ¹š‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ@‘!Glam²!bMÞert_Wm1–¦f-*-“texinfo“-*-ŽŸ?ÿ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlambert_Wm1‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“lambert_Wm1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–:Bcompute“the“secondary‘:Areal-v‘ÿdDalued“brancš²!h“of“the“Lam˜bMÞert“W‘:function,‘_9W_Þ{Ý-Ž¡‘.ùœ1Þ}Ý(x).ŽŸ¹š‘.ùœLam²!bMÞert's›Œ³W‘Œ6functions,–FW(x),“are˜de ned˜to˜bMÞe˜solutions‘Œ´of˜the˜equation˜W(x)Ž¡‘.ùœexp(W(x))–b£=“x.‘ “This“function“has‘b¢mš²!ultiple“branc˜hes“for“x‘b¢Þ<“Ý0;‘@Áho˜w˜ev˜er,‘ѱit“hasŽ¡‘.ùœonly›ct•²!w“o˜real-v‘ÿdDalued˜branc“hes.‘3ÓW‘ÿee˜de ne˜W_0(x)˜to˜bMÞe‘bthe˜principal˜branc“h,‘4âwhereŽ¡‘.ùœW‘}!Þ>–}+Ý-1“for“x“Þ<“Ý0,›…jand“W_Þ{Ý-1Þ}Ý(x)“to“bMÞe“the“other“real“branc²!h,˜where“W‘}!Þ<“Ý-1“for“x“Þ<“Ý0.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤@‘!Glog_1plusx–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlog_1plusx‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“log_1plusx‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–žkroutines“compute“log(1“+›žlx)“for“x“Þ>“Ý-1“using“an“algorithm˜that“is“accurate“forŽ¡‘.ùœsmall‘¦fx.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤@‘!Glog_1plusx_mx–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlog_1plusx_mx‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“log_1plusx_mx‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ŸYroutines›ŸXcompute“log(1˜+“x)“-˜x“for˜x“Þ>˜Ý-1“using“an˜algorithm“that˜is“accurateŽ¡‘.ùœfor–¦fsmall“x.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ@‘!Gpsi–¦f-*-“texinfo“-*-ŽŽŒ‹ QCŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉpsi‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“psi‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“digamma“function“psi(x)“for“general“x,“x“e“0.Ž¤úœ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž© 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤‰n‘!Gpsi_1piy–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉpsi_1piy‘yšâ(éx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“psi_1piy‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–è6routines“compute“the“real“part“of“the“digamma“function“on“the“line“1+i“y‘ÿe,Ž¦‘.ùœRe[psi(1–¦f+“i“y)].ŽŸúœ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸú‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¡‘!Gsync²!hrotron_1–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉsynchrotron_1‘yšâ(éx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“synchrotron_1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–GCroutines“compute‘GDthe“ rst“syncš²!hrotron“function“x“in˜t_xÞ^Ýinft˜y‘GDdt“K_Þ{Ý5/3Þ}Ý(t)“forŽ¦‘.ùœx–¦fÞ>Ý=“0.Ž¤úœ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤‰n‘!Gsync²!hrotron_2–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉsynchrotron_2‘yšâ(éx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“synchrotron_2‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“second“sync²!hrotron“function“x“K_Þ{Ý2/3Þ}Ý(x)“for“x“Þ>Ý=“0.Ž¤úœ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ‰o‘!GtranspMÞort_2–¦f-*-“texinfo“-*-ŽŸ‰n’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉtransport_2‘yšâ(éx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“transport_2‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“transpMÞort“function“J(2,x).Ž¡‘.ùœThe–üztranspMÞort›üyfunctions“J(n,x)“are“de ned˜bš²!y“the“in˜tegral“represen˜tations‘üyJ(n,x)“:=Ž¦‘.ùœin²!t_0Þ^Ýx–¦fdt“tÞ^Ýn“eÞ^Ýt“/(eÞ^Ýt“-“1)Þ^Ý2.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ‰n‘!GtranspMÞort_3–¦f-*-“texinfo“-*-ŽŽŒ‹ ^0ŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉtransport_3‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“transport_3‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“transpMÞort“function“J(3,x).Ž©²‚‘.ùœThe–üztranspMÞort›üyfunctions“J(n,x)“are“de ned˜bš²!y“the“in˜tegral“represen˜tations‘üyJ(n,x)“:=Ž¡‘.ùœin²!t_0Þ^Ýx–¦fdt“tÞ^Ýn“eÞ^Ýt“/(eÞ^Ýt“-“1)Þ^Ý2.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ±‘!GtranspMÞort_4–¦f-*-“texinfo“-*-ŽŸ± ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉtransport_4‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“transport_4‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“transpMÞort“function“J(4,x).ŽŸ²‘.ùœThe–üztranspMÞort›üyfunctions“J(n,x)“are“de ned˜bš²!y“the“in˜tegral“represen˜tations‘üyJ(n,x)“:=Ž¡‘.ùœin²!t_0Þ^Ýx–¦fdt“tÞ^Ýn“eÞ^Ýt“/(eÞ^Ýt“-“1)Þ^Ý2.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ± ‘!GtranspMÞort_5–¦f-*-“texinfo“-*-ŽŸ±’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉtransport_5‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“transport_5‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“transpMÞort“function“J(5,x).Ž¦‘.ùœThe–üztranspMÞort›üyfunctions“J(n,x)“are“de ned˜bš²!y“the“in˜tegral“represen˜tations‘üyJ(n,x)“:=Ž¡‘.ùœin²!t_0Þ^Ýx–¦fdt“tÞ^Ýn“eÞ^Ýt“/(eÞ^Ýt“-“1)Þ^Ý2.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ±‘!Gsinc_gsl–¦f-*-“texinfo“-*-ŽŸ± ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉsinc_gsl‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“sinc_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“sinc(x)“=“sin(pi“x)“/“(pi“x)“for“an²!y“v‘ÿdDalue“of“x.ŽŸ²‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ± ‘!Glnsinh–¦f-*-“texinfo“-*-ŽŸ±’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlnsinh‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“lnsinh‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“log(sinh(x))“for“x“Þ>“Ý0.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹ j:ŸòŽ ƒ3* ý ÌÖ‘!GÝlncosh–¦f-*-“texinfo“-*-Ž©Rµ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlncosh‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“lncosh‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“log(cosh(x))“for“an²!y“x.Ž¤è^‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gzeta–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉzeta‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“zeta‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“Riemann“zeta“function“zeta(s)“for“arbitrary“s,“s“e“1.Ž©è^‘.ùœThe–b¨Riemann›b©zeta“function˜is“de ned“b²!y˜the“in nite˜sum“zeta(s)˜=“sum_Þ{Ýk=1Þ}^Ýinft²!yŽ¡‘.ùœkÞ^{Ý-sÞ}Ý.ŽŸè_‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Rµ‘!Geta–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉeta‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“eta‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“eta“function“eta(s)“for“arbitrary“s.Ž¦‘.ùœThe–¦feta“function“is“de ned“b²!y“eta(s)“=“(1-2Þ^{Ý1-sÞ}Ý)“zeta(s).Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Rµ‘!GbMÞessel_Jn–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_Jn‘yšâ(éná,‘¦féx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_Jn‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“regular“cylindrical“Bessel“function“of“order“n,“J_n(x).Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž©è_‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸRµ‘!GbMÞessel_Yn–¦f-*-“texinfo“-*-ŽŸR´’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_Yn‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_Yn‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–&Üroutines›&Ýcompute“the“irregular˜cylindrical“Bessel“function˜of“order“n,‘FúY_n(x),Ž¡‘.ùœfor‘¦fxÞ>Ý0.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸè^‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹ v¹ŸòŽ ƒ3* ý ÌÖ‘!GÝbMÞessel_In–¦f-*-“texinfo“-*-Ž©’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_In‘yšâ(éná,‘¦féx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_In‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–?ºroutines›?¹compute“the“regular˜moMÞdi ed“cylindrical˜Bessel“function“of˜order“n,Ž¡‘.ùœI_n(x).Ž¤™™‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_In_scaled–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_In_scaled‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_In_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–8©routines›8¨compute“the˜scaled“regular˜moMÞdi ed“cylindrical˜Bessel“function˜ofŽ¡‘.ùœorder–¦fn,“exp(-Þ|ÝxÞ|Ý)“I_n(x)Ž¤™™‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_Kn–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_Kn‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_Kn‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–• routines›•!compute“the“irregular“moMÞdi ed˜cylindrical“Bessel“function“of˜order“n,Ž¡‘.ùœK_n(x),–¦ffor“x“Þ>“Ý0.Ž¤™™‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_Kn_scaled–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_Kn_scaled‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_Kn_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ™™‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_jl–¦f-*-“texinfo“-*-ŽŸÿÿ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_jl‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_jl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–>qroutines“compute“the‘>pregular“spherical“Bessel“function“of“order“l,–dsj_l(x),“for‘>qlŽ¡‘.ùœÞ>Ý=–¦f0“and“x“Þ>Ý=“0.ŽŸ™š‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ™™‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹ ‚}ŸòŽ ƒ3* ý ÌÖ‘!GÝbMÞessel_yl–¦f-*-“texinfo“-*-Ž©å`’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_yl‘yšâ(éná,‘¦féx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_yl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–‚íroutines“compute“the“irregular“spherical“Bessel“function“of“order“l,–Šy_l(x),“for‘‚ílŽ¡‘.ùœÞ>Ý=‘¦f0.ŽŸ I‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ J‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_il_scaled–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_il_scaled‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_il_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–(Òroutines›(Ócompute“the“scaled“regular˜moMÞdi ed“spherical“Bessel“function˜of“orderŽ¡‘.ùœl,–¦fexp(-Þ|ÝxÞ|Ý)“i_l(x)Ž¤ I‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_kl_scaled–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_kl_scaled‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_kl_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–>routines“compute“the“scaled“irregular“moMÞdi ed“spherical“Bessel“function“ofŽ¡‘.ùœorder–¦fl,“exp(x)“k_l(x),“for“xÞ>Ý0.ŽŸ J‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ I‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gexprel_n–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉexprel_n‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“exprel_n‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–“routines“compute“the“N-relativš²!e“expMÞonen˜tial,‘Ÿwhic˜h“is“the“n-th“generalizationŽ¡‘.ùœof–b÷the›bøfunctions“gsl_sf_exprel“and˜gsl_sf_exprel2.‘‘The“N-relativš²!e“expMÞonen˜tial‘bøis“giv˜enŽ¡‘.ùœb²!y‘ÿe,Ž© I‘.ùœexprel_N(x)–ÇF=“N!/xÞ^ÝN‘ƺ(exp(x)“-“sum_Þ{Ýk=0Þ}^{ÝN-1Þ}“ÝxÞ^Ýk/k!)‘ @}=“1“+“x/(N+1)“+Ž¡‘.ùœxÞ^Ý2/((N+1)(N+2))–¦f+“...‘ÝÝ=“1F1“(1,1+N,x)ŽŸ J‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸå`‘!Gfermi_dirac_in²!t–¦f-*-“texinfo“-*-ŽŽŒ‹Ž8ŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉfermi_dirac_int‘yšâ(éná,‘¦féx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“fermi_dirac_int‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–OÖroutines›O×compute“the˜complete“F‘ÿeermi-Dirac˜in²!tegral“with˜an“in²!teger˜index“of˜j,Ž¡‘.ùœF_j(x)–¦f=“(1/Gamma(j+1))“in•²!t_0Þ^Ýinft“y–¦fdt“(tÞ^Ýj“/(exp(t-x)+1)).Ž¤ó3‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž© 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤³3‘!Gta²!ylorcoMÞe –¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉtaylorcoeff‘yšâ(éná,‘¦féx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“taylorcoeff‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“T‘ÿeaš²!ylor“coMÞecien˜t“xÞ^Ýn“/“n!‘ÝÝfor“x“Þ>Ý=“0,“n“Þ>Ý=“0.ŽŸó3‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸó2‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¡‘!Glegendre_Pl–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlegendre_Pl‘yšâ(éná,‘¦féx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“legendre_Pl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–Ojfunctions›Oiev‘ÿdDaluate“the“Legendre“pMÞolynomial˜P_l(x)“for“a˜spMÞeci c“v‘ÿdDalue“of“l,‘yªxŽ¦‘.ùœsub‘›»ject–¦fto“l“Þ>Ý=“0,“Þ|ÝxÞ|“<Ý=“1Ž¤ó3‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤³3‘!Glegendre_Ql–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlegendre_Ql‘yšâ(éná,‘¦féx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“legendre_Ql‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“Legendre“function“Q_l(x)“for“x“Þ>“Ý-1,“x“!=“1“and“l“Þ>Ý=“0.Ž¤ó3‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ³2‘!Gpsi_n–¦f-*-“texinfo“-*-ŽŸ³3’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉpsi_n‘yšâ(éná,‘¦féx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“psi_n‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“pMÞolygamma“function“psiÞ^{Ý(m)Þ}Ý(x)“for“m“Þ>Ý=“0,“x“Þ>“Ý0.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ³3‘!GbMÞessel_Jn²!u–¦f-*-“texinfo“-*-ŽŽŒ‹™HŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Jnu‘yšâ(éxá,‘¦féy‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Jnu‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Ukroutines“compute›Ujthe“regular“cylindrical“Bessel“function“of˜fractional“order“n²!u,Ž¡‘.ùœJ_u(x).Ž¤V¥‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž©z‘!GbMÞessel_Yn²!u–¦f-*-“texinfo“-*-ŽŸz’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Ynu‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Ynu‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–l¦routines›l¥compute“the˜irregular“cylindrical“Bessel˜function“of˜fractional“orderŽ¡‘.ùœn²!u,‘¦fY_u(x).Ž¤V¥‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_In²!u–¦f-*-“texinfo“-*-Ž©z’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Inu‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Inu‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Uroutines“compute“the“regular“moMÞdi ed‘TBessel“function“of“fractional“order“n²!u,Ž¡‘.ùœI_u(x)–¦ffor“xÞ>Ý0,“uÞ>Ý0.Ž¤V¥‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_In²!u_scaled–¦f-*-“texinfo“-*-ŽŸz’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Inu_scaled‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Inu_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Ü_routines›Ü^compute“the“scaled“regular˜moMÞdi ed“Bessel“function“of˜fractional“orderŽ¡‘.ùœn²!u,–¦fexp(-Þ|ÝxÞ|Ý)I_u(x)“for“xÞ>Ý0,“uÞ>Ý0.Ž¤V¥‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_Kn²!u–¦f-*-“texinfo“-*-ŽŸz’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Knu‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Knu‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–q¼routines›q»compute“the˜irregular“moMÞdi ed˜Bessel“function˜of“fractional˜order“n²!u,Ž¡‘.ùœK_u(x)–¦ffor“xÞ>Ý0,“uÞ>Ý0.Ž¤V¥‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™ŽŸ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹¥lŸòŽ ƒ3* ý ÌÖ‘!GÝbMÞessel_lnKn²!u–¦f-*-“texinfo“-*-Ž©Ã’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_lnKnu‘yšâ(éxá,‘¦féy‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_lnKnu‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Îroutines›Îcompute“the“logarithm“of˜the“irregular“moMÞdi ed“Bessel˜function“ofŽ¡‘.ùœfractional–¦forder“n²!u,“ln(K_u(x))“for“xÞ>Ý0,“uÞ>Ý0.Ž¤ Ö‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_Kn²!u_scaled–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Knu_scaled‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Knu_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–êroutines›êcompute“the“scaled˜irregular“moMÞdi ed“Bessel“function˜of“fractionalŽ¡‘.ùœorder–¦fn²!u,“exp(+Þ|ÝxÞ|Ý)“K_u(x)“for“xÞ>Ý0,“uÞ>Ý0.Ž¤ Ö‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gexp_m²!ult–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉexp_mult‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“exp_mult‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ò`routines›ò_expMÞonen²!tiate“x˜and“m•²!ultiply˜b“y–ò`the“factor˜y“to˜return“the˜proMÞduct“yŽ¡‘.ùœexp(x).Ž¤ Ö‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gfermi_dirac_inc_0–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉfermi_dirac_inc_0‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“fermi_dirac_inc_0‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–FÎroutines“compute“the“incomplete“F‘ÿeermi-Dirac‘FÏin²!tegral“with“an“index“of“zero,Ž¡‘.ùœF_0(x,b)–¦f=“ln(1“+“eÞ^{Ýb-xÞ}Ý)“-“(b-x).Ž¤ Ö‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gp•MÞo“c²!h–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉpoch‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“poch‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“P•²!ošMÞc“hhammer‘¦fsym“b˜olŽ¤ Ö‘.ùœ(a)_x–¦f:=“Gamma(a“+“x)/Gamma(a),Ž¡‘.ùœsub‘›»ject–to›a“and“a+x˜not“bMÞeing“negativ•²!e˜in“tegers.‘AàThe›P“oMÞc“hhammer˜sym“bMÞol‘is˜alsoŽŸ 33‘.ùœknoš²!wn–¦fas“the“ApMÞell“sym˜bMÞol.ŽŽŒ‹±ªŸòŽ ƒ3* ý ÌÖ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ“é‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž© 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ôŸ‘!Glnp•MÞo“c²!h–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉlnpoch‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“lnpoch‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–Ò-routines›Ò.compute“the“logarithm˜of“the“P•²!ošMÞc“hhammer‘Ò-sym“b˜ol,‘]log((a)_x)‘Ò-=Ž¦‘.ùœlog(Gamma(a–¦f+“x)/Gamma(a))“for“a“Þ>“Ý0,“a+x“Þ>“Ý0.Ž¤“é‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ôŸ‘!Gp•MÞo“c²!hrel–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉpochrel‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“pochrel‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–Kñroutines›Kòcompute“the˜relativš²!e“P˜oMÞc˜hhammer“sym˜bMÞol›Kò((a,x)“-˜1)/x“where˜(a,x)“=Ž¦‘.ùœ(a)_x–¦f:=“Gamma(a“+“x)/Gamma(a).Ž¤“é‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸôž‘!Ggamma_inc_Q–¦f-*-“texinfo“-*-ŽŸôŸ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉgamma_inc_Q‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“gamma_inc_Q‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–~øroutines›~ùcompute“the“normalized˜incomplete“Gamma“F‘ÿeunction˜Q(a,x)“=Ž¦‘.ùœ1/Gamma(a)›¦fin•²!t_xinft“y˜dt˜tÞ^{Ýa-1Þ}˜Ýexp(-t)˜for˜a˜Þ>˜Ý0,˜x˜Þ>Ý=˜0.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ôŸ‘!Ggamma_inc_P–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉgamma_inc_P‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“gamma_inc_P‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–(ïroutines›(ðcompute“the“complemen²!tary˜normalized“incomplete˜Gamma“F‘ÿeunctionŽ¦‘.ùœP(a,x)–¦f=“1/Gamma(a)“in²!t_0Þ^Ýx“dt“tÞ^{Ýa-1Þ}“Ýexp(-t)“for“a“Þ>“Ý0,“x“Þ>Ý=“0.Ž¤“é‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸôŸ‘!Ggamma_inc–¦f-*-“texinfo“-*-ŽŽŒ‹½ØŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉgamma_inc‘yšâ(éxá,‘¦féy‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“gamma_inc‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–°functions›±compute“the“incomplete˜Gamma“F‘ÿeunction“the˜normalization“factorŽ¡‘.ùœincluded–Þ¦in›Þ¥the“previously˜de ned“functions:‘N\Gamma(a,x)˜=“in•²!t_xinft“y˜dt‘Þ¦tÞ^{Ýa-1Þ}Ž¡‘.ùœÝexp(-t)–¦ffor“a“real“and“x“Þ>Ý=“0.Ž¤V¥‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž©z‘!GbMÞeta_gsl–¦f-*-“texinfo“-*-ŽŸz’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbeta_gsl‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“beta_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–nïroutines“compute“the“Beta“F‘ÿeunction,‘­:B(a,b)“=“Gamma(a)Gamma(b)/Gamma(a+b)Ÿ¼Ì„ ó2Ž¡‘.ùœfor–¦fa“Þ>“Ý0,“b“Þ>“Ý0.Ž¤V¥‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gln²!bMÞeta–¦f-*-“texinfo“-*-Ž©z’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉlnbeta‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“lnbeta‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¸ûroutines“compute“the“logarithm“of‘¸úthe“Beta“F‘ÿeunction,›½ log(B(a,b))“for“a“Þ>“Ý0,˜bŽ¡‘.ùœÞ>‘¦fÝ0.Ž¤V¥‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gh²!ypMÞerg_0F1–¦f-*-“texinfo“-*-ŽŸz’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉhyperg_0F1‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“hyperg_0F1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“h²!ypMÞergeometric“function“0F1(c,x).Ž¤V¥‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GconicalP_half–¦f-*-“texinfo“-*-ŽŸz’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉconicalP_half‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“conicalP_half‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ÍÏroutines›ÍÎcompute“the˜irregular“Spherical“Conical˜F‘ÿeunction“PÞ^{Ý1/2Þ}Ý_Þ{Ý-1/2˜+“iŽ¡‘.ùœlam²!bMÞdaÞ}Ý(x)–¦ffor“x“Þ>“Ý-1.Ž¤V¥‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™ŽŸ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹ÉEŸòŽ ƒ3* ý ÌÖ‘!GÝconicalP_mhalf–¦f-*-“texinfo“-*-Ž©)’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉconicalP_mhalf‘yšâ(éxá,‘¦féy‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“conicalP_mhalf‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–,routines›,compute“the“regular“Spherical˜Conical“F‘ÿeunction“PÞ^{Ý-1/2Þ}Ý_Þ{Ý-1/2˜+“iŽ¡‘.ùœlam²!bMÞdaÞ}Ý(x)–¦ffor“x“Þ>“Ý-1.ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GconicalP_0–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉconicalP_0‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“conicalP_0‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“conical“function“PÞ^Ý0_Þ{Ý-1/2“+“i“lam²!bMÞdaÞ}Ý(x)“for“x“Þ>“Ý-1.ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GconicalP_1–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉconicalP_1‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“conicalP_1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“conical“function“PÞ^Ý1_Þ{Ý-1/2“+“i“lam²!bMÞdaÞ}Ý(x)“for“x“Þ>“Ý-1.ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Ghzeta–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉhzeta‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“hzeta‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“Hurwitz“zeta“function“zeta(s,q)“for“s“Þ>“Ý1,“q“Þ>“Ý0.ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gairy_Ai–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Ai‘yšâ(éxá,‘¦fémode‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Ai‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–cMroutines›cNcompute“the˜Airy“function˜Ai(x)“with˜an“accuracy˜spMÞeci ed“b²!y˜moMÞde.ŽŸ+„‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽ©#ב.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.Ž¦‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.ŽŽŒ‹Õ—ŸòŽ ƒ3* ý ÌÖ‘.ùœÝ2–¦f=“GSL_PREC_APPR•²!O“XŽ¤ 33‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.Ž©¶”‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸà‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ ‘!Gairy_Bi–¦f-*-“texinfo“-*-ŽŸ ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Bi‘yšâ(éxá,‘¦fémode‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Bi‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–m routines“compute“the›m Airy“function“Bi(x)“with“an“accuracy˜spšMÞeci ed“b²!y“mo˜de.ŽŸà‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸ¶•‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.ŽŸà‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.ŽŸà‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž©à‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ ‘!Gairy_Ai_scaled–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Ai_scaled‘yšâ(éxá,‘¦fémode‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Ai_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ßKroutines›ßLcompute“a“scaled“v²!ersion˜of“the“Airy“function˜S_A(x)“Ai(x).‘ˆF‘ÿeor“xÞ>Ý0Ž¡‘.ùœthe–¦fscaling“factor“S_A(x)“is“exp(+(2/3)“xÞ^Ý(3/2)),“and“is“1“for“xÞ<Ý0.Ž¦‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸ¶”‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.Ž©à‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸ¶”‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸà‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ ‘!Gairy_Bi_scaled–¦f-*-“texinfo“-*-ŽŽŒ‹áŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Bi_scaled‘yšâ(éxá,‘¦fémode‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Bi_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–îÞroutines“compute“a“scaled“v²!ersion“of“the‘îÝAiry“function“S_B(x)“Bi(x).‘·EF‘ÿeor“xÞ>Ý0Ž¡‘.ùœthe–¦fscaling“factor“S_B(x)“is“exp(-(2/3)“xÞ^Ý(3/2)),“and“is“1“for“xÞ<Ý0.ŽŸ Ö‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽ©èz‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.ŽŸèy‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸèy‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž© Ö‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Ã‘!Gairy_Ai_deriv–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Ai_deriv‘yšâ(éxá,‘¦fémode‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Ai_deriv‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Ýroutines›Ýcompute“the˜Airy“function˜deriv‘ÿdDativ²!e“Ai'(x)˜with“an˜accuracy“spMÞeci edŽ¡‘.ùœb²!y‘¦fmoMÞde.Ž¦‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽ©èz‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.ŽŸèy‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸèy‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž© Ö‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Ã‘!Gairy_Bi_deriv–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Bi_deriv‘yšâ(éxá,‘¦fémode‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Bi_deriv‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ç²routines›ç±compute“the“Airy“function˜deriv‘ÿdDativ²!e“Bi'(x)“with“an˜accuracy“spMÞeci edŽ¡‘.ùœb²!y‘¦fmoMÞde.Ž¦‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸèz‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.ŽŸèy‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.ŽŽŒ‹뵟òŽ ƒ3* ý ÌÖ‘.ùœÝ2–¦f=“GSL_PREC_APPR•²!O“XŽ¤ 33‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸ%-‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž©0‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Ë+‘!Gairy_Ai_deriv_scaled–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Ai_deriv_scaled‘yšâ(éxá,‘¦fémode‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Ai_deriv_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“deriv‘ÿdDativ²!e“of“the“scaled“Airy“function“S_A(x)“Ai(x).Ž¦‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸ%-‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.Ž©/‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸ%.‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž©/‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸË+‘!Gairy_Bi_deriv_scaled–¦f-*-“texinfo“-*-ŽŸË,’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Bi_deriv_scaled‘yšâ(éxá,‘¦fémode‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Bi_deriv_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“deriv‘ÿdDativ²!e“of“the“scaled“Airy“function“S_B(x)“Bi(x).Ž¦‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽ©%-‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.ŽŸ0‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.ŽŸ/‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ/‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸË,‘!Gellin²!t_Kcomp–¦f-*-“texinfo“-*-ŽŸË+’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉellint_Kcomp‘yšâ(éxá,‘¦fémode‘câ)ŽŽŒ‹öüŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“ellint_Kcomp‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¤ 33‘.ùœÝThese–¦froutines“compute“the“complete“elliptic“in²!tegral“K(k)ŽŸ!N£Ÿý b’¡Ró:  b> ó3 cmmi10åK‘ÈÝ(åkX?Ý)ŽŽ’½ì=‘ §Ÿò&»óú±u cmex10½ZŽŸôŸ‘ ¨ó 0e—rcmmi7´@L=óÙ“ Rcmr7®2ŽŸ@‘˜á0ŽŽŸø—ž‘@Ñ%ådtŽ‘“ÒŸÞȉfeP!ñŸ[rŸó¤‡½qŽ‘ Ÿó¤‡‰feF!ðŸ [yÝ(1–nìó;!",š ó3 cmsy10æ“åkX?ŸüÖ0®2Ž‘§ãÝsinŽ‘™Ÿû(¾®2Ž‘– Ý(åtÝ))ŽŽŽŽŽŽŽŽŽŽŽŸ ²é‘.ùœSee‘¦falso:Ž©÷‘.ùœellip‘›»j,‘¦fellipk²!eŽŸ÷‘.ùœThe–Æ«notation“used“here“is“based“on“Carlson,‘νáNumerisc²!he“Mathematik‘p¯Ý33“(1979)“andŽ¡‘.ùœdi ers–Ìûslighš²!tly“from“that“used“b˜y“Abramo˜witz“&“Stegun,‘øvwhere“the“functions“are“giv˜enŽ¡‘.ùœin–¦fterms“of“the“parameter“åm– §Ý=“åkX?Ÿü¾®2Ž‘Ô²Ý.Ž¦‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽ©» ‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.ŽŸ»‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž©÷‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ~ó‘!Gellin²!t_Ecomp–¦f-*-“texinfo“-*-ŽŸ~ô’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉellint_Ecomp‘yšâ(éxá,‘¦fémode‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“ellint_Ecomp‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Ùroutines“compute›Ùthe“complete“elliptic“in²!tegral“E(k)“to˜the“accuracy“spMÞeci edŽ¡‘.ùœb²!y–¦fthe“mošMÞde“v‘ÿdDariable“mo˜de.Ž¤÷Ÿ–iŸ#’ž`ÞåE‘¡’Ý(åkX?Ý)ŽŽ’¸²F=‘ §Ÿò&»½ZŽŸôŸ‘ ¨´@L=®2ŽŸ@‘˜á0ŽŽ‘`ŸŸóv½qŽ‘&` Ÿóv‰feF!ðŸ åŠÝ(1–nìæ“åkX?ŸüÖ0®2Ž‘§ãÝsinŽ‘™Ÿû(¾®2Ž‘– Ý(åtÝ))ŽŽŽ‘l‚ådtŽŽŽŽŽŸÇ'‘.ùœÝSee‘¦falso:Ž¡‘.ùœellip‘›»j,‘¦fellipk²!eŽ¦‘.ùœThe–Æ«notation“used“here“is“based“on“Carlson,‘νáNumerisc²!he“Mathematik‘p¯Ý33“(1979)“andŽ¤ 33‘.ùœdi ers–Ìûslighš²!tly“from“that“used“b˜y“Abramo˜witz“&“Stegun,‘øvwhere“the“functions“are“giv˜enŽ¡‘.ùœin–¦fterms“of“the“parameter“åm– §Ý=“åkX?Ÿü¾®2Ž‘Ô²Ý.Ž¦‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽ©» ‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.ŽŸ»‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŽŒ‹dŸòŽ ƒ3* ý ÌÖ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸC‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž© 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Rú‘!Gairy_zero_Ai–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_zero_Ai‘yšâ(én‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_zero_Ai‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“loMÞcation“of“the“s-th“zero“of“the“Airy“function“Ai(x).Ž¤C‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸRú‘!Gairy_zero_Bi–¦f-*-“texinfo“-*-ŽŸRû’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_zero_Bi‘yšâ(én‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_zero_Bi‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“loMÞcation“of“the“s-th“zero“of“the“Airy“function“Bi(x).ŽŸC‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸRú‘!Gairy_zero_Ai_deriv–¦f-*-“texinfo“-*-ŽŸRû’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_zero_Ai_deriv‘yšâ(én‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_zero_Ai_deriv‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–ñ¡routines“compute›ñ¢the“loMÞcation“of“the˜s-th“zero“of“the˜Airy“function“deriv‘ÿdDativ²!eŽ¦‘.ùœAi(x).ŽŸC‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸRú‘!Gairy_zero_Bi_deriv–¦f-*-“texinfo“-*-ŽŸRû’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_zero_Bi_deriv‘yšâ(én‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_zero_Bi_deriv‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–ñ¡routines“compute›ñ¢the“loMÞcation“of“the˜s-th“zero“of“the˜Airy“function“deriv‘ÿdDativ²!eŽ¦‘.ùœBi(x).Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸC‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸRû‘!GbMÞessel_zero_J0–¦f-*-“texinfo“-*-ŽŸRú’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_zero_J0‘yšâ(én‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_zero_J0‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–+routines“compute“the“lošMÞcation“of“the“s-th“p˜ositiv²!e“zero“of“the“Bessel“functionŽ¦‘.ùœJ_0(x).ŽŽŒ‹ ÓŸòŽ ƒ3* ý ÌÖ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸt#‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž© 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ö‘!GbMÞessel_zero_J1–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_zero_J1‘yšâ(én‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_zero_J1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–+routines“compute“the“lošMÞcation“of“the“s-th“p˜ositiv²!e“zero“of“the“Bessel“functionŽ¦‘.ùœJ_1(x).Ž¤t#‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ö‘!Gpsi_1_in²!t–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉpsi_1_int‘yšâ(én‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“psi_1_int‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“T‘ÿerigamma“function“psi(n)“for“pMÞositivš²!e“in˜teger“n.ŽŸt#‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸt"‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸö‘!Gzeta_in²!t–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉzeta_int‘yšâ(én‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“zeta_int‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“Riemann“zeta“function“zeta(n)“for“in²!teger“n,“n“e“1.ŽŸt#‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸt"‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¡‘!Geta_in²!t–¦f-*-“texinfo“-*-ŽŸö’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉeta_int‘yšâ(én‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“eta_int‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“eta“function“eta(n)“for“in²!teger“n.ŽŸt"‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸt#‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¡‘!Glegendre_Plm–¦f-*-“texinfo“-*-ŽŸö’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlegendre_Plm‘yšâ(éná,–¦fémá,“éx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“legendre_Plm‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–ãÎroutines“compute“the“assošMÞciated“Legendre“p˜olynomial‘ãÍP_lÞ^Ým(x)“for“m“Þ>Ý=“0,‘ó(lŽ¦‘.ùœÞ>Ý=–¦fm,“Þ|ÝxÞ|“<Ý=“1.ŽŸt"‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸt#‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹­ŸòŽ ƒ3* ý ÌÖ‘!GÝlegendre_sphPlm–¦f-*-“texinfo“-*-Ž©Ã’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlegendre_sphPlm‘yšâ(éná,–¦fémá,“éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“legendre_sphPlm‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese– *9routines“compute“the‘ *8normalized“assošMÞciated“Legendre“p˜olynomialŽ¡‘.ùœ$sqrtÞ{Ý(2l+1)/(4pi)Þ}– ØÝsqrtÞ{Ý(l-m)!/(l+m)!Þ}› ÙÝP_lÞ^Ým(x)$“suitable˜for“use˜in“sphericalŽ¡‘.ùœharmonics.‘ÎUThe–wÎparameters›wÍm²!ust“satisfy˜m“Þ>Ý=“0,‘l˜Þ>Ý=“m,‘Þ|ÝxÞ|“<Ý=˜1.‘ÎUTheses“routinesŽ¡‘.ùœa•²!v“oid–¦fthe“o•²!v“er o“ws–¦fthat“oMÞccur“for“the“standard“normalization“of“P_lÞ^Ým(x).Ž¤ Ö‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gh²!ypMÞerg_U–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géout‘°Yè=‘LÉhyperg_U‘yšâ(éx0á,–¦féx1á,“éx2‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éoutè,–LÉéerr‘cè]“=“hyperg_U‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝSecondary›M‰Con uen²!t‘MˆHyp•MÞergo“emetric˜U‘M]function˜A&E‘M^13.1.3–MˆAll˜inputs“are˜doubleŽ¡‘.ùœas–¦fis“the“output.Ž¤ Ö‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áoutÝ.a.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gh²!ypMÞerg_1F1–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géout‘°Yè=‘LÉhyperg_1F1‘yšâ(éx0á,–¦féx1á,“éx2‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éoutè,–LÉéerr‘cè]“=“hyperg_1F1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝPrimary–ã¶Con uen²!t“Hyp•MÞergo“emetric›ã·U‘ã¦function–ã¶A&E‘ã§13.1.3“All“inputs˜are“double“asŽ¡‘.ùœis–¦fthe“output.Ž¤ Ö‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áoutÝ.a.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Ggsl_sf–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gègsl_sf‘yšâ()Ž¡‘.ùœÝOcta•²!v“e–W=bindings›W>to“the˜GNU–W)Scien²!ti c˜Library‘ÿe.‘ÃzAll˜GSL“functions˜can–W=bMÞe˜called“withŽ¡‘.ùœbš²!y–¦fthe“GSL“names“within“oMÞcta˜v˜e.ŽŸÃ‘!Gclausen–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉclausen‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“clausen‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThe–¦fClausen“function“is“de ned“bš²!y“the“follo˜wing“in˜tegral,Ž¤ Ö‘.ùœCl_2(x)–¦f=“-“in²!t_0Þ^Ýx“dt“log(2“sin(t/2))ŽŸ ב.ùœIt–¦fis“related“to“the“dilogarithm“b²!y“Cl_2(theta)“=“Im“Li_2(exp(i“theta)).Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™ŽŸ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹%-ŸòŽ ƒ3* ý ÌÖ‘!GÝda²!wson–¦f-*-“texinfo“-*-Ž©G®’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉdawson‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“dawson‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThe›šÊDa•²!wson‘šÉin“tegral˜is˜de ned‘šÉb“y˜exp(-xÞ^Ý2)˜in“t_0Þ^Ýx–šÉdt˜exp(tÞ^Ý2).‘ÙþA‘šÇtable“of˜Da²!wsonŽ¡‘.ùœinš²!tegral–¦fcan“bMÞe“found“in“Abramo˜witz“&“Stegun,“T‘ÿeable“7.5.Ž¤=p‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gdeb•²!y“e_1–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉdebye_1‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“debye_1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThe›¦fDeb•²!y“e˜functions˜are˜de ned˜b“y˜the˜in“tegralŽ¤=p‘.ùœD_n(x)–¦f=“n/xÞ^Ýn“in²!t_0Þ^Ýx“dt“(tÞ^Ýn/(eÞ^Ýt“-“1)).ŽŸ=q‘.ùœF‘ÿeor–¦ffurther“information“see“Abramo²!witz“&“Stegun,“Section“27.1.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gdeb•²!y“e_2–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉdebye_2‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“debye_2‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThe›¦fDeb•²!y“e˜functions˜are˜de ned˜b“y˜the˜in“tegralŽ¤=p‘.ùœD_n(x)–¦f=“n/xÞ^Ýn“in²!t_0Þ^Ýx“dt“(tÞ^Ýn/(eÞ^Ýt“-“1)).ŽŸ=q‘.ùœF‘ÿeor–¦ffurther“information“see“Abramo²!witz“&“Stegun,“Section“27.1.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gdeb•²!y“e_3–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉdebye_3‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“debye_3‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThe›¦fDeb•²!y“e˜functions˜are˜de ned˜b“y˜the˜in“tegralŽ¤=p‘.ùœD_n(x)–¦f=“n/xÞ^Ýn“in²!t_0Þ^Ýx“dt“(tÞ^Ýn/(eÞ^Ýt“-“1)).ŽŸ=q‘.ùœF‘ÿeor–¦ffurther“information“see“Abramo²!witz“&“Stegun,“Section“27.1.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™ŽŸ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gdeb•²!y“e_4–¦f-*-“texinfo“-*-ŽŽŒ‹1€ŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉdebye_4‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“debye_4‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThe›¦fDeb•²!y“e˜functions˜are˜de ned˜b“y˜the˜in“tegralŽ¤""‘.ùœD_n(x)–¦f=“n/xÞ^Ýn“in²!t_0Þ^Ýx“dt“(tÞ^Ýn/(eÞ^Ýt“-“1)).Ž¡‘.ùœF‘ÿeor–¦ffurther“information“see“Abramo²!witz“&“Stegun,“Section“27.1.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž©ÿÿ‘!Gerf_gsl–¦f-*-“texinfo“-*-ŽŸ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉerf_gsl‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“erf_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–q¼routines›q»compute“the“error“function˜erf(x)“=“(2/sqrt(pi))“in²!t_0Þ^Ýx˜dt“exp(-tÞ^Ý2).Ž¤""‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gerfc_gsl–¦f-*-“texinfo“-*-ŽŸ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉerfc_gsl‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“erfc_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–.·routines›.¸compute“the“complemen²!tary˜error“function“erfc(x)˜=“1“-˜erf(x)“=Ž¡‘.ùœ(2/sqrt(pi))›¦fin•²!t_xÞ^Ýinft“y˜exp(-tÞ^Ý2).Ž¤""‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Glog_erfc–¦f-*-“texinfo“-*-Ž©’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlog_erfc‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“log_erfc‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–€vroutines›€ucompute“the˜logarithm“of˜the“complemen²!tary˜error“functionŽ¡‘.ùœlog(erfc(x)).Ž¤""‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gerf_Z–¦f-*-“texinfo“-*-ŽŸÿÿ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉerf_Z‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“erf_Z‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ÿroutines“compute›the“Gaussian“probabilit²!y“function“Z(x)˜=“(1/(2pi))“exp(-Ž¡‘.ùœxÞ^Ý2/2).Ž¤""‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™ŽŸ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹Ý=‘¦f0.Ž¤B‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GSi–¦f-*-“texinfo“-*-ŽŸQì’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉSi‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“Si‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“Sine“inš²!tegral“Si(x)“=“in˜t_0Þ^Ýx“dt“sin(t)/t.Ž¤B‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GCi–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉCi‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“Ci‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Qroutines›Qcompute“the“Cosine“in²!tegral˜Ci(x)“=“-in•²!t_xÞ^Ýinft“y˜dt–Qcos(t)/t“for“x˜Þ>“Ý0.Ž¤B‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸQì‘!Gatanin²!t–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉatanint‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“atanint‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–@routines“compute“the“Arctangenš²!t“in˜tegral‘@A˜tanIn˜t(x)“=“in˜t_0Þ^Ýx“dt“arctan(t)/t.Ž¤B‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™ŽŸ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹ _‰ŸòŽ ƒ3* ý ÌÖ‘!GÝfermi_dirac_mhalf–¦f-*-“texinfo“-*-Ž©Ÿ"’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉfermi_dirac_mhalf‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“fermi_dirac_mhalf‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“complete“F‘ÿeermi-Dirac“in²!tegral“F_Þ{Ý-1/2Þ}Ý(x).ŽŸW.‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸW-‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gfermi_dirac_half–¦f-*-“texinfo“-*-ŽŸŸ#’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉfermi_dirac_half‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“fermi_dirac_half‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“complete“F‘ÿeermi-Dirac“in²!tegral“F_Þ{Ý1/2Þ}Ý(x).ŽŸW-‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸW.‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gfermi_dirac_3half–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉfermi_dirac_3half‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“fermi_dirac_3half‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“complete“F‘ÿeermi-Dirac“in²!tegral“F_Þ{Ý3/2Þ}Ý(x).ŽŸW.‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸW-‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Ggamma_gsl–¦f-*-“texinfo“-*-ŽŸŸ#’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉgamma_gsl‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“gamma_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–garoutines›gbcompute“the“Gamma“function˜Gamma(x),‘— sub‘›»ject“to“x“not˜bMÞeing“aŽ¡‘.ùœnegativ•²!e›¿in“teger.‘ çThe˜function–¾is˜computed˜using˜the“real˜Lanczos˜methoMÞd.‘ çTheŽ¡‘.ùœmaxim²!um–]v‘ÿdDalue›\of“x˜suc²!h“that˜Gamma(x)“is“not˜considered“an˜o•²!v“er o“w‘]is˜giv“en‘]b“yŽ¡‘.ùœthe–¦fmacro“GSL_SF_GAMMA_XMAX“and“is“171.0.ŽŸW-‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸW.‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Glngamma_gsl–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlngamma_gsl‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“lngamma_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–gžroutines“compute›gthe“logarithm“of“the“Gamma˜function,‘t-log(Gamma(x)),‘t,sub-Ž¡‘.ùœject–£¾to“x›£½not“a“bMÞeing“negativ•²!e˜in“teger.‘ÕåF‘ÿeor˜xÞ<Ý0–£¾the“real“part˜of“log(Gamma(x))“isŽ¡‘.ùœreturned,‘rwhic•²!h›ðÖis‘ðÕequiv‘ÿdDalen“t˜to˜log(Þ|ÝGamma(x)Þ|Ý).‘½-The‘ðÕfunction˜is˜computed˜usingŽ¡‘.ùœthe–¦freal“Lanczos“methoMÞd.ŽŸW.‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸW-‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹!kŸòŽ ƒ3* ý ÌÖ‘!GÝgammastar–¦f-*-“texinfo“-*-Ž©ÜÌ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉgammastar‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“gammastar‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–oÙroutines›oÚcompute“the“regulated“Gamma˜F‘ÿeunction“GammaÞ^Ý*(x)“for“x˜Þ>“Ý0.‘Ë®TheŽ¡‘.ùœregulated–¦fgamma“function“is“givš²!en“b˜y‘ÿe,ŽŸg‘.ùœGammaÞ^Ý*(x)–ƒ<=›ƒ;Gamma(x)/(sqrtÞ{Ý2piÞ}“ÝxÞ^{Ý(x-1/2)Þ}“Ýexp(-x))“=˜(1“+“(1/12x)˜+“...)Ž¡‘.ùœfor–¦fx“to“inft²!yŽ¤f‘.ùœand–¦fis“a“useful“suggestion“of“T‘ÿeemme.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÜÍ‘!Ggammain²!v_gsl–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉgammainv_gsl‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“gammainv_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¤5routines›¤4compute“the˜reciproMÞcal“of˜the“gamma“function,‘ã§1/Gamma(x)“usingŽ¡‘.ùœthe–¦freal“Lanczos“methoMÞd.Ž¤f‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÜÍ‘!Glam²!bMÞert_W0–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlambert_W0‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“lambert_W0‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦fcompute“the“principal“brancš²!h“of“the“Lam˜bMÞert“W“function,“W_0(x).Ž©f‘.ùœLam²!bMÞert's›Œ³W‘Œ6functions,–FW(x),“are˜de ned˜to˜bMÞe˜solutions‘Œ´of˜the˜equation˜W(x)Ž¡‘.ùœexp(W(x))–b£=“x.‘ “This“function“has‘b¢mš²!ultiple“branc˜hes“for“x‘b¢Þ<“Ý0;‘@Áho˜w˜ev˜er,‘ѱit“hasŽ¡‘.ùœonly›ct•²!w“o˜real-v‘ÿdDalued˜branc“hes.‘3ÓW‘ÿee˜de ne˜W_0(x)˜to˜bMÞe‘bthe˜principal˜branc“h,‘4âwhereŽ¡‘.ùœW‘}!Þ>–}+Ý-1“for“x“Þ<“Ý0,›…jand“W_Þ{Ý-1Þ}Ý(x)“to“bMÞe“the“other“real“branc²!h,˜where“W‘}!Þ<“Ý-1“for“x“Þ<“Ý0.ŽŸg‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÜÌ‘!Glam²!bMÞert_Wm1–¦f-*-“texinfo“-*-ŽŸÜÍ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlambert_Wm1‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“lambert_Wm1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–:Bcompute“the“secondary‘:Areal-v‘ÿdDalued“brancš²!h“of“the“Lam˜bMÞert“W‘:function,‘_9W_Þ{Ý-Ž¡‘.ùœ1Þ}Ý(x).Ž¦‘.ùœLam²!bMÞert's›Œ³W‘Œ6functions,–FW(x),“are˜de ned˜to˜bMÞe˜solutions‘Œ´of˜the˜equation˜W(x)Ž¡‘.ùœexp(W(x))–b£=“x.‘ “This“function“has‘b¢mš²!ultiple“branc˜hes“for“x‘b¢Þ<“Ý0;‘@Áho˜w˜ev˜er,‘ѱit“hasŽ¡‘.ùœonly›ct•²!w“o˜real-v‘ÿdDalued˜branc“hes.‘3ÓW‘ÿee˜de ne˜W_0(x)˜to˜bMÞe‘bthe˜principal˜branc“h,‘4âwhereŽ¡‘.ùœW‘}!Þ>–}+Ý-1“for“x“Þ<“Ý0,›…jand“W_Þ{Ý-1Þ}Ý(x)“to“bMÞe“the“other“real“branc²!h,˜where“W‘}!Þ<“Ý-1“for“x“Þ<“Ý0.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŽŒ‹"x˜ŸòŽ ƒ3* ý ÌÖ‘.ùœÝThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž©Šø‘!Glog_1plusx–¦f-*-“texinfo“-*-ŽŸŠù’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlog_1plusx‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“log_1plusx‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–žkroutines“compute“log(1“+›žlx)“for“x“Þ>“Ý-1“using“an“algorithm˜that“is“accurate“forŽ¡‘.ùœsmall‘¦fx.ŽŸ_‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ_‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Glog_1plusx_mx–¦f-*-“texinfo“-*-Ž©Šù’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlog_1plusx_mx‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“log_1plusx_mx‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ŸYroutines›ŸXcompute“log(1˜+“x)“-˜x“for˜x“Þ>˜Ý-1“using“an˜algorithm“that˜is“accurateŽ¡‘.ùœfor–¦fsmall“x.ŽŸ_‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ_‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gpsi–¦f-*-“texinfo“-*-ŽŸŠø’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉpsi‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“psi‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“digamma“function“psi(x)“for“general“x,“x“e“0.ŽŸ_‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ_‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gpsi_1piy–¦f-*-“texinfo“-*-ŽŸŠø’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉpsi_1piy‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“psi_1piy‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–è6routines“compute“the“real“part“of“the“digamma“function“on“the“line“1+i“y‘ÿe,Ž¡‘.ùœRe[psi(1–¦f+“i“y)].ŽŸ_‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ_‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gsync²!hrotron_1–¦f-*-“texinfo“-*-ŽŸŠø’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉsynchrotron_1‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“synchrotron_1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–GCroutines“compute‘GDthe“ rst“syncš²!hrotron“function“x“in˜t_xÞ^Ýinft˜y‘GDdt“K_Þ{Ý5/3Þ}Ý(t)“forŽ¡‘.ùœx–¦fÞ>Ý=“0.ŽŽŒ‹#…ÚŸòŽ ƒ3* ý ÌÖ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž©B‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸQë‘!Gsync²!hrotron_2–¦f-*-“texinfo“-*-ŽŸQì’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉsynchrotron_2‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“synchrotron_2‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“second“sync²!hrotron“function“x“K_Þ{Ý2/3Þ}Ý(x)“for“x“Þ>Ý=“0.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Që‘!GtranspMÞort_2–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉtransport_2‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“transport_2‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“transpMÞort“function“J(2,x).Ž¦‘.ùœThe–üztranspMÞort›üyfunctions“J(n,x)“are“de ned˜bš²!y“the“in˜tegral“represen˜tations‘üyJ(n,x)“:=Ž¡‘.ùœin²!t_0Þ^Ýx–¦fdt“tÞ^Ýn“eÞ^Ýt“/(eÞ^Ýt“-“1)Þ^Ý2.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸQì‘!GtranspMÞort_3–¦f-*-“texinfo“-*-ŽŸQë’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉtransport_3‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“transport_3‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“transpMÞort“function“J(3,x).Ž¦‘.ùœThe–üztranspMÞort›üyfunctions“J(n,x)“are“de ned˜bš²!y“the“in˜tegral“represen˜tations‘üyJ(n,x)“:=Ž¡‘.ùœin²!t_0Þ^Ýx–¦fdt“tÞ^Ýn“eÞ^Ýt“/(eÞ^Ýt“-“1)Þ^Ý2.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸQë‘!GtranspMÞort_4–¦f-*-“texinfo“-*-ŽŸQì’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉtransport_4‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“transport_4‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“transpMÞort“function“J(4,x).Ž¦‘.ùœThe–üztranspMÞort›üyfunctions“J(n,x)“are“de ned˜bš²!y“the“in˜tegral“represen˜tations‘üyJ(n,x)“:=Ž¡‘.ùœin²!t_0Þ^Ýx–¦fdt“tÞ^Ýn“eÞ^Ýt“/(eÞ^Ýt“-“1)Þ^Ý2.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸQë‘!GtranspMÞort_5–¦f-*-“texinfo“-*-ŽŽŒ‹$‘+ŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉtransport_5‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“transport_5‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“transpMÞort“function“J(5,x).Ž©•ñ‘.ùœThe–üztranspMÞort›üyfunctions“J(n,x)“are“de ned˜bš²!y“the“in˜tegral“represen˜tations‘üyJ(n,x)“:=Ž¡‘.ùœin²!t_0Þ^Ýx–¦fdt“tÞ^Ýn“eÞ^Ýt“/(eÞ^Ýt“-“1)Þ^Ý2.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸø°‘!Gsinc_gsl–¦f-*-“texinfo“-*-ŽŸø¯’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉsinc_gsl‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“sinc_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“sinc(x)“=“sin(pi“x)“/“(pi“x)“for“an²!y“v‘ÿdDalue“of“x.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ø¯‘!Glnsinh–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlnsinh‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“lnsinh‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“log(sinh(x))“for“x“Þ>“Ý0.ŽŸ•ò‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ø¯‘!Glncosh–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlncosh‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“lncosh‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“log(cosh(x))“for“an²!y“x.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸø¯‘!Gzeta–¦f-*-“texinfo“-*-ŽŸø°’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉzeta‘yšâ(éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“zeta‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“Riemann“zeta“function“zeta(s)“for“arbitrary“s,“s“e“1.Ž¦‘.ùœThe–b¨Riemann›b©zeta“function˜is“de ned“b²!y˜the“in nite˜sum“zeta(s)˜=“sum_Þ{Ýk=1Þ}^Ýinft²!yŽ¡‘.ùœkÞ^{Ý-sÞ}Ý.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹% ŸòŽ ƒ3* ý ÌÖ‘!GÝeta–¦f-*-“texinfo“-*-Ž©‰n’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉeta‘yšâ(éx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“eta‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“eta“function“eta(s)“for“arbitrary“s.Ž¤úœ‘.ùœThe–¦feta“function“is“de ned“b²!y“eta(s)“=“(1-2Þ^{Ý1-sÞ}Ý)“zeta(s).Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_Jn–¦f-*-“texinfo“-*-ŽŸ‰o’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_Jn‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_Jn‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“regular“cylindrical“Bessel“function“of“order“n,“J_n(x).Ž¤úœ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_Yn–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_Yn‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_Yn‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–&Üroutines›&Ýcompute“the“irregular˜cylindrical“Bessel“function˜of“order“n,‘FúY_n(x),Ž¡‘.ùœfor‘¦fxÞ>Ý0.Ž¤úœ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_In–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_In‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_In‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–?ºroutines›?¹compute“the“regular˜moMÞdi ed“cylindrical˜Bessel“function“of˜order“n,Ž¡‘.ùœI_n(x).ŽŸú‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸúœ‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_In_scaled–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_In_scaled‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_In_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–8©routines›8¨compute“the˜scaled“regular˜moMÞdi ed“cylindrical˜Bessel“function˜ofŽ¡‘.ùœorder–¦fn,“exp(-Þ|ÝxÞ|Ý)“I_n(x)Ž¤úœ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™ŽŸ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹&¨£ŸòŽ ƒ3* ý ÌÖ‘!GÝbMÞessel_Kn–¦f-*-“texinfo“-*-Ž©’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_Kn‘yšâ(éná,‘¦féx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_Kn‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–• routines›•!compute“the“irregular“moMÞdi ed˜cylindrical“Bessel“function“of˜order“n,Ž¡‘.ùœK_n(x),–¦ffor“x“Þ>“Ý0.Ž¤™™‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_Kn_scaled–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_Kn_scaled‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_Kn_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ™™‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_jl–¦f-*-“texinfo“-*-ŽŸÿÿ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_jl‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_jl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–>qroutines“compute“the‘>pregular“spherical“Bessel“function“of“order“l,–dsj_l(x),“for‘>qlŽ¡‘.ùœÞ>Ý=–¦f0“and“x“Þ>Ý=“0.ŽŸ™š‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ™™‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_yl–¦f-*-“texinfo“-*-ŽŸÿÿ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_yl‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_yl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–‚íroutines“compute“the“irregular“spherical“Bessel“function“of“order“l,–Šy_l(x),“for‘‚ílŽ¡‘.ùœÞ>Ý=‘¦f0.ŽŸ™š‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ™™‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_il_scaled–¦f-*-“texinfo“-*-ŽŸÿÿ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_il_scaled‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_il_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–(Òroutines›(Ócompute“the“scaled“regular˜moMÞdi ed“spherical“Bessel“function˜of“orderŽ¡‘.ùœl,–¦fexp(-Þ|ÝxÞ|Ý)“i_l(x)ŽŸ™š‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ™™‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹'´ŸòŽ ƒ3* ý ÌÖ‘!GÝbMÞessel_kl_scaled–¦f-*-“texinfo“-*-Ž©’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_kl_scaled‘yšâ(éná,‘¦féx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_kl_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–>routines“compute“the“scaled“irregular“moMÞdi ed“spherical“Bessel“function“ofŽ¡‘.ùœorder–¦fl,“exp(x)“k_l(x),“for“xÞ>Ý0.ŽŸ""‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ"!‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gexprel_n–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉexprel_n‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“exprel_n‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–“routines“compute“the“N-relativš²!e“expMÞonen˜tial,‘Ÿwhic˜h“is“the“n-th“generalizationŽ¡‘.ùœof–b÷the›bøfunctions“gsl_sf_exprel“and˜gsl_sf_exprel2.‘‘The“N-relativš²!e“expMÞonen˜tial‘bøis“giv˜enŽ¡‘.ùœb²!y‘ÿe,Ž©""‘.ùœexprel_N(x)–ÇF=“N!/xÞ^ÝN‘ƺ(exp(x)“-“sum_Þ{Ýk=0Þ}^{ÝN-1Þ}“ÝxÞ^Ýk/k!)‘ @}=“1“+“x/(N+1)“+Ž¡‘.ùœxÞ^Ý2/((N+1)(N+2))–¦f+“...‘ÝÝ=“1F1“(1,1+N,x)Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ"!‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤‘!Gfermi_dirac_in²!t–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉfermi_dirac_int‘yšâ(éná,‘¦féx‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“fermi_dirac_int‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–OÖroutines›O×compute“the˜complete“F‘ÿeermi-Dirac˜in²!tegral“with˜an“in²!teger˜index“of˜j,Ž¡‘.ùœF_j(x)–¦f=“(1/Gamma(j+1))“in•²!t_0Þ^Ýinft“y–¦fdt“(tÞ^Ýj“/(exp(t-x)+1)).Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÿÿ‘!Gta²!ylorcoMÞe –¦f-*-“texinfo“-*-ŽŸ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉtaylorcoeff‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“taylorcoeff‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“T‘ÿeaš²!ylor“coMÞecien˜t“xÞ^Ýn“/“n!‘ÝÝfor“x“Þ>Ý=“0,“n“Þ>Ý=“0.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÿÿ‘!Glegendre_Pl–¦f-*-“texinfo“-*-ŽŸ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlegendre_Pl‘yšâ(éná,‘¦féx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“legendre_Pl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Ojfunctions›Oiev‘ÿdDaluate“the“Legendre“pMÞolynomial˜P_l(x)“for“a˜spMÞeci c“v‘ÿdDalue“of“l,‘yªxŽ¡‘.ùœsub‘›»ject–¦fto“l“Þ>Ý=“0,“Þ|ÝxÞ|“<Ý=“1ŽŽŒ‹(ÀXŸòŽ ƒ3* ý ÌÖ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸC‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž© 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Rú‘!Glegendre_Ql–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlegendre_Ql‘yšâ(éná,‘¦féx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“legendre_Ql‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“Legendre“function“Q_l(x)“for“x“Þ>“Ý-1,“x“!=“1“and“l“Þ>Ý=“0.Ž¤C‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸRú‘!Gpsi_n–¦f-*-“texinfo“-*-ŽŸRû’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉpsi_n‘yšâ(éná,‘¦féx‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“psi_n‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–¦froutines“compute“the“pMÞolygamma“function“psiÞ^{Ý(m)Þ}Ý(x)“for“m“Þ>Ý=“0,“x“Þ>“Ý0.ŽŸC‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸRú‘!GbMÞessel_Jn²!u–¦f-*-“texinfo“-*-ŽŸRû’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Jnu‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Jnu‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–Ukroutines“compute›Ujthe“regular“cylindrical“Bessel“function“of˜fractional“order“n²!u,Ž¦‘.ùœJ_u(x).ŽŸC‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸRú‘!GbMÞessel_Yn²!u–¦f-*-“texinfo“-*-ŽŸRû’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Ynu‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Ynu‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–l¦routines›l¥compute“the˜irregular“cylindrical“Bessel˜function“of˜fractional“orderŽ¦‘.ùœn²!u,‘¦fY_u(x).Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸC‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸRû‘!GbMÞessel_In²!u–¦f-*-“texinfo“-*-ŽŸRú’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Inu‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Inu‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–Uroutines“compute“the“regular“moMÞdi ed‘TBessel“function“of“fractional“order“n²!u,Ž¦‘.ùœI_u(x)–¦ffor“xÞ>Ý0,“uÞ>Ý0.ŽŽŒ‹)ÌìŸòŽ ƒ3* ý ÌÖ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ“é‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž© 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ôŸ‘!GbMÞessel_In²!u_scaled–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Inu_scaled‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Inu_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–Ü_routines›Ü^compute“the“scaled“regular˜moMÞdi ed“Bessel“function“of˜fractional“orderŽ¦‘.ùœn²!u,–¦fexp(-Þ|ÝxÞ|Ý)I_u(x)“for“xÞ>Ý0,“uÞ>Ý0.Ž¤“é‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ôŸ‘!GbMÞessel_Kn²!u–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Knu‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Knu‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–q¼routines›q»compute“the˜irregular“moMÞdi ed˜Bessel“function˜of“fractional˜order“n²!u,Ž¦‘.ùœK_u(x)–¦ffor“xÞ>Ý0,“uÞ>Ý0.Ž¤“é‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸôž‘!GbMÞessel_lnKn²!u–¦f-*-“texinfo“-*-ŽŸôŸ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_lnKnu‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_lnKnu‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–Îroutines›Îcompute“the“logarithm“of˜the“irregular“moMÞdi ed“Bessel˜function“ofŽ¦‘.ùœfractional–¦forder“n²!u,“ln(K_u(x))“for“xÞ>Ý0,“uÞ>Ý0.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ôŸ‘!GbMÞessel_Kn²!u_scaled–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbessel_Knu_scaled‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“bessel_Knu_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–êroutines›êcompute“the“scaled˜irregular“moMÞdi ed“Bessel“function˜of“fractionalŽ¦‘.ùœorder–¦fn²!u,“exp(+Þ|ÝxÞ|Ý)“K_u(x)“for“xÞ>Ý0,“uÞ>Ý0.Ž¤“é‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸôŸ‘!Gexp_m²!ult–¦f-*-“texinfo“-*-ŽŽŒ‹*ØŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉexp_mult‘yšâ(éxá,‘¦féy‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“exp_mult‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ò`routines›ò_expMÞonen²!tiate“x˜and“m•²!ultiply˜b“y–ò`the“factor˜y“to˜return“the˜proMÞduct“yŽ¡‘.ùœexp(x).Ž¤ff‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÌÍ‘!Gfermi_dirac_inc_0–¦f-*-“texinfo“-*-Ž©ÌÌ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉfermi_dirac_inc_0‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“fermi_dirac_inc_0‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–FÎroutines“compute“the“incomplete“F‘ÿeermi-Dirac‘FÏin²!tegral“with“an“index“of“zero,Ž¡‘.ùœF_0(x,b)–¦f=“ln(1“+“eÞ^{Ýb-xÞ}Ý)“-“(b-x).ŽŸff‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸfg‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gp•MÞo“c²!h–¦f-*-“texinfo“-*-ŽŸÌÍ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉpoch‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“poch‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“P•²!ošMÞc“hhammer‘¦fsym“b˜olŽ¤ff‘.ùœ(a)_x–¦f:=“Gamma(a“+“x)/Gamma(a),Ž¡‘.ùœsub‘›»ject–to›a“and“a+x˜not“bMÞeing“negativ•²!e˜in“tegers.‘AàThe›P“oMÞc“hhammer˜sym“bMÞol‘is˜alsoŽ© 33‘.ùœknoš²!wn–¦fas“the“ApMÞell“sym˜bMÞol.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÌÍ‘!Glnp•MÞo“c²!h–¦f-*-“texinfo“-*-ŽŸÌÌ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉlnpoch‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“lnpoch‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–Ò-routines›Ò.compute“the“logarithm˜of“the“P•²!ošMÞc“hhammer‘Ò-sym“b˜ol,‘]log((a)_x)‘Ò-=Ž¦‘.ùœlog(Gamma(a–¦f+“x)/Gamma(a))“for“a“Þ>“Ý0,“a+x“Þ>“Ý0.Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸfg‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÌÌ‘!Gp•MÞo“c²!hrel–¦f-*-“texinfo“-*-ŽŸÌÍ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉpochrel‘yšâ(éxá,‘¦féy‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“pochrel‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–Kñroutines›Kòcompute“the˜relativš²!e“P˜oMÞc˜hhammer“sym˜bMÞol›Kò((a,x)“-˜1)/x“where˜(a,x)“=Ž¦‘.ùœ(a)_x–¦f:=“Gamma(a“+“x)/Gamma(a).Ž¡‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹+ä;ŸòŽ ƒ3* ý ÌÖ‘!GÝgamma_inc_Q–¦f-*-“texinfo“-*-Ž©Ÿ"’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉgamma_inc_Q‘yšâ(éxá,‘¦féy‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“gamma_inc_Q‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–~øroutines›~ùcompute“the“normalized˜incomplete“Gamma“F‘ÿeunction˜Q(a,x)“=Ž¡‘.ùœ1/Gamma(a)›¦fin•²!t_xinft“y˜dt˜tÞ^{Ýa-1Þ}˜Ýexp(-t)˜for˜a˜Þ>˜Ý0,˜x˜Þ>Ý=˜0.ŽŸW.‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸW-‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Ggamma_inc_P–¦f-*-“texinfo“-*-ŽŸŸ#’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉgamma_inc_P‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“gamma_inc_P‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–(ïroutines›(ðcompute“the“complemen²!tary˜normalized“incomplete˜Gamma“F‘ÿeunctionŽ¡‘.ùœP(a,x)–¦f=“1/Gamma(a)“in²!t_0Þ^Ýx“dt“tÞ^{Ýa-1Þ}“Ýexp(-t)“for“a“Þ>“Ý0,“x“Þ>Ý=“0.ŽŸW-‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸW.‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Ggamma_inc–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉgamma_inc‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“gamma_inc‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–°functions›±compute“the“incomplete˜Gamma“F‘ÿeunction“the˜normalization“factorŽ¡‘.ùœincluded–Þ¦in›Þ¥the“previously˜de ned“functions:‘N\Gamma(a,x)˜=“in•²!t_xinft“y˜dt‘Þ¦tÞ^{Ýa-1Þ}Ž¡‘.ùœÝexp(-t)–¦ffor“a“real“and“x“Þ>Ý=“0.ŽŸW.‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸW-‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞeta_gsl–¦f-*-“texinfo“-*-ŽŸŸ#’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉbeta_gsl‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“beta_gsl‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–nïroutines“compute“the“Beta“F‘ÿeunction,‘­:B(a,b)“=“Gamma(a)Gamma(b)/Gamma(a+b)Ÿ¼Ì„ ó2Ž¡‘.ùœfor–¦fa“Þ>“Ý0,“b“Þ>“Ý0.ŽŸW-‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸW.‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gln²!bMÞeta–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉlnbeta‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“lnbeta‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¸ûroutines“compute“the“logarithm“of‘¸úthe“Beta“F‘ÿeunction,›½ log(B(a,b))“for“a“Þ>“Ý0,˜bŽ¡‘.ùœÞ>‘¦fÝ0.ŽŸW.‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸW-‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹,ñŸòŽ ƒ3* ý ÌÖ‘!GÝh²!ypMÞerg_0F1–¦f-*-“texinfo“-*-Ž©)’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉhyperg_0F1‘yšâ(éxá,‘¦féy‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“hyperg_0F1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“h²!ypMÞergeometric“function“0F1(c,x).ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GconicalP_half–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉconicalP_half‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“conicalP_half‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ÍÏroutines›ÍÎcompute“the˜irregular“Spherical“Conical˜F‘ÿeunction“PÞ^{Ý1/2Þ}Ý_Þ{Ý-1/2˜+“iŽ¡‘.ùœlam²!bMÞdaÞ}Ý(x)–¦ffor“x“Þ>“Ý-1.ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GconicalP_mhalf–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉconicalP_mhalf‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“conicalP_mhalf‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–,routines›,compute“the“regular“Spherical˜Conical“F‘ÿeunction“PÞ^{Ý-1/2Þ}Ý_Þ{Ý-1/2˜+“iŽ¡‘.ùœlam²!bMÞdaÞ}Ý(x)–¦ffor“x“Þ>“Ý-1.ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GconicalP_0–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉconicalP_0‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“conicalP_0‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“conical“function“PÞ^Ý0_Þ{Ý-1/2“+“i“lam²!bMÞdaÞ}Ý(x)“for“x“Þ>“Ý-1.ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GconicalP_1–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉconicalP_1‘yšâ(éxá,‘¦féy‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“conicalP_1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“conical“function“PÞ^Ý1_Þ{Ý-1/2“+“i“lam²!bMÞdaÞ}Ý(x)“for“x“Þ>“Ý-1.ŽŸ+„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.ŽŸ+…‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Ghzeta–¦f-*-“texinfo“-*-ŽŽŒ‹-ýýŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géz‘°Yè=‘LÉhzeta‘yšâ(éxá,‘¦féy‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[ézè,–LÉéerr‘cè]“=“hzeta‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“Hurwitz“zeta“function“zeta(s,q)“for“s“Þ>“Ý1,“q“Þ>“Ý0.Ž¤è‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“ázÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž© 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Ø‘!Gairy_Ai–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Ai‘yšâ(éxá,‘¦fémode‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Ai‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–cMroutines›cNcompute“the˜Airy“function˜Ai(x)“with˜an“accuracy˜spMÞeci ed“b²!y˜moMÞde.ŽŸé‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸïB‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¦‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.Ž¤è‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¦‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¡‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¦‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸïC‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸè‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Ø‘!Gairy_Bi–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Bi‘yšâ(éxá,‘¦fémode‘câ)Ž¦’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Bi‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¦‘.ùœÝThese–m routines“compute“the›m Airy“function“Bi(x)“with“an“accuracy˜spšMÞeci ed“b²!y“mo˜de.ŽŸè‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸïC‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¦‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.Ž¤è‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¦‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¡‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¦‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸïC‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸè‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¦‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸØ‘!Gairy_Ai_scaled–¦f-*-“texinfo“-*-ŽŽŒ‹. ŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Ai_scaled‘yšâ(éxá,‘¦fémode‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Ai_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ßKroutines›ßLcompute“a“scaled“v²!ersion˜of“the“Airy“function˜S_A(x)“Ai(x).‘ˆF‘ÿeor“xÞ>Ý0Ž¡‘.ùœthe–¦fscaling“factor“S_A(x)“is“exp(+(2/3)“xÞ^Ý(3/2)),“and“is“1“for“xÞ<Ý0.ŽŸ Ö‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽ©èz‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.ŽŸèy‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸèy‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž© Ö‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Ã‘!Gairy_Bi_scaled–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Bi_scaled‘yšâ(éxá,‘¦fémode‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Bi_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–îÞroutines“compute“a“scaled“v²!ersion“of“the‘îÝAiry“function“S_B(x)“Bi(x).‘·EF‘ÿeor“xÞ>Ý0Ž¡‘.ùœthe–¦fscaling“factor“S_B(x)“is“exp(-(2/3)“xÞ^Ý(3/2)),“and“is“1“for“xÞ<Ý0.Ž¦‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽ©èz‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.ŽŸèy‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸèy‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž© Ö‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤Ã‘!Gairy_Ai_deriv–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Ai_deriv‘yšâ(éxá,‘¦fémode‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Ai_deriv‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Ýroutines›Ýcompute“the˜Airy“function˜deriv‘ÿdDativ²!e“Ai'(x)˜with“an˜accuracy“spMÞeci edŽ¡‘.ùœb²!y‘¦fmoMÞde.Ž¦‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸèz‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.ŽŸèy‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.ŽŽŒ‹/eŸòŽ ƒ3* ý ÌÖ‘.ùœÝ2–¦f=“GSL_PREC_APPR•²!O“XŽ¤ 33‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.Ž©¶”‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸà‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ ‘!Gairy_Bi_deriv–¦f-*-“texinfo“-*-ŽŸ ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Bi_deriv‘yšâ(éxá,‘¦fémode‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Bi_deriv‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ç²routines›ç±compute“the“Airy“function˜deriv‘ÿdDativ²!e“Bi'(x)“with“an˜accuracy“spMÞeci edŽ¡‘.ùœb²!y‘¦fmoMÞde.ŽŸà‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸ¶•‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.ŽŸà‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.ŽŸà‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž©à‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ ‘!Gairy_Ai_deriv_scaled–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Ai_deriv_scaled‘yšâ(éxá,‘¦fémode‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Ai_deriv_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“deriv‘ÿdDativ²!e“of“the“scaled“Airy“function“S_A(x)“Ai(x).Ž¦‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸ¶”‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.Ž©à‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸ¶”‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸà‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸ ‘!Gairy_Bi_deriv_scaled–¦f-*-“texinfo“-*-ŽŽŒ‹0èŸòŽ ƒ3* ý ÌÖ’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_Bi_deriv_scaled‘yšâ(éxá,‘¦fémode‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_Bi_deriv_scaled‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“deriv‘ÿdDativ²!e“of“the“scaled“Airy“function“S_B(x)“Bi(x).ŽŸDŠ‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸM5‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.Ž©DŠ‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸM5‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž©DŠ‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸUá‘!Gellin²!t_Kcomp–¦f-*-“texinfo“-*-ŽŸUà’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉellint_Kcomp‘yšâ(éxá,‘¦fémode‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“ellint_Kcomp‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“complete“elliptic“in²!tegral“K(k)ŽŸ#…eŸý b’¡RåK‘ÈÝ(åkX?Ý)ŽŽ’½ì=‘ §Ÿò&»½ZŽŸôŸ‘ ¨´@L=®2ŽŸ@‘˜á0ŽŽŸø—ž‘@Ñ%ådtŽ‘“ÒŸÞȉfeP!ñŸ[rŸó¤‡½qŽ‘ Ÿó¤‡‰feF!ðŸ [yÝ(1–nìæ“åkX?ŸüÖ0®2Ž‘§ãÝsinŽ‘™Ÿû(¾®2Ž‘– Ý(åtÝ))ŽŽŽŽŽŽŽŽŽŽŽŸ&–¼‘.ùœThe–Æ«notation“used“here“is“based“on“Carlson,‘νáNumerisc²!he“Mathematik‘p¯Ý33“(1979)“andŽ¡‘.ùœdi ers–Ìûslighš²!tly“from“that“used“b˜y“Abramo˜witz“&“Stegun,‘øvwhere“the“functions“are“giv˜enŽ¡‘.ùœin–¦fterms“of“the“parameter“åm– §Ý=“åkX?Ÿü¾®2Ž‘Ô²Ý.Ž¦‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸM5‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.Ž©DŠ‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸM5‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸDŠ‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸUà‘!Gellin²!t_Ecomp–¦f-*-“texinfo“-*-ŽŸUá’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉellint_Ecomp‘yšâ(éxá,‘¦fémode‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“ellint_Ecomp‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–Ùroutines“compute›Ùthe“complete“elliptic“in²!tegral“E(k)“to˜the“accuracy“spMÞeci edŽ¡‘.ùœb²!y–¦fthe“mošMÞde“v‘ÿdDariable“mo˜de.ŽŽŒ‹1*ŸòŽ ƒ3* ý ÌÖŸ!GŸ#’ž`ÞåE‘¡’Ý(åkX?Ý)ŽŽ’¸²F=‘ §Ÿò&»½ZŽŸôŸ‘ ¨´@L=®2ŽŸ@‘˜á0ŽŽ‘`ŸŸóv½qŽ‘&` Ÿóv‰feF!ðŸ åŠÝ(1–nìæ“åkX?ŸüÖ0®2Ž‘§ãÝsinŽ‘™Ÿû(¾®2Ž‘– Ý(åtÝ))ŽŽŽ‘l‚ådtŽŽŽŽŽŸ:©‘.ùœÝThe–Æ«notation“used“here“is“based“on“Carlson,‘νáNumerisc²!he“Mathematik‘p¯Ý33“(1979)“andŽ¤ 33‘.ùœdi ers–Ìûslighš²!tly“from“that“used“b˜y“Abramo˜witz“&“Stegun,‘øvwhere“the“functions“are“giv˜enŽ¡‘.ùœin–¦fterms“of“the“parameter“åm– §Ý=“åkX?Ÿü¾®2Ž‘Ô²Ý.ŽŸÇ‘.ùœThe–¦fsecond“argumenš²!t“ámoMÞde‘CmÝm˜ust“bMÞe“an“in˜teger“correspMÞonding“toŽŸ¾‘.ùœ0–¦f=“GSL_PREC_DOUBLEŽ¡‘hÊDouble-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ2“*“10^-16Ý.Ž©Ç‘.ùœ1–¦f=“GSL_PREC_SINGLEŽ¡‘hÊSingle-precision,–¦fa“relativš²!e“accuracy“of“appro˜ximately“Þ10^-7Ý.Ž¦‘.ùœ2–¦f=“GSL_PREC_APPR•²!O“XŽ¡‘hÊApproš²!ximate–¦fv‘ÿdDalues,“a“relativ˜e“accuracy“of“appro˜ximately“Þ5“*“10^-4Ý.ŽŸ¾‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž©Ç‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ì[‘!Gairy_zero_Ai–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_zero_Ai‘yšâ(én‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_zero_Ai‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“loMÞcation“of“the“s-th“zero“of“the“Airy“function“Ai(x).Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ì[‘!Gairy_zero_Bi–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_zero_Bi‘yšâ(én‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_zero_Bi‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“loMÞcation“of“the“s-th“zero“of“the“Airy“function“Bi(x).Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¤ì[‘!Gairy_zero_Ai_deriv–¦f-*-“texinfo“-*-Ž¡’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_zero_Ai_deriv‘yšâ(én‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_zero_Ai_deriv‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ñ¡routines“compute›ñ¢the“loMÞcation“of“the˜s-th“zero“of“the˜Airy“function“deriv‘ÿdDativ²!eŽ¡‘.ùœAi(x).Ž¦‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¦‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹25‰ŸòŽ ƒ3* ý ÌÖ‘!GÝairy_zero_Bi_deriv–¦f-*-“texinfo“-*-Ž©ÁÔ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉairy_zero_Bi_deriv‘yšâ(én‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“airy_zero_Bi_deriv‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ñ¡routines“compute›ñ¢the“loMÞcation“of“the˜s-th“zero“of“the˜Airy“function“deriv‘ÿdDativ²!eŽ¡‘.ùœBi(x).ŽŸzƒ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸz„‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÁÓ‘!GbMÞessel_zero_J0–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_zero_J0‘yšâ(én‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_zero_J0‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–+routines“compute“the“lošMÞcation“of“the“s-th“p˜ositiv²!e“zero“of“the“Bessel“functionŽ¡‘.ùœJ_0(x).ŽŸz„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸzƒ‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!GbMÞessel_zero_J1–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉbessel_zero_J1‘yšâ(én‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“bessel_zero_J1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–+routines“compute“the“lošMÞcation“of“the“s-th“p˜ositiv²!e“zero“of“the“Bessel“functionŽ¡‘.ùœJ_1(x).Ž¤zƒ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.Ž¡‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¤ 33‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gpsi_1_in²!t–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉpsi_1_int‘yšâ(én‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“psi_1_int‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“T‘ÿerigamma“function“psi(n)“for“pMÞositivš²!e“in˜teger“n.ŽŸzƒ‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸz„‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸÁÓ‘!Gzeta_in²!t–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉzeta_int‘yšâ(én‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“zeta_int‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“Riemann“zeta“function“zeta(n)“for“in²!teger“n,“n“e“1.ŽŸz„‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸzƒ‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒ‹3AŸòŽ ƒ3* ý ÌÖ‘!GÝeta_in²!t–¦f-*-“texinfo“-*-Ž©JÔ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉeta_int‘yšâ(én‘câ)Ž¤ 33’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“eta_int‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–¦froutines“compute“the“eta“function“eta(n)“for“in²!teger“n.ŽŸ;‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ;‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸJÕ‘!Glegendre_Plm–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlegendre_Plm‘yšâ(éná,–¦fémá,“éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“legendre_Plm‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese–ãÎroutines“compute“the“assošMÞciated“Legendre“p˜olynomial‘ãÍP_lÞ^Ým(x)“for“m“Þ>Ý=“0,‘ó(lŽ¡‘.ùœÞ>Ý=–¦fm,“Þ|ÝxÞ|“<Ý=“1.ŽŸ;‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ;‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Glegendre_sphPlm–¦f-*-“texinfo“-*-ŽŸJÕ’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géy‘°Yè=‘LÉlegendre_sphPlm‘yšâ(éná,–¦fémá,“éx‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éyè,–LÉéerr‘cè]“=“legendre_sphPlm‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝThese– *9routines“compute“the‘ *8normalized“assošMÞciated“Legendre“p˜olynomialŽ¡‘.ùœ$sqrtÞ{Ý(2l+1)/(4pi)Þ}– ØÝsqrtÞ{Ý(l-m)!/(l+m)!Þ}› ÙÝP_lÞ^Ým(x)$“suitable˜for“use˜in“sphericalŽ¡‘.ùœharmonics.‘ÎUThe–wÎparameters›wÍm²!ust“satisfy˜m“Þ>Ý=“0,‘l˜Þ>Ý=“m,‘Þ|ÝxÞ|“<Ý=˜1.‘ÎUTheses“routinesŽ¡‘.ùœa•²!v“oid–¦fthe“o•²!v“er o“ws–¦fthat“oMÞccur“for“the“standard“normalization“of“P_lÞ^Ým(x).ŽŸ;‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áyÝ.ŽŸ;‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.Ž¦‘!Gh²!ypMÞerg_U–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géout‘°Yè=‘LÉhyperg_U‘yšâ(éx0á,–¦féx1á,“éx2‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éoutè,–LÉéerr‘cè]“=“hyperg_U‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝSecondary–iõCon uen²!t“Hyp•MÞergo“emetric›iôU‘iæfunction–iõA&E‘iå13.1.3“All“input˜are“double“asŽ¡‘.ùœis–¦fthe“output.ŽŸ;‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áoutÝ.a.ŽŸ;‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŸJÕ‘!Gh²!ypMÞerg_1F1–¦f-*-“texinfo“-*-Ž¦’d{³[Loadable‘¦fF‘ÿeunction]ŽŽ‘Géout‘°Yè=‘LÉhyperg_1F1‘yšâ(éx0á,–¦féx1á,“éx2‘câ)Ž¡’d{³Ý[Loadable‘¦fF‘ÿeunction]ŽŽ‘Gè[éoutè,–LÉéerr‘cè]“=“hyperg_1F1‘yšâ(‘©äá.–§‘.“.Ž‘lÏâ)Ž¡‘.ùœÝPrimary–ã¶Con uen²!t“Hyp•MÞergo“emetric›ã·U‘ã¦function–ã¶A&E‘ã§13.1.3“All“inputs˜are“double“asŽ¡‘.ùœis–¦fthe“output.ŽŸ;‘.ùœáerr‘oÝcon²!tains–¦fan“estimate“of“the“absolute“error“in“the“v‘ÿdDalue“áoutÝ.a.ŽŸ;‘.ùœThis–nïfunction“is“from“the“GNU‘n Scien²!ti c“Library‘ÿe,‘­:see“Þhttp://www.gnu.org/software/gsl/Ÿnï„ ™Ž¡‘.ùœÝfor‘¦fdoMÞcumen²!tation.ŽŽŒøL׃’À;è…ïöïÿ 3ó>ßê ó3 cmmi10ó7m#½R ó3 cmss10ó6p®0J ó3 cmsl10ó3ßê= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn Si -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} Si (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Si (@dots{}) These routines compute the Sine integral Si(x) = \\int_0^x dt \\sin(t)/t. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn Ci -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} Ci (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Ci (@dots{}) These routines compute the Cosine integral Ci(x) = -\\int_x^\\infty dt \\cos(t)/t for x > 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn atanint -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} atanint (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} atanint (@dots{}) These routines compute the Arctangent integral AtanInt(x) = \\int_0^x dt \\arctan(t)/t. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_mhalf -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_mhalf (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_mhalf (@dots{}) These routines compute the complete Fermi-Dirac integral F_@{-1/2@}(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_half -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_half (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_half (@dots{}) These routines compute the complete Fermi-Dirac integral F_@{1/2@}(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_3half -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_3half (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_3half (@dots{}) These routines compute the complete Fermi-Dirac integral F_@{3/2@}(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gamma_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} gamma_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} gamma_gsl (@dots{}) These routines compute the Gamma function \\Gamma(x), subject to x not being a negative integer. The function is computed using the real Lanczos method. The maximum value of x such that \\Gamma(x) is not considered an overflow is given by the macro GSL_SF_GAMMA_XMAX and is 171.0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lngamma_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lngamma_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lngamma_gsl (@dots{}) These routines compute the logarithm of the Gamma function, \\log(\\Gamma(x)), subject to x not a being negative integer. For x<0 the real part of \\log(\\Gamma(x)) is returned, which is equivalent to \\log(|\\Gamma(x)|). The function is computed using the real Lanczos method. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gammastar -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} gammastar (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} gammastar (@dots{}) These routines compute the regulated Gamma Function \\Gamma^*(x) for x > 0. The regulated gamma function is given by, \\Gamma^*(x) = \\Gamma(x)/(\\sqrt@{2\\pi@} x^@{(x-1/2)@} \\exp(-x)) = (1 + (1/12x) + ...) for x \\to \\infty and is a useful suggestion of Temme. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gammainv_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} gammainv_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} gammainv_gsl (@dots{}) These routines compute the reciprocal of the gamma function, 1/\\Gamma(x) using the real Lanczos method. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lambert_W0 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lambert_W0 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lambert_W0 (@dots{}) These compute the principal branch of the Lambert W function, W_0(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@{-1@}(x) to be the other real branch, where W < -1 for x < 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lambert_Wm1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lambert_Wm1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lambert_Wm1 (@dots{}) These compute the secondary real-valued branch of the Lambert W function, W_@{-1@}(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@{-1@}(x) to be the other real branch, where W < -1 for x < 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn log_1plusx -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} log_1plusx (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} log_1plusx (@dots{}) These routines compute \\log(1 + x) for x > -1 using an algorithm that is accurate for small x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn log_1plusx_mx -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} log_1plusx_mx (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} log_1plusx_mx (@dots{}) These routines compute \\log(1 + x) - x for x > -1 using an algorithm that is accurate for small x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn psi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} psi (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi (@dots{}) These routines compute the digamma function \\psi(x) for general x, x \ e 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn psi_1piy -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} psi_1piy (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi_1piy (@dots{}) These routines compute the real part of the digamma function on the line 1+i y, Re[\\psi(1 + i y)]. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn synchrotron_1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} synchrotron_1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} synchrotron_1 (@dots{}) These routines compute the first synchrotron function x \\int_x^\\infty dt K_@{5/3@}(t) for x >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn synchrotron_2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} synchrotron_2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} synchrotron_2 (@dots{}) These routines compute the second synchrotron function x K_@{2/3@}(x) for x >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn transport_2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} transport_2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_2 (@dots{}) These routines compute the transport function J(2,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn transport_3 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} transport_3 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_3 (@dots{}) These routines compute the transport function J(3,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn transport_4 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} transport_4 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_4 (@dots{}) These routines compute the transport function J(4,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn transport_5 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} transport_5 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_5 (@dots{}) These routines compute the transport function J(5,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn sinc_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} sinc_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} sinc_gsl (@dots{}) These routines compute \\sinc(x) = \\sin(\\pi x) / (\\pi x) for any value of x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lnsinh -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lnsinh (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lnsinh (@dots{}) These routines compute \\log(\\sinh(x)) for x > 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lncosh -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lncosh (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lncosh (@dots{}) These routines compute \\log(\\cosh(x)) for any x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn zeta -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} zeta (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} zeta (@dots{}) These routines compute the Riemann zeta function \\zeta(s) for arbitrary s, s \ e 1. The Riemann zeta function is defined by the infinite sum \\zeta(s) = \\sum_@{k=1@}^\\infty k^@{-s@}. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn eta -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} eta (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} eta (@dots{}) These routines compute the eta function \\eta(s) for arbitrary s. The eta function is defined by \\eta(s) = (1-2^@{1-s@}) \\zeta(s). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Jn -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_Jn (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Jn (@dots{}) These routines compute the regular cylindrical Bessel function of order n, J_n(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Yn -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_Yn (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Yn (@dots{}) These routines compute the irregular cylindrical Bessel function of order n, Y_n(x), for x>0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_In -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_In (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_In (@dots{}) These routines compute the regular modified cylindrical Bessel function of order n, I_n(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_In_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_In_scaled (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_In_scaled (@dots{}) These routines compute the scaled regular modified cylindrical Bessel function of order n, \\exp(-|x|) I_n(x) @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Kn -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_Kn (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Kn (@dots{}) These routines compute the irregular modified cylindrical Bessel function of order n, K_n(x), for x > 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Kn_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_Kn_scaled (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Kn_scaled (@dots{}) @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_jl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_jl (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_jl (@dots{}) These routines compute the regular spherical Bessel function of order l, j_l(x), for l >= 0 and x >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_yl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_yl (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_yl (@dots{}) These routines compute the irregular spherical Bessel function of order l, y_l(x), for l >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_il_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_il_scaled (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_il_scaled (@dots{}) These routines compute the scaled regular modified spherical Bessel function of order l, \\exp(-|x|) i_l(x) @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_kl_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_kl_scaled (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_kl_scaled (@dots{}) These routines compute the scaled irregular modified spherical Bessel function of order l, \\exp(x) k_l(x), for x>0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn exprel_n -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} exprel_n (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} exprel_n (@dots{}) These routines compute the N-relative exponential, which is the n-th generalization of the functions gsl_sf_exprel and gsl_sf_exprel2. The N-relative exponential is given by, exprel_N(x) = N!/x^N (\\exp(x) - \\sum_@{k=0@}^@{N-1@} x^k/k!) = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ... = 1F1 (1,1+N,x) @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_int -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_int (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_int (@dots{}) These routines compute the complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/\\Gamma(j+1)) \\int_0^\\infty dt (t^j /(\\exp(t-x)+1)). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn taylorcoeff -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} taylorcoeff (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} taylorcoeff (@dots{}) These routines compute the Taylor coefficient x^n / n! for x >= 0, n >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn legendre_Pl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} legendre_Pl (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_Pl (@dots{}) These functions evaluate the Legendre polynomial P_l(x) for a specific value of l, x subject to l >= 0, |x| <= 1 @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn legendre_Ql -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} legendre_Ql (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_Ql (@dots{}) These routines compute the Legendre function Q_l(x) for x > -1, x != 1 and l >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn psi_n -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} psi_n (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi_n (@dots{}) These routines compute the polygamma function \\psi^@{(m)@}(x) for m >= 0, x > 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Jnu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Jnu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Jnu (@dots{}) These routines compute the regular cylindrical Bessel function of fractional order nu, J_\ u(x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Ynu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Ynu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Ynu (@dots{}) These routines compute the irregular cylindrical Bessel function of fractional order nu, Y_\ u(x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Inu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Inu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Inu (@dots{}) These routines compute the regular modified Bessel function of fractional order nu, I_\ u(x) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Inu_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Inu_scaled (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Inu_scaled (@dots{}) These routines compute the scaled regular modified Bessel function of fractional order nu, \\exp(-|x|)I_\ u(x) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Knu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Knu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Knu (@dots{}) These routines compute the irregular modified Bessel function of fractional order nu, K_\ u(x) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_lnKnu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_lnKnu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_lnKnu (@dots{}) These routines compute the logarithm of the irregular modified Bessel function of fractional order nu, \\ln(K_\ u(x)) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Knu_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Knu_scaled (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Knu_scaled (@dots{}) These routines compute the scaled irregular modified Bessel function of fractional order nu, \\exp(+|x|) K_\ u(x) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn exp_mult -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} exp_mult (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} exp_mult (@dots{}) These routines exponentiate x and multiply by the factor y to return the product y \\exp(x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_inc_0 -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} fermi_dirac_inc_0 (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} fermi_dirac_inc_0 (@dots{}) These routines compute the incomplete Fermi-Dirac integral with an index of zero, F_0(x,b) = \\ln(1 + e^@{b-x@}) - (b-x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn poch -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} poch (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} poch (@dots{}) These routines compute the Pochhammer symbol (a)_x := \\Gamma(a + x)/\\Gamma(a), subject to a and a+x not being negative integers. The Pochhammer symbol is also known as the Apell symbol. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lnpoch -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} lnpoch (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} lnpoch (@dots{}) These routines compute the logarithm of the Pochhammer symbol, \\log((a)_x) = \\log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn pochrel -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} pochrel (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} pochrel (@dots{}) These routines compute the relative Pochhammer symbol ((a,x) - 1)/x where (a,x) = (a)_x := \\Gamma(a + x)/\\Gamma(a). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gamma_inc_Q -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} gamma_inc_Q (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} gamma_inc_Q (@dots{}) These routines compute the normalized incomplete Gamma Function Q(a,x) = 1/\\Gamma(a) \\int_x\\infty dt t^@{a-1@} \\exp(-t) for a > 0, x >= 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gamma_inc_P -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} gamma_inc_P (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} gamma_inc_P (@dots{}) These routines compute the complementary normalized incomplete Gamma Function P(a,x) = 1/\\Gamma(a) \\int_0^x dt t^@{a-1@} \\exp(-t) for a > 0, x >= 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gamma_inc -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} gamma_inc (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} gamma_inc (@dots{}) These functions compute the incomplete Gamma Function the normalization factor included in the previously defined functions: \\Gamma(a,x) = \\int_x\\infty dt t^@{a-1@} \\exp(-t) for a real and x >= 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn beta_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} beta_gsl (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} beta_gsl (@dots{}) These routines compute the Beta Function, B(a,b) = \\Gamma(a)\\Gamma(b)/\\Gamma(a+b) for a > 0, b > 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lnbeta -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} lnbeta (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} lnbeta (@dots{}) These routines compute the logarithm of the Beta Function, \\log(B(a,b)) for a > 0, b > 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hyperg_0F1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} hyperg_0F1 (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} hyperg_0F1 (@dots{}) These routines compute the hypergeometric function 0F1(c,x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn conicalP_half -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} conicalP_half (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_half (@dots{}) These routines compute the irregular Spherical Conical Function P^@{1/2@}_@{-1/2 + i \\lambda@}(x) for x > -1. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn conicalP_mhalf -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} conicalP_mhalf (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_mhalf (@dots{}) These routines compute the regular Spherical Conical Function P^@{-1/2@}_@{-1/2 + i \\lambda@}(x) for x > -1. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn conicalP_0 -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} conicalP_0 (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_0 (@dots{}) These routines compute the conical function P^0_@{-1/2 + i \\lambda@}(x) for x > -1. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn conicalP_1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} conicalP_1 (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_1 (@dots{}) These routines compute the conical function P^1_@{-1/2 + i \\lambda@}(x) for x > -1. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hzeta -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} hzeta (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} hzeta (@dots{}) These routines compute the Hurwitz zeta function \\zeta(s,q) for s > 1, q > 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Ai -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Ai (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai (@dots{}) These routines compute the Airy function Ai(x) with an accuracy specified by mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Bi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Bi (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi (@dots{}) These routines compute the Airy function Bi(x) with an accuracy specified by mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Ai_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Ai_scaled (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai_scaled (@dots{}) These routines compute a scaled version of the Airy function S_A(x) Ai(x). For x>0 the scaling factor S_A(x) is \\exp(+(2/3) x^(3/2)), and is 1 for x<0. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Bi_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Bi_scaled (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi_scaled (@dots{}) These routines compute a scaled version of the Airy function S_B(x) Bi(x). For x>0 the scaling factor S_B(x) is exp(-(2/3) x^(3/2)), and is 1 for x<0. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Ai_deriv -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Ai_deriv (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai_deriv (@dots{}) These routines compute the Airy function derivative Ai'(x) with an accuracy specified by mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Bi_deriv -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Bi_deriv (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi_deriv (@dots{}) These routines compute the Airy function derivative Bi'(x) with an accuracy specified by mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Ai_deriv_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Ai_deriv_scaled (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai_deriv_scaled (@dots{}) These routines compute the derivative of the scaled Airy function S_A(x) Ai(x). The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Bi_deriv_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Bi_deriv_scaled (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi_deriv_scaled (@dots{}) These routines compute the derivative of the scaled Airy function S_B(x) Bi(x). The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn ellint_Kcomp -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} ellint_Kcomp (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} ellint_Kcomp (@dots{}) These routines compute the complete elliptic integral K(k) @tex \\beforedisplay $$ \\eqalign{ K(k) &= \\int_0^{\\pi/2} {dt \\over \\sqrt{(1 - k^2 \\sin^2(t))}} \\cr } $$ \\afterdisplay See also: @end tex @ifinfo @group @example pi --- 2 / | 1 ellint_Kcomp(k) = | ------------------- dt | 2 2 / sqrt(1 - k sin (t)) 0 @end example @end group @end ifinfo @ifhtml @group @example pi --- 2 / | 1 ellint_Kcomp(k) = | ------------------- dt | 2 2 / sqrt(1 - k sin (t)) 0 @end example @end group @end ifhtml @seealso{ellipj, ellipke} The notation used here is based on Carlson, @cite{Numerische Mathematik} 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter @math{m = k^2}. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn ellint_Ecomp -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} ellint_Ecomp (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} ellint_Ecomp (@dots{}) These routines compute the complete elliptic integral E(k) to the accuracy specified by the mode variable mode. @tex \\beforedisplay $$ \\eqalign{ E(k) &= \\int_0^{\\pi/2} \\sqrt{(1 - k^2 \\sin^2(t))} dt \\cr } $$ \\afterdisplay See also: @end tex @ifinfo @group @example pi --- 2 / | 2 2 ellint_Ecomp(k) = | sqrt(1 - k sin (t)) dt | / 0 @end example @end group @end ifinfo @ifhtml @group @example pi --- 2 / | 2 2 ellint_Ecomp(k) = | sqrt(1 - k sin (t)) dt | / 0 @end example @end group @end ifhtml @seealso{ellipj, ellipke} The notation used here is based on Carlson, @cite{Numerische Mathematik} 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter @math{m = k^2}. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_zero_Ai -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_zero_Ai (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Ai (@dots{}) These routines compute the location of the s-th zero of the Airy function Ai(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_zero_Bi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_zero_Bi (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Bi (@dots{}) These routines compute the location of the s-th zero of the Airy function Bi(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_zero_Ai_deriv -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_zero_Ai_deriv (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Ai_deriv (@dots{}) These routines compute the location of the s-th zero of the Airy function derivative Ai(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_zero_Bi_deriv -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_zero_Bi_deriv (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Bi_deriv (@dots{}) These routines compute the location of the s-th zero of the Airy function derivative Bi(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_zero_J0 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_zero_J0 (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_zero_J0 (@dots{}) These routines compute the location of the s-th positive zero of the Bessel function J_0(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_zero_J1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_zero_J1 (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_zero_J1 (@dots{}) These routines compute the location of the s-th positive zero of the Bessel function J_1(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn psi_1_int -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} psi_1_int (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi_1_int (@dots{}) These routines compute the Trigamma function \\psi(n) for positive integer n. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn zeta_int -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} zeta_int (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} zeta_int (@dots{}) These routines compute the Riemann zeta function \\zeta(n) for integer n, n \ e 1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn eta_int -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} eta_int (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} eta_int (@dots{}) These routines compute the eta function \\eta(n) for integer n. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn legendre_Plm -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} legendre_Plm (@var{n}, @var{m}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_Plm (@dots{}) These routines compute the associated Legendre polynomial P_l^m(x) for m >= 0, l >= m, |x| <= 1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn legendre_sphPlm -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} legendre_sphPlm (@var{n}, @var{m}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_sphPlm (@dots{}) These routines compute the normalized associated Legendre polynomial $\\sqrt@{(2l+1)/(4\\pi)@} \\sqrt@{(l-m)!/(l+m)!@} P_l^m(x)$ suitable for use in spherical harmonics. The parameters must satisfy m >= 0, l >= m, |x| <= 1. Theses routines avoid the overflows that occur for the standard normalization of P_l^m(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hyperg_U -*- texinfo -*- @deftypefn {Loadable Function} {@var{out} =} hyperg_U (@var{x0}, @var{x1}, @var{x2}) @deftypefnx {Loadable Function} {[@var{out}, @var{err}] =} hyperg_U (@dots{}) Secondary Confluent Hypergoemetric U function A&E 13.1.3 All inputs are double as is the output. @var{err} contains an estimate of the absolute error in the value @var{out}.a. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hyperg_1F1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{out} =} hyperg_1F1 (@var{x0}, @var{x1}, @var{x2}) @deftypefnx {Loadable Function} {[@var{out}, @var{err}] =} hyperg_1F1 (@dots{}) Primary Confluent Hypergoemetric U function A&E 13.1.3 All inputs are double as is the output. @var{err} contains an estimate of the absolute error in the value @var{out}.a. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gsl_sf -*- texinfo -*- @deftypefn {Loadable Function} {} gsl_sf () Octave bindings to the GNU Scientific Library. All GSL functions can be called with by the GSL names within octave. @end deftypefn clausen -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} clausen (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} clausen (@dots{}) The Clausen function is defined by the following integral, Cl_2(x) = - \\int_0^x dt \\log(2 \\sin(t/2)) It is related to the dilogarithm by Cl_2(\\theta) = \\Im Li_2(\\exp(i \\theta)). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn dawson -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} dawson (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} dawson (@dots{}) The Dawson integral is defined by \\exp(-x^2) \\int_0^x dt \\exp(t^2). A table of Dawson integral can be found in Abramowitz & Stegun, Table 7.5. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn debye_1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} debye_1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_1 (@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn debye_2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} debye_2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_2 (@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn debye_3 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} debye_3 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_3 (@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn debye_4 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} debye_4 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_4 (@dots{}) The Debye functions are defined by the integral D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn erf_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} erf_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erf_gsl (@dots{}) These routines compute the error function erf(x) = (2/\\sqrt(\\pi)) \\int_0^x dt \\exp(-t^2). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn erfc_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} erfc_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erfc_gsl (@dots{}) These routines compute the complementary error function erfc(x) = 1 - erf(x) = (2/\\sqrt(\\pi)) \\int_x^\\infty \\exp(-t^2). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn log_erfc -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} log_erfc (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} log_erfc (@dots{}) These routines compute the logarithm of the complementary error function \\log(\\erfc(x)). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn erf_Z -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} erf_Z (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erf_Z (@dots{}) These routines compute the Gaussian probability function Z(x) = (1/(2\\pi)) \\exp(-x^2/2). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn erf_Q -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} erf_Q (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erf_Q (@dots{}) These routines compute the upper tail of the Gaussian probability function Q(x) = (1/(2\\pi)) \\int_x^\\infty dt \\exp(-t^2/2). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hazard -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} hazard (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} hazard (@dots{}) The hazard function for the normal distrbution, also known as the inverse Mill\\'s ratio, is defined as h(x) = Z(x)/Q(x) = \\sqrt@{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2)@}. It decreases rapidly as x approaches -\\infty and asymptotes to h(x) \\sim x as x approaches +\\infty. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn expm1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} expm1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expm1 (@dots{}) These routines compute the quantity \\exp(x)-1 using an algorithm that is accurate for small x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn exprel -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} exprel (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} exprel (@dots{}) These routines compute the quantity (\\exp(x)-1)/x using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion (\\exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\dots. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn exprel_2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} exprel_2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} exprel_2 (@dots{}) These routines compute the quantity 2(\\exp(x)-1-x)/x^2 using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion 2(\\exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\dots. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn expint_E1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} expint_E1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_E1 (@dots{}) These routines compute the exponential integral E_1(x), E_1(x) := Re \\int_1^\\infty dt \\exp(-xt)/t. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn expint_E2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} expint_E2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_E2 (@dots{}) These routines compute the second-order exponential integral E_2(x), E_2(x) := \\Re \\int_1^\\infty dt \\exp(-xt)/t^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn expint_Ei -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} expint_Ei (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_Ei (@dots{}) These routines compute the exponential integral E_i(x), Ei(x) := - PV(\\int_@{-x@}^\\infty dt \\exp(-t)/t) where PV denotes the principal value of the integral. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn Shi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} Shi (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Shi (@dots{}) These routines compute the integral Shi(x) = \\int_0^x dt \\sinh(t)/t. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn Chi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} Chi (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Chi (@dots{}) These routines compute the integral Chi(x) := Re[ \\gamma_E + \\log(x) + \\int_0^x dt (\\cosh[t]-1)/t] , where \\gamma_E is the Euler constant. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn expint_3 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} expint_3 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_3 (@dots{}) These routines compute the exponential integral Ei_3(x) = \\int_0^x dt \\exp(-t^3) for x >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn Si -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} Si (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Si (@dots{}) These routines compute the Sine integral Si(x) = \\int_0^x dt \\sin(t)/t. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn Ci -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} Ci (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Ci (@dots{}) These routines compute the Cosine integral Ci(x) = -\\int_x^\\infty dt \\cos(t)/t for x > 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn atanint -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} atanint (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} atanint (@dots{}) These routines compute the Arctangent integral AtanInt(x) = \\int_0^x dt \\arctan(t)/t. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_mhalf -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_mhalf (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_mhalf (@dots{}) These routines compute the complete Fermi-Dirac integral F_@{-1/2@}(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_half -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_half (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_half (@dots{}) These routines compute the complete Fermi-Dirac integral F_@{1/2@}(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_3half -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_3half (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_3half (@dots{}) These routines compute the complete Fermi-Dirac integral F_@{3/2@}(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gamma_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} gamma_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} gamma_gsl (@dots{}) These routines compute the Gamma function \\Gamma(x), subject to x not being a negative integer. The function is computed using the real Lanczos method. The maximum value of x such that \\Gamma(x) is not considered an overflow is given by the macro GSL_SF_GAMMA_XMAX and is 171.0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lngamma_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lngamma_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lngamma_gsl (@dots{}) These routines compute the logarithm of the Gamma function, \\log(\\Gamma(x)), subject to x not a being negative integer. For x<0 the real part of \\log(\\Gamma(x)) is returned, which is equivalent to \\log(|\\Gamma(x)|). The function is computed using the real Lanczos method. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gammastar -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} gammastar (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} gammastar (@dots{}) These routines compute the regulated Gamma Function \\Gamma^*(x) for x > 0. The regulated gamma function is given by, \\Gamma^*(x) = \\Gamma(x)/(\\sqrt@{2\\pi@} x^@{(x-1/2)@} \\exp(-x)) = (1 + (1/12x) + ...) for x \\to \\infty and is a useful suggestion of Temme. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gammainv_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} gammainv_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} gammainv_gsl (@dots{}) These routines compute the reciprocal of the gamma function, 1/\\Gamma(x) using the real Lanczos method. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lambert_W0 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lambert_W0 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lambert_W0 (@dots{}) These compute the principal branch of the Lambert W function, W_0(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@{-1@}(x) to be the other real branch, where W < -1 for x < 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lambert_Wm1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lambert_Wm1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lambert_Wm1 (@dots{}) These compute the secondary real-valued branch of the Lambert W function, W_@{-1@}(x). Lambert\\'s W functions, W(x), are defined to be solutions of the equation W(x) \\exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@{-1@}(x) to be the other real branch, where W < -1 for x < 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn log_1plusx -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} log_1plusx (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} log_1plusx (@dots{}) These routines compute \\log(1 + x) for x > -1 using an algorithm that is accurate for small x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn log_1plusx_mx -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} log_1plusx_mx (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} log_1plusx_mx (@dots{}) These routines compute \\log(1 + x) - x for x > -1 using an algorithm that is accurate for small x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn psi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} psi (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi (@dots{}) These routines compute the digamma function \\psi(x) for general x, x \ e 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn psi_1piy -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} psi_1piy (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi_1piy (@dots{}) These routines compute the real part of the digamma function on the line 1+i y, Re[\\psi(1 + i y)]. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn synchrotron_1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} synchrotron_1 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} synchrotron_1 (@dots{}) These routines compute the first synchrotron function x \\int_x^\\infty dt K_@{5/3@}(t) for x >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn synchrotron_2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} synchrotron_2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} synchrotron_2 (@dots{}) These routines compute the second synchrotron function x K_@{2/3@}(x) for x >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn transport_2 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} transport_2 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_2 (@dots{}) These routines compute the transport function J(2,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn transport_3 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} transport_3 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_3 (@dots{}) These routines compute the transport function J(3,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn transport_4 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} transport_4 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_4 (@dots{}) These routines compute the transport function J(4,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn transport_5 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} transport_5 (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_5 (@dots{}) These routines compute the transport function J(5,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn sinc_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} sinc_gsl (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} sinc_gsl (@dots{}) These routines compute \\sinc(x) = \\sin(\\pi x) / (\\pi x) for any value of x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lnsinh -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lnsinh (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lnsinh (@dots{}) These routines compute \\log(\\sinh(x)) for x > 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lncosh -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} lncosh (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lncosh (@dots{}) These routines compute \\log(\\cosh(x)) for any x. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn zeta -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} zeta (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} zeta (@dots{}) These routines compute the Riemann zeta function \\zeta(s) for arbitrary s, s \ e 1. The Riemann zeta function is defined by the infinite sum \\zeta(s) = \\sum_@{k=1@}^\\infty k^@{-s@}. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn eta -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} eta (@var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} eta (@dots{}) These routines compute the eta function \\eta(s) for arbitrary s. The eta function is defined by \\eta(s) = (1-2^@{1-s@}) \\zeta(s). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Jn -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_Jn (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Jn (@dots{}) These routines compute the regular cylindrical Bessel function of order n, J_n(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Yn -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_Yn (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Yn (@dots{}) These routines compute the irregular cylindrical Bessel function of order n, Y_n(x), for x>0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_In -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_In (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_In (@dots{}) These routines compute the regular modified cylindrical Bessel function of order n, I_n(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_In_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_In_scaled (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_In_scaled (@dots{}) These routines compute the scaled regular modified cylindrical Bessel function of order n, \\exp(-|x|) I_n(x) @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Kn -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_Kn (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Kn (@dots{}) These routines compute the irregular modified cylindrical Bessel function of order n, K_n(x), for x > 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Kn_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_Kn_scaled (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Kn_scaled (@dots{}) @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_jl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_jl (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_jl (@dots{}) These routines compute the regular spherical Bessel function of order l, j_l(x), for l >= 0 and x >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_yl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_yl (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_yl (@dots{}) These routines compute the irregular spherical Bessel function of order l, y_l(x), for l >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_il_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_il_scaled (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_il_scaled (@dots{}) These routines compute the scaled regular modified spherical Bessel function of order l, \\exp(-|x|) i_l(x) @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_kl_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_kl_scaled (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_kl_scaled (@dots{}) These routines compute the scaled irregular modified spherical Bessel function of order l, \\exp(x) k_l(x), for x>0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn exprel_n -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} exprel_n (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} exprel_n (@dots{}) These routines compute the N-relative exponential, which is the n-th generalization of the functions gsl_sf_exprel and gsl_sf_exprel2. The N-relative exponential is given by, exprel_N(x) = N!/x^N (\\exp(x) - \\sum_@{k=0@}^@{N-1@} x^k/k!) = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ... = 1F1 (1,1+N,x) @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_int -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} fermi_dirac_int (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_int (@dots{}) These routines compute the complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/\\Gamma(j+1)) \\int_0^\\infty dt (t^j /(\\exp(t-x)+1)). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn taylorcoeff -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} taylorcoeff (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} taylorcoeff (@dots{}) These routines compute the Taylor coefficient x^n / n! for x >= 0, n >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn legendre_Pl -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} legendre_Pl (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_Pl (@dots{}) These functions evaluate the Legendre polynomial P_l(x) for a specific value of l, x subject to l >= 0, |x| <= 1 @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn legendre_Ql -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} legendre_Ql (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_Ql (@dots{}) These routines compute the Legendre function Q_l(x) for x > -1, x != 1 and l >= 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn psi_n -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} psi_n (@var{n}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi_n (@dots{}) These routines compute the polygamma function \\psi^@{(m)@}(x) for m >= 0, x > 0. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Jnu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Jnu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Jnu (@dots{}) These routines compute the regular cylindrical Bessel function of fractional order nu, J_\ u(x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Ynu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Ynu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Ynu (@dots{}) These routines compute the irregular cylindrical Bessel function of fractional order nu, Y_\ u(x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Inu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Inu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Inu (@dots{}) These routines compute the regular modified Bessel function of fractional order nu, I_\ u(x) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Inu_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Inu_scaled (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Inu_scaled (@dots{}) These routines compute the scaled regular modified Bessel function of fractional order nu, \\exp(-|x|)I_\ u(x) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Knu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Knu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Knu (@dots{}) These routines compute the irregular modified Bessel function of fractional order nu, K_\ u(x) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_lnKnu -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_lnKnu (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_lnKnu (@dots{}) These routines compute the logarithm of the irregular modified Bessel function of fractional order nu, \\ln(K_\ u(x)) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_Knu_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} bessel_Knu_scaled (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Knu_scaled (@dots{}) These routines compute the scaled irregular modified Bessel function of fractional order nu, \\exp(+|x|) K_\ u(x) for x>0, \ u>0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn exp_mult -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} exp_mult (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} exp_mult (@dots{}) These routines exponentiate x and multiply by the factor y to return the product y \\exp(x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn fermi_dirac_inc_0 -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} fermi_dirac_inc_0 (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} fermi_dirac_inc_0 (@dots{}) These routines compute the incomplete Fermi-Dirac integral with an index of zero, F_0(x,b) = \\ln(1 + e^@{b-x@}) - (b-x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn poch -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} poch (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} poch (@dots{}) These routines compute the Pochhammer symbol (a)_x := \\Gamma(a + x)/\\Gamma(a), subject to a and a+x not being negative integers. The Pochhammer symbol is also known as the Apell symbol. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lnpoch -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} lnpoch (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} lnpoch (@dots{}) These routines compute the logarithm of the Pochhammer symbol, \\log((a)_x) = \\log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn pochrel -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} pochrel (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} pochrel (@dots{}) These routines compute the relative Pochhammer symbol ((a,x) - 1)/x where (a,x) = (a)_x := \\Gamma(a + x)/\\Gamma(a). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gamma_inc_Q -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} gamma_inc_Q (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} gamma_inc_Q (@dots{}) These routines compute the normalized incomplete Gamma Function Q(a,x) = 1/\\Gamma(a) \\int_x\\infty dt t^@{a-1@} \\exp(-t) for a > 0, x >= 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gamma_inc_P -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} gamma_inc_P (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} gamma_inc_P (@dots{}) These routines compute the complementary normalized incomplete Gamma Function P(a,x) = 1/\\Gamma(a) \\int_0^x dt t^@{a-1@} \\exp(-t) for a > 0, x >= 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gamma_inc -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} gamma_inc (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} gamma_inc (@dots{}) These functions compute the incomplete Gamma Function the normalization factor included in the previously defined functions: \\Gamma(a,x) = \\int_x\\infty dt t^@{a-1@} \\exp(-t) for a real and x >= 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn beta_gsl -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} beta_gsl (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} beta_gsl (@dots{}) These routines compute the Beta Function, B(a,b) = \\Gamma(a)\\Gamma(b)/\\Gamma(a+b) for a > 0, b > 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn lnbeta -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} lnbeta (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} lnbeta (@dots{}) These routines compute the logarithm of the Beta Function, \\log(B(a,b)) for a > 0, b > 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hyperg_0F1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} hyperg_0F1 (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} hyperg_0F1 (@dots{}) These routines compute the hypergeometric function 0F1(c,x). @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn conicalP_half -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} conicalP_half (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_half (@dots{}) These routines compute the irregular Spherical Conical Function P^@{1/2@}_@{-1/2 + i \\lambda@}(x) for x > -1. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn conicalP_mhalf -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} conicalP_mhalf (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_mhalf (@dots{}) These routines compute the regular Spherical Conical Function P^@{-1/2@}_@{-1/2 + i \\lambda@}(x) for x > -1. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn conicalP_0 -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} conicalP_0 (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_0 (@dots{}) These routines compute the conical function P^0_@{-1/2 + i \\lambda@}(x) for x > -1. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn conicalP_1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} conicalP_1 (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_1 (@dots{}) These routines compute the conical function P^1_@{-1/2 + i \\lambda@}(x) for x > -1. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hzeta -*- texinfo -*- @deftypefn {Loadable Function} {@var{z} =} hzeta (@var{x}, @var{y}) @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} hzeta (@dots{}) These routines compute the Hurwitz zeta function \\zeta(s,q) for s > 1, q > 0. @var{err} contains an estimate of the absolute error in the value @var{z}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Ai -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Ai (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai (@dots{}) These routines compute the Airy function Ai(x) with an accuracy specified by mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Bi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Bi (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi (@dots{}) These routines compute the Airy function Bi(x) with an accuracy specified by mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Ai_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Ai_scaled (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai_scaled (@dots{}) These routines compute a scaled version of the Airy function S_A(x) Ai(x). For x>0 the scaling factor S_A(x) is \\exp(+(2/3) x^(3/2)), and is 1 for x<0. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Bi_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Bi_scaled (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi_scaled (@dots{}) These routines compute a scaled version of the Airy function S_B(x) Bi(x). For x>0 the scaling factor S_B(x) is exp(-(2/3) x^(3/2)), and is 1 for x<0. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Ai_deriv -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Ai_deriv (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai_deriv (@dots{}) These routines compute the Airy function derivative Ai'(x) with an accuracy specified by mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Bi_deriv -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Bi_deriv (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi_deriv (@dots{}) These routines compute the Airy function derivative Bi'(x) with an accuracy specified by mode. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Ai_deriv_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Ai_deriv_scaled (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai_deriv_scaled (@dots{}) These routines compute the derivative of the scaled Airy function S_A(x) Ai(x). The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_Bi_deriv_scaled -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_Bi_deriv_scaled (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi_deriv_scaled (@dots{}) These routines compute the derivative of the scaled Airy function S_B(x) Bi(x). The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn ellint_Kcomp -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} ellint_Kcomp (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} ellint_Kcomp (@dots{}) These routines compute the complete elliptic integral K(k) @tex \\beforedisplay $$ \\eqalign{ K(k) &= \\int_0^{\\pi/2} {dt \\over \\sqrt{(1 - k^2 \\sin^2(t))}} \\cr } $$ \\afterdisplay @end tex The notation used here is based on Carlson, @cite{Numerische Mathematik} 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter @math{m = k^2}. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn ellint_Ecomp -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} ellint_Ecomp (@var{x}, @var{mode}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} ellint_Ecomp (@dots{}) These routines compute the complete elliptic integral E(k) to the accuracy specified by the mode variable mode. @tex \\beforedisplay $$ \\eqalign{ E(k) &= \\int_0^{\\pi/2} \\sqrt{(1 - k^2 \\sin^2(t))} dt \\cr } $$ \\afterdisplay @end tex The notation used here is based on Carlson, @cite{Numerische Mathematik} 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter @math{m = k^2}. The second argument @var{mode} must be an integer corresponding to @table @asis @item 0 = GSL_PREC_DOUBLE Double-precision, a relative accuracy of approximately @code{2 * 10^-16}. @item 1 = GSL_PREC_SINGLE Single-precision, a relative accuracy of approximately @code{10^-7}. @item 2 = GSL_PREC_APPROX Approximate values, a relative accuracy of approximately @code{5 * 10^-4}. @end table @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_zero_Ai -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_zero_Ai (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Ai (@dots{}) These routines compute the location of the s-th zero of the Airy function Ai(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_zero_Bi -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_zero_Bi (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Bi (@dots{}) These routines compute the location of the s-th zero of the Airy function Bi(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_zero_Ai_deriv -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_zero_Ai_deriv (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Ai_deriv (@dots{}) These routines compute the location of the s-th zero of the Airy function derivative Ai(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn airy_zero_Bi_deriv -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} airy_zero_Bi_deriv (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Bi_deriv (@dots{}) These routines compute the location of the s-th zero of the Airy function derivative Bi(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_zero_J0 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_zero_J0 (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_zero_J0 (@dots{}) These routines compute the location of the s-th positive zero of the Bessel function J_0(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn bessel_zero_J1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} bessel_zero_J1 (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_zero_J1 (@dots{}) These routines compute the location of the s-th positive zero of the Bessel function J_1(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn psi_1_int -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} psi_1_int (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi_1_int (@dots{}) These routines compute the Trigamma function \\psi(n) for positive integer n. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn zeta_int -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} zeta_int (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} zeta_int (@dots{}) These routines compute the Riemann zeta function \\zeta(n) for integer n, n \ e 1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn eta_int -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} eta_int (@var{n}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} eta_int (@dots{}) These routines compute the eta function \\eta(n) for integer n. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn legendre_Plm -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} legendre_Plm (@var{n}, @var{m}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_Plm (@dots{}) These routines compute the associated Legendre polynomial P_l^m(x) for m >= 0, l >= m, |x| <= 1. @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn legendre_sphPlm -*- texinfo -*- @deftypefn {Loadable Function} {@var{y} =} legendre_sphPlm (@var{n}, @var{m}, @var{x}) @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_sphPlm (@dots{}) These routines compute the normalized associated Legendre polynomial $\\sqrt@{(2l+1)/(4\\pi)@} \\sqrt@{(l-m)!/(l+m)!@} P_l^m(x)$ suitable for use in spherical harmonics. The parameters must satisfy m >= 0, l >= m, |x| <= 1. Theses routines avoid the overflows that occur for the standard normalization of P_l^m(x). @var{err} contains an estimate of the absolute error in the value @var{y}. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hyperg_U -*- texinfo -*- @deftypefn {Loadable Function} {@var{out} =} hyperg_U (@var{x0}, @var{x1}, @var{x2}) @deftypefnx {Loadable Function} {[@var{out}, @var{err}] =} hyperg_U (@dots{}) Secondary Confluent Hypergoemetric U function A&E 13.1.3 All input are double as is the output. @var{err} contains an estimate of the absolute error in the value @var{out}.a. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn hyperg_1F1 -*- texinfo -*- @deftypefn {Loadable Function} {@var{out} =} hyperg_1F1 (@var{x0}, @var{x1}, @var{x2}) @deftypefnx {Loadable Function} {[@var{out}, @var{err}] =} hyperg_1F1 (@dots{}) Primary Confluent Hypergoemetric U function A&E 13.1.3 All inputs are double as is the output. @var{err} contains an estimate of the absolute error in the value @var{out}.a. This function is from the GNU Scientific Library, see @url{http://www.gnu.org/software/gsl/} for documentation. @end deftypefn gsl-1.0.8/COPYING0000644000175000017500000004307711201030403011141 0ustar shsh GNU GENERAL PUBLIC LICENSE Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc. Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users. This General Public License applies to most of the Free Software Foundation's software and to any other program whose authors commit to using it. (Some other Free Software Foundation software is covered by the GNU Library General Public License instead.) You can apply it to your programs, too. When we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for this service if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free programs; and that you know you can do these things. To protect your rights, we need to make restrictions that forbid anyone to deny you these rights or to ask you to surrender the rights. These restrictions translate to certain responsibilities for you if you distribute copies of the software, or if you modify it. For example, if you distribute copies of such a program, whether gratis or for a fee, you must give the recipients all the rights that you have. You must make sure that they, too, receive or can get the source code. And you must show them these terms so they know their rights. We protect your rights with two steps: (1) copyright the software, and (2) offer you this license which gives you legal permission to copy, distribute and/or modify the software. Also, for each author's protection and ours, we want to make certain that everyone understands that there is no warranty for this free software. If the software is modified by someone else and passed on, we want its recipients to know that what they have is not the original, so that any problems introduced by others will not reflect on the original authors' reputations. Finally, any free program is threatened constantly by software patents. We wish to avoid the danger that redistributors of a free program will individually obtain patent licenses, in effect making the program proprietary. To prevent this, we have made it clear that any patent must be licensed for everyone's free use or not licensed at all. The precise terms and conditions for copying, distribution and modification follow. GNU GENERAL PUBLIC LICENSE TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION 0. This License applies to any program or other work which contains a notice placed by the copyright holder saying it may be distributed under the terms of this General Public License. The "Program", below, refers to any such program or work, and a "work based on the Program" means either the Program or any derivative work under copyright law: that is to say, a work containing the Program or a portion of it, either verbatim or with modifications and/or translated into another language. (Hereinafter, translation is included without limitation in the term "modification".) Each licensee is addressed as "you". Activities other than copying, distribution and modification are not covered by this License; they are outside its scope. The act of running the Program is not restricted, and the output from the Program is covered only if its contents constitute a work based on the Program (independent of having been made by running the Program). Whether that is true depends on what the Program does. 1. You may copy and distribute verbatim copies of the Program's source code as you receive it, in any medium, provided that you conspicuously and appropriately publish on each copy an appropriate copyright notice and disclaimer of warranty; keep intact all the notices that refer to this License and to the absence of any warranty; and give any other recipients of the Program a copy of this License along with the Program. You may charge a fee for the physical act of transferring a copy, and you may at your option offer warranty protection in exchange for a fee. 2. You may modify your copy or copies of the Program or any portion of it, thus forming a work based on the Program, and copy and distribute such modifications or work under the terms of Section 1 above, provided that you also meet all of these conditions: a) You must cause the modified files to carry prominent notices stating that you changed the files and the date of any change. b) You must cause any work that you distribute or publish, that in whole or in part contains or is derived from the Program or any part thereof, to be licensed as a whole at no charge to all third parties under the terms of this License. c) If the modified program normally reads commands interactively when run, you must cause it, when started running for such interactive use in the most ordinary way, to print or display an announcement including an appropriate copyright notice and a notice that there is no warranty (or else, saying that you provide a warranty) and that users may redistribute the program under these conditions, and telling the user how to view a copy of this License. (Exception: if the Program itself is interactive but does not normally print such an announcement, your work based on the Program is not required to print an announcement.) These requirements apply to the modified work as a whole. If identifiable sections of that work are not derived from the Program, and can be reasonably considered independent and separate works in themselves, then this License, and its terms, do not apply to those sections when you distribute them as separate works. But when you distribute the same sections as part of a whole which is a work based on the Program, the distribution of the whole must be on the terms of this License, whose permissions for other licensees extend to the entire whole, and thus to each and every part regardless of who wrote it. Thus, it is not the intent of this section to claim rights or contest your rights to work written entirely by you; rather, the intent is to exercise the right to control the distribution of derivative or collective works based on the Program. In addition, mere aggregation of another work not based on the Program with the Program (or with a work based on the Program) on a volume of a storage or distribution medium does not bring the other work under the scope of this License. 3. You may copy and distribute the Program (or a work based on it, under Section 2) in object code or executable form under the terms of Sections 1 and 2 above provided that you also do one of the following: a) Accompany it with the complete corresponding machine-readable source code, which must be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange; or, b) Accompany it with a written offer, valid for at least three years, to give any third party, for a charge no more than your cost of physically performing source distribution, a complete machine-readable copy of the corresponding source code, to be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange; or, c) Accompany it with the information you received as to the offer to distribute corresponding source code. (This alternative is allowed only for noncommercial distribution and only if you received the program in object code or executable form with such an offer, in accord with Subsection b above.) The source code for a work means the preferred form of the work for making modifications to it. For an executable work, complete source code means all the source code for all modules it contains, plus any associated interface definition files, plus the scripts used to control compilation and installation of the executable. However, as a special exception, the source code distributed need not include anything that is normally distributed (in either source or binary form) with the major components (compiler, kernel, and so on) of the operating system on which the executable runs, unless that component itself accompanies the executable. If distribution of executable or object code is made by offering access to copy from a designated place, then offering equivalent access to copy the source code from the same place counts as distribution of the source code, even though third parties are not compelled to copy the source along with the object code. 4. You may not copy, modify, sublicense, or distribute the Program except as expressly provided under this License. Any attempt otherwise to copy, modify, sublicense or distribute the Program is void, and will automatically terminate your rights under this License. However, parties who have received copies, or rights, from you under this License will not have their licenses terminated so long as such parties remain in full compliance. 5. You are not required to accept this License, since you have not signed it. However, nothing else grants you permission to modify or distribute the Program or its derivative works. These actions are prohibited by law if you do not accept this License. Therefore, by modifying or distributing the Program (or any work based on the Program), you indicate your acceptance of this License to do so, and all its terms and conditions for copying, distributing or modifying the Program or works based on it. 6. Each time you redistribute the Program (or any work based on the Program), the recipient automatically receives a license from the original licensor to copy, distribute or modify the Program subject to these terms and conditions. You may not impose any further restrictions on the recipients' exercise of the rights granted herein. You are not responsible for enforcing compliance by third parties to this License. 7. If, as a consequence of a court judgment or allegation of patent infringement or for any other reason (not limited to patent issues), conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot distribute so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not distribute the Program at all. For example, if a patent license would not permit royalty-free redistribution of the Program by all those who receive copies directly or indirectly through you, then the only way you could satisfy both it and this License would be to refrain entirely from distribution of the Program. If any portion of this section is held invalid or unenforceable under any particular circumstance, the balance of the section is intended to apply and the section as a whole is intended to apply in other circumstances. It is not the purpose of this section to induce you to infringe any patents or other property right claims or to contest validity of any such claims; this section has the sole purpose of protecting the integrity of the free software distribution system, which is implemented by public license practices. Many people have made generous contributions to the wide range of software distributed through that system in reliance on consistent application of that system; it is up to the author/donor to decide if he or she is willing to distribute software through any other system and a licensee cannot impose that choice. This section is intended to make thoroughly clear what is believed to be a consequence of the rest of this License. 8. If the distribution and/or use of the Program is restricted in certain countries either by patents or by copyrighted interfaces, the original copyright holder who places the Program under this License may add an explicit geographical distribution limitation excluding those countries, so that distribution is permitted only in or among countries not thus excluded. In such case, this License incorporates the limitation as if written in the body of this License. 9. The Free Software Foundation may publish revised and/or new versions of the General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies a version number of this License which applies to it and "any later version", you have the option of following the terms and conditions either of that version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of this License, you may choose any version ever published by the Free Software Foundation. 10. If you wish to incorporate parts of the Program into other free programs whose distribution conditions are different, write to the author to ask for permission. For software which is copyrighted by the Free Software Foundation, write to the Free Software Foundation; we sometimes make exceptions for this. Our decision will be guided by the two goals of preserving the free status of all derivatives of our free software and of promoting the sharing and reuse of software generally. NO WARRANTY 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. END OF TERMS AND CONDITIONS How to Apply These Terms to Your New Programs If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms. To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively convey the exclusion of warranty; and each file should have at least the "copyright" line and a pointer to where the full notice is found. Copyright (C) This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, see . Also add information on how to contact you by electronic and paper mail. If the program is interactive, make it output a short notice like this when it starts in an interactive mode: Gnomovision version 69, Copyright (C) year name of author Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the program `Gnomovision' (which makes passes at compilers) written by James Hacker. , 1 April 1989 Ty Coon, President of Vice This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Library General Public License instead of this License. gsl-1.0.8/PKG_ADD0000644000175000017500000002236111201030403011113 0ustar shshautoload ("airy_Ai_deriv", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("airy_Ai_deriv_scaled", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("airy_Ai", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("airy_Ai_scaled", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("airy_Bi_deriv", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("airy_Bi_deriv_scaled", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("airy_Bi", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("airy_Bi_scaled", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("airy_zero_Ai_deriv", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("airy_zero_Ai", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("airy_zero_Bi_deriv", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("airy_zero_Bi", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("atanint", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("bessel_il_scaled", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("bessel_In", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("bessel_In_scaled", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("bessel_Inu", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("bessel_Inu_scaled", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("bessel_jl", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("bessel_Jn", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("bessel_Jnu", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("bessel_kl_scaled", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("bessel_Kn", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("bessel_Kn_scaled", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("bessel_Knu", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("bessel_Knu_scaled", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("bessel_lnKnu", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("bessel_yl", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("bessel_Yn", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("bessel_Ynu", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("bessel_zero_J0", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("bessel_zero_J1", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("beta_gsl", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("Chi", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("Ci", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("clausen", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("conicalP_0", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("conicalP_1", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("conicalP_half", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("conicalP_mhalf", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("dawson", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("debye_1", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("debye_2", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("debye_3", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("debye_4", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("ellint_Ecomp", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("ellint_Kcomp", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("erfc_gsl", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("erf_gsl", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("erf_Q", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("erf_Z", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("eta_int", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("eta", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("expint_3", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("expint_E1", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("expint_E2", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("expint_Ei", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("expm1", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("exp_mult", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("exprel_2", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("exprel_n", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("exprel", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("fermi_dirac_3half", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("fermi_dirac_half", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("fermi_dirac_inc_0", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("fermi_dirac_int", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("fermi_dirac_mhalf", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("gamma_gsl", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("gamma_inc", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("gamma_inc_P", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("gamma_inc_Q", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("gammainv_gsl", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("gammastar", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("hazard", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("hyperg_0F1", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("hzeta", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("lambert_W0", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("lambert_Wm1", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("legendre_Plm", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("legendre_Pl", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("legendre_Ql", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("legendre_sphPlm", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("lnbeta", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("lncosh", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("lngamma_gsl", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("lnpoch", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("lnsinh", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("log_1plusx_mx", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("log_1plusx", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("log_erfc", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("poch", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("pochrel", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("psi_1_int", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("psi_1piy", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("psi_n", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("psi", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("Shi", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("sinc_gsl", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("Si", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("synchrotron_1", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("synchrotron_2", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("taylorcoeff", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("transport_2", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("transport_3", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("transport_4", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("transport_5", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("zeta_int", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("zeta", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("hyperg_1F1", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); autoload ("hyperg_U", fullfile (fileparts (mfilename ("fullpath")), "gsl_sf.oct")); gsl-1.0.8/src/0000755000175000017500000000000011201031723010670 5ustar shshgsl-1.0.8/src/precode.cc.template0000644000175000017500000000250211201030403014423 0ustar shsh/* Copyright (C) 2004 Teemu Ikonen This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, see . */ #include #include #include #include void octave_gsl_errorhandler (const char * reason, const char * file, int line, int gsl_errno) { error("GSL error %d at %s, line %d: %s\n", gsl_errno, file, line, reason); } DEFUN_DLD (gsl_sf, args, nargout, "-*- texinfo -*-\n\ @deftypefn {Loadable Function} {} gsl_sf ()\n\ \n\ Octave bindings to the GNU Scientific Library. All GSL functions can be\n\ called with by the GSL names within octave.\n\ @end deftypefn") { usage("gsl_sf"); return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ gsl-1.0.8/src/coupling_3j.cc0000644000175000017500000000671411201030403013415 0ustar shsh/* Copyright (C) 2004 Teemu Ikonen This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; If not, see . */ #include #include #include #include void octave_gsl_errorhandler (const char * reason, const char * file, int line, int gsl_errno) { error("GSL error %d at %s, line %d: %s\n", gsl_errno, file, line, reason); } DEFUN_DLD(coupling_3j, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} coupling_3j (@var{two_ja}, @var{two_jb}, @var{two_jc}, @var{two_ma}, @var{two_mb}, @var{two_mc})\n\ \n\ These routines compute the Wigner 3-j coefficient,\n\ \n\ @example\n\ @group\n\ (ja jb jc\n\ ma mb mc)\n\ @end group\n\ @end example\n\ \n\ where the arguments are given in half-integer units,\n\ @code{ja = two_ja/2}, @code{ma = two_ma/2}, etc.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 6) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type() || !args(2).is_real_type() || !args(3).is_real_type() || !args(4).is_real_type() || !args(5).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } int len = args(0).length(); if(len != args(1).length() || len != args(2).length() || len != args(3).length() || len != args(4).length() || len != args(5).length()) { error("The arguments have the same length."); print_usage (); return octave_value(); } NDArray ja = args(0).array_value(); NDArray jb = args(1).array_value(); NDArray jc = args(2).array_value(); NDArray ma = args(3).array_value(); NDArray mb = args(4).array_value(); NDArray mc = args(5).array_value(); NDArray y(ja.dims()); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_coupling_3j (static_cast(ja.xelem(i)), static_cast(jb.xelem(i)), static_cast(jc.xelem(i)), static_cast(ma.xelem(i)), static_cast(mb.xelem(i)), static_cast(mc.xelem(i))); } return octave_value(y); } else { NDArray err(ja.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_coupling_3j_e (static_cast(ja.xelem(i)), static_cast(jb.xelem(i)), static_cast(jc.xelem(i)), static_cast(ma.xelem(i)), static_cast(mb.xelem(i)), static_cast(mc.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(0) = octave_value(y); retval.append(err); return retval; } return octave_value(); } gsl-1.0.8/src/coupling_9j.cc0000644000175000017500000001012511201030403013412 0ustar shsh/* Copyright (C) 2004 Teemu Ikonen This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; If not, see . */ #include #include #include #include void octave_gsl_errorhandler (const char * reason, const char * file, int line, int gsl_errno) { error("GSL error %d at %s, line %d: %s\n", gsl_errno, file, line, reason); } DEFUN_DLD(coupling_9j, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} coupling_9j (@var{two_ja}, @var{two_jb}, @var{two_jc}, @var{two_jd}, @var{two_je}, @var{two_jf}, @var{two_jg}, @var{two_jh}, @var{two_ji})\n\ \n\ These routines compute the Wigner 9-j coefficient,\n\ \n\ @example\n\ @group\n\ @{ja jb jc\n\ jd je jf\n\ jg jh ji@}\n\ @end group\n\ @end example\n\ \n\ where the arguments are given in half-integer units,\n\ @code{ja = two_ja/2}, @code{jd = two_jd/2}, etc.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 9) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type() || !args(2).is_real_type() || !args(3).is_real_type() || !args(4).is_real_type() || !args(5).is_real_type() || !args(6).is_real_type() || !args(7).is_real_type() || !args(8).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } int len = args(0).length(); if(len != args(1).length() || len != args(2).length() || len != args(3).length() || len != args(4).length() || len != args(5).length() || len != args(6).length() || len != args(7).length() || len != args(8).length()) { error("The arguments have the same length."); print_usage (); return octave_value(); } NDArray ja = args(0).array_value(); NDArray jb = args(1).array_value(); NDArray jc = args(2).array_value(); NDArray jd = args(3).array_value(); NDArray je = args(4).array_value(); NDArray jf = args(5).array_value(); NDArray jg = args(6).array_value(); NDArray jh = args(7).array_value(); NDArray ji = args(8).array_value(); NDArray y(ja.dims()); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_coupling_9j (static_cast(ja.xelem(i)), static_cast(jb.xelem(i)), static_cast(jc.xelem(i)), static_cast(jd.xelem(i)), static_cast(je.xelem(i)), static_cast(jf.xelem(i)), static_cast(jg.xelem(i)), static_cast(jh.xelem(i)), static_cast(ji.xelem(i))); } return octave_value(y); } else { NDArray err(ja.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_coupling_9j_e (static_cast(ja.xelem(i)), static_cast(jb.xelem(i)), static_cast(jc.xelem(i)), static_cast(jd.xelem(i)), static_cast(je.xelem(i)), static_cast(jf.xelem(i)), static_cast(jg.xelem(i)), static_cast(jh.xelem(i)), static_cast(ji.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(0) = octave_value(y); retval.append(err); return retval; } return octave_value_list(); } gsl-1.0.8/src/double_double_to_double.cc.template0000644000175000017500000000562311201030403017651 0ustar shshDEFUN_DLD(GSL_OCTAVE_NAME, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{z} =} GSL_OCTAVE_NAME (@var{x}, @var{y})\n\ @deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} GSL_OCTAVE_NAME (@dots{})\n\ \n\ GSL_FUNC_DOCSTRING \n\ @var{err} contains an estimate of the absolute error in the value @var{z}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray x = args(1).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = GSL_FUNC_NAME (n.xelem(i), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { GSL_FUNC_NAME_e (n.xelem(i), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); double ndouble = n.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = GSL_FUNC_NAME (ndouble, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { GSL_FUNC_NAME_e (ndouble, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = GSL_FUNC_NAME (n.xelem(i), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { GSL_FUNC_NAME_e (n.xelem(i), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("First and second argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ gsl-1.0.8/src/int_to_double.cc.template0000644000175000017500000000272211201030403015634 0ustar shshDEFUN_DLD(GSL_OCTAVE_NAME, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} GSL_OCTAVE_NAME (@var{n})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} GSL_OCTAVE_NAME (@dots{})\n\ \n\ GSL_FUNC_DOCSTRING \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = GSL_FUNC_NAME (static_cast(x.xelem(i))); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { GSL_FUNC_NAME_e (static_cast(x.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value_list(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ gsl-1.0.8/src/Makefile0000644000175000017500000000155411201030403012327 0ustar shshsinclude Makeconf SF_BUILDSCRIPT=buildgsl_sf.sh RM=rm #LIBGSL=$(shell gsl-config --libs-without-cblas) LIBGSL=-lgsl # all automatically generated functions SF_ALL_FNS=$(shell grep octave_name $(SF_BUILDSCRIPT) | sed 's/^.*octave_name=\([[:alnum:]_]*\) *$$/\1/g') SF_AVAILABLE=$(filter-out $(GSL_MISSING),$(SF_ALL_FNS)) # all separately compiled functions PROGS=coupling_3j.oct coupling_6j.oct coupling_9j.oct legendre_sphPlm_array.oct gsl_sf.oct DEFINES= ifeq ($(canonical_host_type),i686-pc-msdosmsvc) DEFINES=-DWIN32 -DGSL_DLL endif %.oct: %.cc ; $(MKOCTFILE) $(DEFINES) $< $(LIBGSL) ifeq ($(HAVE_GSL),yes) all: gsl_sf.cc $(SF_LINKS) $(PROGS) else all: @echo "GSL libraries or headers not installed" false endif $(PROGS): Makefile gsl_sf.cc: $(SF_BUILDSCRIPT) ${SHELL} $(SF_BUILDSCRIPT) $(GSL_MISSING) clean: ; -$(RM) -f gsl_sf.cc *.o core octave-core *.oct *~ gsl-1.0.8/src/README0000644000175000017500000000343111201030403011543 0ustar shshWrapper for the GNU Scientific Library special functions. GSL special functions are automatically generated. When a new version of GSL comes out with new functions, add the octave name, the GSL name and the documentation string to buildgsl_sf.sh. To protect against users having an older version of GSL installed, you will also need to test for these new functions in configure.add, listing as missing any that are not available. If several functions are added by one release of GSL you only need to test for one and list the rest. Trim gsl_sf_ from the name when listing it as missing. Each new definition will look like the following: if test -n "${missing##* FN *}"; then export octave_name=FN export funcname=gsl_sf_FN cat < docstring.txt FN_DESCRIPTION EOF ./replace_template.sh INPUTS_to_double.template >> gsl_sf.cc fi Replace FN, gsl_sf_FN, FN_DESCRIPTION and INPUTS as appropriate. There are several different templates to use depending on the inputs to the special function. For example, if the function takes two doubles and returns a double, use the double_double_to_double.cc template. To see the available templates, use: ls *template As of this writing there are: double fn(double) double fn(double,double) double fn(int) double fn(int,double) double fn(int,int,double) double fn(double,mode) mode is a precision mode accepting a gsl_mode_t value. If there is not appropriate template, you will have to write your own, or write a specialized C++ function for the new form. Note that GSL special functions have an _e form which returns an estimate of the absolute error of the returned value. These are handled automatically by the templates. If there is no _e form available you will need to write a specialized template for the function. gsl-1.0.8/src/coupling_6j.cc0000644000175000017500000000672311201030403013420 0ustar shsh/* Copyright (C) 2004 Teemu Ikonen This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; If not, see . */ #include #include #include #include void octave_gsl_errorhandler (const char * reason, const char * file, int line, int gsl_errno) { error("GSL error %d at %s, line %d: %s\n", gsl_errno, file, line, reason); } DEFUN_DLD(coupling_6j, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} coupling_6j (@var{two_ja}, @var{two_jb}, @var{two_jc}, @var{two_jd}, @var{two_je}, @var{two_jf})\n\ \n\ These routines compute the Wigner 6-j coefficient,\n\ \n\ @example\n\ @group\n\ @{ja jb jc\n\ jd je jf@}\n\ @end group\n\ @end example\n\ \n\ where the arguments are given in half-integer units,\n\ @code{ja = two_ja/2}, @code{jd = two_jd/2}, etc.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 6) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type() || !args(2).is_real_type() || !args(3).is_real_type() || !args(4).is_real_type() || !args(5).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } int len = args(0).length(); if(len != args(1).length() || len != args(2).length() || len != args(3).length() || len != args(4).length() || len != args(5).length()) { error("The arguments have the same length."); print_usage (); return octave_value(); } NDArray ja = args(0).array_value(); NDArray jb = args(1).array_value(); NDArray jc = args(2).array_value(); NDArray jd = args(3).array_value(); NDArray je = args(4).array_value(); NDArray jf = args(5).array_value(); NDArray y(ja.dims()); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = gsl_sf_coupling_6j (static_cast(ja.xelem(i)), static_cast(jb.xelem(i)), static_cast(jc.xelem(i)), static_cast(jd.xelem(i)), static_cast(je.xelem(i)), static_cast(jf.xelem(i))); } return octave_value(y); } else { NDArray err(ja.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { gsl_sf_coupling_6j_e (static_cast(ja.xelem(i)), static_cast(jb.xelem(i)), static_cast(jc.xelem(i)), static_cast(jd.xelem(i)), static_cast(je.xelem(i)), static_cast(jf.xelem(i)), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(0) = octave_value(y); retval.append(err); return retval; } return octave_value_list(); } gsl-1.0.8/src/test/0000755000175000017500000000000011201031723011647 5ustar shshgsl-1.0.8/src/test/test_hyperg.c0000644000175000017500000012265511201030403014355 0ustar shsh/* specfunc/test_hyperg.c * * Copyright (C) 2007 Brian Gough * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004 Gerard Jungman * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 3 of the License, or (at * your option) any later version. * * This program is distributed in the hope that it will be useful, but * WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */ /* Author: G. Jungman */ #include #include #include #include "test_sf.h" int test_hyperg(void) { gsl_sf_result r; int s = 0; /* 0F1 */ TEST_SF(s, gsl_sf_hyperg_0F1_e, (1, 0.5, &r), 1.5660829297563505373, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_0F1_e, (5, 0.5, &r), 1.1042674404828684574, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_0F1_e, (100, 30, &r), 1.3492598639485110176, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_0F1_e, (-0.5, 3, &r), -39.29137997543434276, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_0F1_e, (-100.5, 50, &r), 0.6087930289227538496, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_0F1_e, (1, -5.0, &r), -0.3268752818235339109, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_0F1_e, (-0.5, -5.0, &r),-4.581634759005381184, TEST_TOL1, GSL_SUCCESS); /* 1F1 for integer parameters */ TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (1, 1, 0.5, &r), 1.6487212707001281468, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (1, 2, 500.0, &r), 2.8071844357056748215e+214, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (1, 2, -500.0, &r), 0.002, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (8, 1, 0.5, &r), 13.108875178030540372, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 1, 1.0, &r), 131.63017574352619931, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 1, 10.0, &r), 8.514625476546280796e+09, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 1, 100.0, &r), 1.5671363646800353320e+56, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 20, 1.0, &r), 1.6585618002669675465, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 20, 10.0, &r), 265.26686430340188871, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 20, 100.0, &r), 3.640477355063227129e+34, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, 1.0, &r), 1.1056660194025527099, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, 10.0, &r), 2.8491063634727594206, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, 40.0, &r), 133.85880835831230986, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, 80.0, &r), 310361.16228011433406, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, 100.0, &r), 8.032171336754168282e+07, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, 500.0, &r), 7.633961202528731426e+123, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 1, 1.0, &r), 6.892842729046469965e+07, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 1, 10.0, &r), 2.4175917112200409098e+28, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 1, 100.0, &r), 1.9303216896309102993e+110, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 200, 1.0, &r), 1.6497469106162459226, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 200, 10.0, &r), 157.93286197349321981, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 200, 100.0, &r), 2.1819577501255075240e+24, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 200, 400.0, &r), 3.728975529926573300e+119, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 400, 10.0, &r), 12.473087623658878813, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 400, 100.0, &r), 9.071230376818550241e+11, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 400, 150.0, &r), 7.160949515742170775e+18, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 400, 200.0, &r), 2.7406690412731576823e+26, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 400, 300.0, &r), 6.175110613473276193e+43, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 400, 400.0, &r), 1.1807417662711371440e+64, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 400, 600.0, &r), 2.4076076354888886030e+112, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 1, -1.0, &r), 0.11394854824644542810, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 1, -10.0, &r), 0.0006715506365396127863, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 1, -100.0, &r), -4.208138537480269868e-32, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 50, -1.0, &r), 0.820006196079380, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, -10.0, &r), 0.38378859043466243, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, -100.0, &r), 0.0008460143401464189061, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, -500.0, &r), 1.1090822141973655929e-08, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, -10000.0, &r), 5.173783508088272292e-21, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (50, 1, -90.0, &r), -1.6624258547648311554e-21, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (50, 1, -100.0, &r), 4.069661775122048204e-24, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (50, 1, -110.0, &r), 1.0072444993946236025e-25, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 10, -100.0, &r), -2.7819353611733941962e-37, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 1, -90.0, &r), 7.501705041159802854e-22, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 1, -100.0, &r), 6.305128893152291187e-25, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 1, -110.0, &r), -7.007122115422439755e-26, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 10, -100.0, &r), -2.7819353611733941962e-37, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (200, 50, -1.0, &r), 0.016087060191732290813, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (200, 50, -300.0, &r), -4.294975979706421471e-121, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (200, 100, -1.0, &r), 0.13397521083325179687, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (200, 100, -10.0, &r), 5.835134393749807387e-10, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (200, 100, -100.0, &r), 4.888460453078914804e-74, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (200, 100, -500.0, &r), -1.4478509059582015053e-195, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-1, 1, 2.0, &r), -1.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-1, -2, 2.0, &r), 2.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-2, -3, 2.0, &r), 3.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, 1, 1.0, &r), 0.4189459325396825397, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, 1, 10.0, &r), 27.984126984126984127, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, 1, 100.0, &r), 9.051283795429571429e+12, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-100, 20, 1.0, &r), 0.0020203016320697069566, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -20, 1.0, &r), 1.6379141878548080173, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -20, 10.0, &r), 78.65202404521289970, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -20, 100.0, &r), 4.416169713262624315e+08, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -100, 1.0, &r), 1.1046713999681950919, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -100, 10.0, &r), 2.6035952191039006838, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -100, 100.0, &r), 1151.6852040836932392, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-100, -200, 1.0, &r), 1.6476859702535324743, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-100, -200, 10.0, &r), 139.38026829540687270, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-100, -200, 100.0, &r), 1.1669433576237933752e+19, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -20, -1.0, &r), 0.6025549561148035735, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -20, -10.0, &r), 0.00357079636732993491, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -20, -100.0, &r), 1.64284868563391159e-35, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -100, -1.0, &r), 0.90442397250313899, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -100, -10.0, &r), 0.35061515251367215, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -100, -100.0, &r), 8.19512187960476424e-09, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-100, -200, -1.0, &r), 0.6061497939628952629, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-100, -200, -10.0, &r), 0.0063278543908877674, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-100, -200, -100.0, &r), 4.34111795007336552e-25, TEST_TOL2, GSL_SUCCESS); /* 1F1 */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, 1, &r), 2.0300784692787049755, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, 10, &r), 6172.859561078406855, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, 100, &r), 2.3822817898485692114e+42, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, 500, &r), 5.562895351723513581e+215, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1.5, 2.5, 1, &r), 1.8834451238277954398, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1.5, 2.5, 10, &r), 3128.7352996840916381, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, 1, &r), 110.17623733873889579, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, 10, &r), 6.146657975268385438e+09, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, 100, &r), 9.331833897230312331e+55, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, 500, &r), 4.519403368795715843e+235, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 50.1, 2, &r), 1.5001295507968071788, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 50.1, 10, &r), 8.713385849265044908, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 50.1, 100, &r), 5.909423932273380330e+18, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 50.1, 500, &r), 9.740060618457198900e+165, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, 1, &r), 5.183531067116809033e+07, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, 10, &r), 1.6032649110096979462e+28, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, 100, &r), 1.1045151213192280064e+110, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 50.1, 1, &r), 7.222953133216603757, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 50.1, 10, &r), 1.0998696410887171538e+08, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 50.1, 100, &r), 7.235304862322283251e+63, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, -1, &r), 0.5380795069127684191, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, -10, &r), 0.05303758099290164485, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, -100, &r), 0.005025384718759852803, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, -500, &r), 0.0010010030151059555322, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.1, -500, &r), 0.00020036137599690208265, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, -1, &r), 0.07227645648935938168, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, -10, &r), 0.0003192415409695588126, TEST_TOL1, GSL_SUCCESS); /* sensitive to the pair_ratio hack in hyperg_1F1.c TEST_SF_RLX(s, gsl_sf_hyperg_1F1_e, (10, 1.1, -100, &r), -8.293425316123158950e-16, 50.0*TEST_SNGL, GSL_SUCCESS); */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, -500, &r), -3.400379216707701408e-23, TEST_TOL2, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_1F1_e, (50, 1.1, -90, &r), -7.843129411802921440e-22, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (50, 1.1, -100, &r), 4.632883869540640460e-24, TEST_SQRT_TOL0, GSL_SUCCESS); /* FIXME: tolerance is poor, but is consistent within reported error */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (50, 1.1, -110.0, &r), 5.642684651305310023e-26, 0.03, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -1, &r), 0.0811637344096042096, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -10, &r), 0.00025945610092231574387, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -50, &r), 2.4284830988994084452e-13, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -90, &r), 2.4468224638378426461e-22, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -99, &r), 1.0507096272617608461e-23, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -100, &r), 1.8315497474210138602e-24, TEST_TOL2, GSL_SUCCESS); /* FIXME: Reported error is too small. TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -101, &r), -2.3916306291344452490e-24, 0.04, GSL_SUCCESS); */ /* FIXME: Reported error is too small. TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -110, &r), -4.517581986037732280e-26, TEST_TOL0, GSL_SUCCESS); */ /* FIXME: Result is terrible, but reported error is very large, so consistent. TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 10.1, -220, &r), -4.296130300021696573e-64, TEST_TOL1, GSL_SUCCESS); */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -10.1, 10.0, &r), 10959.603204633058116, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -10.1, 1000.0, &r), 2.0942691895502242831e+23, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -100.1, 10.0, &r), 2.6012036337980078062, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-1000, -1000.1, 10.0, &r), 22004.341698908631636, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-1000, -1000.1, 200.0, &r), 7.066514294896245043e+86, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-8.1, -10.1, -10.0, &r), 0.00018469685276347199258, TEST_TOL0, GSL_SUCCESS); /* TEST_SF(s, gsl_sf_hyperg_1F1_e, (-8.1, -1000.1, -10.0, &r), 0.9218280185080036020, TEST_TOL0, GSL_SUCCESS); */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -5.1, 1, &r), 16.936141866089601635, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -5.1, 10, &r), 771534.0349543820541, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -5.1, 100, &r), 2.2733956505084964469e+17, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, -1, &r), 0.13854540373629275583, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, -10, &r), -9.142260314353376284e+19, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, -100, &r), -1.7437371339223929259e+87, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, 1, &r), 7.516831748170351173, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, 10, &r), 1.0551632286359671976e+11, TEST_SQRT_TOL0, GSL_SUCCESS); /* These come out way off. On the other hand, the error estimates are also very large; so much so that the answers are consistent within the reported error. Something will need to be done about this eventually TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, 50, &r), -7.564755600940346649e+36, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, 100, &r), 4.218776962675977e+55, TEST_TOL3, GSL_SUCCESS); */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10.5, -8.1, 0.1, &r), 1.1387201443786421724, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10.5, -11.1, 1, &r), 2.5682766147138452362, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100.5, -80.1, 10, &r), 355145.4517305220603, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100.5, -102.1, 10, &r), 18678.558725244365016, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100.5, -500.1, 10, &r), 7.342209011101454, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100.5, -500.1, 100, &r), 1.2077443075367177662e+8, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-500.5, -80.1, 2, &r), 774057.8541325341699, TEST_TOL4, GSL_SUCCESS); /* UNIMPL TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, 1, &r), -2.1213846338338567395e+12, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, 10, &r), -6.624849346145112398e+39, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, 100, &r), -1.2413466759089171904e+129, TEST_TOL0, GSL_SUCCESS); */ /* UNIMPL TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, -1, &r), 34456.29405305551691, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, -10, &r), -7.809224251467710833e+07, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, -100, &r), -5.214065452753988395e-07, TEST_TOL0, GSL_SUCCESS); */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, 1, &r), 0.21519810496314438414, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, 10, &r), 8.196123715597869948, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, 100, &r), -1.4612966715976530293e+20, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 20.1, 1, &r), 0.0021267655527278456412, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 20.1, 10, &r), 2.0908665169032186979e-11, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 20.1, 100, &r), -0.04159447537001340412, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, -1, &r), 2.1214770215694685282e+07, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, -10, &r), 1.0258848879387572642e+24, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, -100, &r), 1.1811367147091759910e+67, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 50.1, -1, &r), 6.965259317271427390, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 50.1, -10, &r), 1.0690052487716998389e+07, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 50.1, -100, &r), 6.889644435777096248e+36, TEST_TOL3, GSL_SUCCESS); /* Bug report from Fernando Pilotto */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (-2.05, 1.0, 5.05, &r), 3.79393389516785e+00, TEST_TOL3, GSL_SUCCESS); /* Bug reports from Ivan Liu */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (-26, 2.0, 100.0, &r), 1.444786781107436954e+19, TEST_TOL3, GSL_SUCCESS); #if 0 /* This one is computed with a huge error, there is loss of precision but the error estimate flags the problem (assuming the user looks at it). We should probably trap any return with err>|val| and signal loss of precision */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (-26.1, 2.0, 100.0, &r), 1.341557199575986995e+19, TEST_TOL3, GSL_SUCCESS); #endif /* Bug report H.Moseby */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (1.2, 1.1e-15, 1.5, &r), 8254503159672429.02, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1.0, 1000000.5, 0.8e6 + 0.5, &r), 4.999922505099443804e+00, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1.0, 1000000.5, 1001000.5, &r), 3480.3699557431856166, TEST_TOL4, GSL_SUCCESS); #if 0 /* FIX THESE NEXT RELEASE */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (1.1, 1000000.5, 1001000.5, &r), 7304.6126942641350122, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (0.9, 1000000.5, 1001000.5, &r), 1645.4879293475410982, TEST_TOL3, GSL_SUCCESS); #endif TEST_SF(s, gsl_sf_hyperg_1F1_e, (-1.1, 1000000.5, 1001000.5, &r), -5.30066488697455e-04, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1.5, 1000000.5, 0.8e6 + 0.5, &r), 11.18001288977894650469927615, TEST_TOL4, GSL_SUCCESS); /* U for integer parameters */ TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 0.0001, &r), 8.634088070212725330, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 0.01, &r), 4.078511443456425847, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 0.5, &r), 0.9229106324837304688, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 2.0, &r), 0.3613286168882225847, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 100, &r), 0.009901942286733018406, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 1000, &r), 0.0009990019940238807150, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 0.01, &r), 7.272361203006010000e+16, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 1, &r), 1957.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 5, &r), 1.042496, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 8, &r), 0.3207168579101562500, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 50, &r), 0.022660399001600000000, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 100, &r), 0.010631236727200000000, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 1000, &r), 0.0010060301203607207200, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 20, 1, &r), 1.7403456103284421000e+16, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 20, 20, &r), 0.22597813610531052969, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 50, 1, &r), 3.374452117521520758e+61, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 50, 50, &r), 0.15394136814987651785, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 0.1, &r), 1.0418325171990852858e+253, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 1, &r), 2.5624945006073464385e+154, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 50, &r), 3.0978624160896431391e+07, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 100, &r), 0.11323192555773717475, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 200, &r), 0.009715680951406713589, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 1000, &r), 0.0011085142546061528661, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1000, 2000, &r), 0.0009970168547036318206, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -1, 1, &r), 0.29817368116159703717, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -1, 10, &r), 0.07816669698940409380, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -10, 1, &r), 0.08271753756946041959, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -10, 5, &r), 0.06127757419425055261, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -10, 10, &r), 0.04656199948873187212, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -10, 20, &r), 0.031606421847946077709, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 0.01, &r), 0.009900000099999796950, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 1, &r), 0.009802970197050404429, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 10, &r), 0.009001648897173103447, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 20, &r), 0.008253126487166557546, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 50, &r), 0.006607993916432051008, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 90, &r), 0.005222713769726871937, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 110, &r), 0.004727658137692606210, TEST_TOL2, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_U_int_e, (1, -1000, 1, &r), 0.0009980029970019970050, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -1000, 1010, &r), 0.0004971408839859245170, TEST_TOL4, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 1, 0.001, &r), 0.0007505359326875706975, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 1, 0.5, &r), 6.449509938973479986e-06, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 1, 8, &r), 6.190694573035761284e-10, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 1, 20, &r), 3.647213845460374016e-12, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 8, 1, &r), 0.12289755012652317578, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 8, 10, &r), 5.687710359507564272e-09, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 8, 20, &r), 2.8175404594901039724e-11, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (100, 100, 0.01, &r), 1.0099979491941914867e+196, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (100, 100, 0.1, &r), 1.0090713562719862833e+97, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (100, 100, 1, &r), 0.009998990209084729106, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (100, 100, 20, &r), 1.3239363905866130603e-131, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 1, 0.01, &r), 3.274012540759009536e+06, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 1, 1, &r), 1.5202710000000000000e+06, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 1, 10, &r), 1.0154880000000000000e+08, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 1, 100, &r), 3.284529863685482880e+19, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 10, 1, &r), 1.1043089864100000000e+11, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 100, 1, &r), 1.3991152402448957897e+20, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 100, 10, &r), 5.364469916567136000e+19, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 100, 100, &r), 3.909797568000000000e+12, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 100, 500, &r), 8.082625576697984130e+25, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 1, 0.01, &r), 1.6973422555823855798e+64, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 1, 1, &r), 7.086160198304780325e+63, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 1, 10, &r), 5.332862895528712200e+65, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 10, 1, &r), -7.106713471565790573e+71, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 100, 1, &r), 2.4661377199407186476e+104, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 10, 10, &r), 5.687538583671241287e+68, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 100, 10, &r), 1.7880761664553373445e+102, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 1, 0.01, &r), 4.185245354032917715e+137, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 1, 0.1, &r), 2.4234043408007841358e+137, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 1, 10, &r), -1.8987677149221888807e+139, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 10, 10, &r), -5.682999988842066677e+143, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 100, 10, &r), 2.3410029853990624280e+189, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 1000, 10, &r), 1.9799451517572225316e+271, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, -1, 10, &r), -9.083195466262584149e+64, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, -10, 10, &r), -1.4418257327071634407e+62, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, -100, 0.01, &r), 3.0838993811468983931e+93, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, -100, 10, &r), 4.014552630378340665e+95, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-100, -100, 10, &r), 2.0556466922347982030e+162, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-100, -200, 10, &r), 1.1778399522973555582e+219, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-100, -200, 100, &r), 9.861313408898201873e+235, TEST_TOL3, GSL_SUCCESS); /* U */ TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 0.0001, 0.0001, &r), 1.0000576350699863577, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 0.0001, 1.0, &r), 0.9999403679233247536, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 0.0001, 100.0, &r), 0.9995385992657260887, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 1, 0.0001, &r), 1.0009210608660065989, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 1.0, 1.0, &r), 0.9999999925484179084, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 10, 1, &r), 13.567851006281412726, TEST_TOL3, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.0001, 10, 5, &r), 1.0006265020064596364, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 10, 10, &r), 0.9999244381454633265, TEST_TOL0, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.0001, 100, 1, &r), 2.5890615708804247881e+150, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.0001, 100, 10, &r), 2.3127845417739661466e+55, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.0001, 100, 50, &r), 6402.818715083582554, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 100, 98, &r), 0.9998517867411840044, TEST_TOL2, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.0001, 1000, 300, &r), 2.5389557274938010716e+213, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 1000, 999, &r), 0.9997195294193261604, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 1000, 1100, &r), 0.9995342990014584713, TEST_TOL1, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.5, 1000, 300, &r), 1.1977955438214207486e+217, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.5, 1000, 800, &r), 9.103916020464797207e+08, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.5, 1000, 998, &r), 0.21970269691801966806, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.5, 0.5, 1.0, &r), 0.7578721561413121060, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (1, 0.0001, 0.0001, &r), 0.9992361337764090785, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (1, 0.0001, 1, &r), 0.4036664068111504538, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (1, 0.0001, 100, &r), 0.009805780851264329587, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (1, 1.2, 2.0, &r), 0.3835044780075602550, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (1, -0.0001, 1, &r), 0.4036388693605999482, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (8, 10.5, 1, &r), 27.981926466707438538, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (8, 10.5, 10, &r), 2.4370135607662056809e-8, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (8, 10.5, 100, &r), 1.1226567526311488330e-16, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (10, -2.5, 10, &r), 6.734690720346560349e-14, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (10, 2.5, 10, &r), 6.787780794037971638e-13, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (10, 2.5, 50, &r), 2.4098720076596087125e-18, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 1, &r), -3.990841457734147e+6, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 10, &r), 1.307472052129343e+8, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 50, &r), 3.661978424114088e+16, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 90, &r), 8.09469542130868e+19, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 99, &r), 2.546328328942063e+20, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 100, &r), 2.870463201832814e+20, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 200, &r), 8.05143453769373e+23, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 10.1, 0.1, &r), -3.043016255306515e+20, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 10.1, 1, &r), -3.194745265896115e+12, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 10.1, 4, &r), -6.764203430361954e+07, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 10.1, 10, &r), -2.067399425480545e+09, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 10.1, 50, &r), 4.661837330822824e+14, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 100.4, 10, &r), -6.805460513724838e+66, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 100.4, 50, &r), -2.081052558162805e+18, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 100.4, 80, &r), 2.034113191014443e+14, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 100.4, 100, &r), 6.85047268436107e+13, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 100.4, 200, &r), 1.430815706105649e+20, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-19.5, 82.1, 10, &r), 5.464313196201917432e+60, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-50.5, 100.1, 10, &r), -5.5740216266953e+126, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-50.5, 100.1, 40, &r), 5.937463786613894e+91, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-50.5, 100.1, 50, &r), -1.631898534447233e+89, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-50.5, 100.1, 70, &r), 3.249026971618851e+84, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-50.5, 100.1, 100, &r), 1.003401902126641e+85, TEST_TOL1, GSL_SUCCESS); /* 2F1 */ TEST_SF(s, gsl_sf_hyperg_2F1_e, (1, 1, 1, 0.5, &r), 2.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, 8, 1, 0.5, &r), 12451584.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, -8, 1, 0.5, &r), 0.13671875, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, -8.1, 1, 0.5, &r), 0.14147385378899930422, TEST_TOL4, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, -8, 1, -0.5, &r), 4945.136718750000000, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, -8, -5.5, 0.5, &r), -906.6363636363636364, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, -8, -5.5, -0.5, &r), 24565.363636363636364, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, 8, 1, -0.5, &r), -0.006476312098196747669, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, 8, 5, 0.5, &r), 4205.714285714285714, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, 8, 5, -0.5, &r), 0.0028489656290296436616, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, 1, 0.99, &r), 1.2363536673577259280e+38 , TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -1.5, 0.99, &r), 3.796186436458346579e+46, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -1.5, -0.99, &r), 0.14733409946001025146, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -8.5, 0.99, &r), -1.1301780432998743440e+65, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -8.5, -0.99, &r), -8.856462606575344483, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -21.5, 0.99, &r), 2.0712920991876073253e+95, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -21.5, -0.99, &r), -74.30517015382249216, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -100.5, 0.99, &r), -3.186778061428268980e+262, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -100.5, -0.99, &r), 2.4454358338375677520, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (25, 25, 1, -0.5, &r), -2.9995530823639545027e-06, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, 1.0-1.0/64.0, &r), 3.17175539044729373926, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, 1.0-1.0/128.0, &r), 3.59937243502024563424, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, 1.0-1.0/256.0, &r), 4.03259299524392504369, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, 1.0-1.0/1024.0, &r), 4.90784159359675398250, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, 1.0-1.0/65536.0, &r), 7.552266033399683914, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, 1.0-1.0/16777216.0, &r), 11.08235454026043830363, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, -1.0+1.0/1024.0, &r), 0.762910940909954974527, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, -1.0+1.0/65536.0, &r), 0.762762124908845424449, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, -1.0+1.0/1048576.0, &r), 0.762759911089064738044, TEST_TOL0, GSL_SUCCESS); /* added special handling with x == 1.0 , Richard J. Mathar, 2008-01-09 */ TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 3.0, 1.0, &r), 1.6976527263135502482014268 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, -4.2, 3.0, 1.0, &r), .15583601560025710649555254 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (-7.4, 0.7, -1.5, 1.0, &r), -.34478866959246584996859 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (0.1, -2.7, -1.5, 1.0, &r), 1.059766766063610122925 , TEST_TOL0, GSL_SUCCESS); /* 2F1 conj */ TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (1, 1, 1, 0.5, &r), 3.352857095662929028, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (8, 8, 1, 0.5, &r), 1.7078067538891293983e+09, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (8, 8, 5, 0.5, &r), 285767.15696901140627, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (8, 8, 1, -0.5, &r), 0.007248196261471276276, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (8, 8, 5, -0.5, &r), 0.00023301916814505902809, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (25, 25, 1, -0.5, &r), 5.1696944096e-06, TEST_SQRT_TOL0, GSL_SUCCESS); /* updated correct values, testing enabled, Richard J. Mathar, 2008-01-09 */ TEST_SF(s, gsl_sf_hyperg_2F0_e, (0.01, 1.0, -0.02, &r), .99980388665511730901180717 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F0_e, (0.1, 0.5, -0.02, &r), .99901595171179281891589794 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F0_e, (1, 1, -0.02, &r), .98075549650574351826538049000 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F0_e, (8, 8, -0.02, &r), .32990592849626965538692141 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F0_e, (50, 50, -0.02, &r), .2688995263772964415245902e-12 , TEST_TOL0, GSL_SUCCESS); /* 2F1 renorm */ TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (1, 1, 1, 0.5, &r), 2.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, 8, 1, 0.5, &r), 12451584.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, -8, 1, 0.5, &r), 0.13671875, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, -8, 1, -0.5, &r), 4945.13671875, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, -8, -5.5, 0.5, &r), -83081.19167659493609, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, -8, -5.5, -0.5, &r), 2.2510895952730178518e+06, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, 8, 5, 0.5, &r), 175.2380952380952381, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (9, 9, -1.5, 0.99, &r), 1.6063266334913066551e+46, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (9, 9, -1.5, -0.99, &r), 0.06234327316254516616, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (5, 5, -1, 0.5, &r), 4949760.0, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (5, 5, -10, 0.5, &r), 139408493229637632000.0, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (5, 5, -100, 0.5, &r), 3.0200107544594411315e+206, TEST_TOL3, GSL_SUCCESS); /* 2F1 conj renorm */ TEST_SF(s, gsl_sf_hyperg_2F1_conj_renorm_e, (9, 9, -1.5, 0.99, &r), 5.912269095984229412e+49, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_renorm_e, (9, 9, -1.5, -0.99, &r), 0.10834020229476124874, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_renorm_e, (5, 5, -1, 0.5, &r), 1.4885106335357933625e+08, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_renorm_e, (5, 5, -10, 0.5, &r), 7.968479361426355095e+21, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_renorm_e, (5, 5, -100, 0.5, &r), 3.1113180227052313057e+208, TEST_TOL3, GSL_SUCCESS); return s; } gsl-1.0.8/src/test/check.m0000755000175000017500000001036011201030403013077 0ustar shsh## Copyright (C) 2008 Raymond E. Rogers ## ## This program is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; if not, see . # # # Testing initialization/header for special functions # Octave format # It is intended to read test_hyperg.c from the GNU GSL hyperg test file # and use the test lines. If you don't want to duplicate thier # errors, comment out the bad tests with // # Compare test_hyperg.c vs. test_hyperg_corr.c # # R. Rogers v1, testing only hyperg_1F1 and hyperg_U in double # KummerM and KummerU # Some array verification is done; since I messed it up once. global GSL_DBL_EPSILON= 2.2204460492503131e-16 global GSL_SQRT_DBL_EPSILON= 1.4901161193847656e-08 global TEST_TOL0= (2.0*GSL_DBL_EPSILON) global TEST_TOL1= (16.0*GSL_DBL_EPSILON) global TEST_TOL2= (256.0*GSL_DBL_EPSILON) global TEST_TOL3= (2048.0*GSL_DBL_EPSILON) global TEST_TOL4= (16384.0*GSL_DBL_EPSILON) global TEST_TOL5= (131072.0*GSL_DBL_EPSILON) global TEST_TOL6= (1048576.0*GSL_DBL_EPSILON) global TEST_SQRT_TOL0= (2.0*GSL_SQRT_DBL_EPSILON) global TEST_SNGL= (1.0e-06) global TEST_SF_INCONS= 1 global TEST_SF_ERRNEG= 2 global TEST_SF_TOLBAD= 4 global TEST_SF_RETBAD= 8 global TEST_SF_ERRBAD= 16 global TEST_SF_ERRBIG= 32 global TEST_SF_EXPBAD= 64 global TEST_FACTOR= 100 function res=READ_TEST_SF_hyperg_Kummer(input_name) global GSL_DBL_EPSILON global GSL_SQRT_DBL_EPSILON global TEST_TOL0 global TEST_TOL1 global TEST_TOL2 global TEST_TOL3 global TEST_TOL4 global TEST_TOL5 global TEST_TOL6 global TEST_SQRT_TOL0 global TEST_SNGL global TEST_SF_INCONS global TEST_SF_ERRNEG global TEST_SF_TOLBAD global TEST_SF_RETBAD global TEST_SF_ERRBAD global TEST_SF_ERRBIG global TEST_SF_EXPBAD global TEST_FACTOR [source_id,source_msg]=fopen(input_name,"r","native") while (! feof(source_id)) do input_line=fgetl(source_id); until( index(input_line,"//") == 0); str_p=index(input_line,"hyperg_1F1_e"); if (str_p != 0) # Take it apart string_split=split(input_line,","); arg1=str2double(substr(string_split(3,:),3)); arg2=str2double(string_split(4,:)); arg3=str2double(string_split(5,:)); val=str2double(string_split(7,:)); tol=eval(string_split(8,:)); [ret,err]=hyperg_1F1(arg1,arg2,arg3); # This is to prevent extanious stops on some errors if ret==NaN ret=Inf endif if (abs((ret-val)/val) #include #include #include "test_sf.h" int test_hyperg(void) { gsl_sf_result r; int s = 0; /* 0F1 */ TEST_SF(s, gsl_sf_hyperg_0F1_e, (1, 0.5, &r), 1.5660829297563505373, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_0F1_e, (5, 0.5, &r), 1.1042674404828684574, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_0F1_e, (100, 30, &r), 1.3492598639485110176, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_0F1_e, (-0.5, 3, &r), -39.29137997543434276, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_0F1_e, (-100.5, 50, &r), 0.6087930289227538496, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_0F1_e, (1, -5.0, &r), -0.3268752818235339109, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_0F1_e, (-0.5, -5.0, &r),-4.581634759005381184, TEST_TOL1, GSL_SUCCESS); /* 1F1 for integer parameters */ TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (1, 1, 0.5, &r), 1.6487212707001281468, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (1, 2, 500.0, &r), 2.8071844357056748215e+214, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (1, 2, -500.0, &r), 0.002, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (8, 1, 0.5, &r), 13.108875178030540372, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 1, 1.0, &r), 131.63017574352619931, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 1, 10.0, &r), 8.514625476546280796e+09, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 1, 100.0, &r), 1.5671363646800353320e+56, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 20, 1.0, &r), 1.6585618002669675465, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 20, 10.0, &r), 265.26686430340188871, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 20, 100.0, &r), 3.640477355063227129e+34, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, 1.0, &r), 1.1056660194025527099, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, 10.0, &r), 2.8491063634727594206, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, 40.0, &r), 133.85880835831230986, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, 80.0, &r), 310361.16228011433406, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, 100.0, &r), 8.032171336754168282e+07, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, 500.0, &r), 7.633961202528731426e+123, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 1, 1.0, &r), 6.892842729046469965e+07, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 1, 10.0, &r), 2.4175917112200409098e+28, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 1, 100.0, &r), 1.9303216896309102993e+110, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 200, 1.0, &r), 1.6497469106162459226, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 200, 10.0, &r), 157.93286197349321981, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 200, 100.0, &r), 2.1819577501255075240e+24, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 200, 400.0, &r), 3.728975529926573300e+119, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 400, 10.0, &r), 12.473087623658878813, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 400, 100.0, &r), 9.071230376818550241e+11, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 400, 150.0, &r), 7.160949515742170775e+18, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 400, 200.0, &r), 2.7406690412731576823e+26, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 400, 300.0, &r), 6.175110613473276193e+43, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 400, 400.0, &r), 1.1807417662711371440e+64, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 400, 600.0, &r), 2.4076076354888886030e+112, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 1, -1.0, &r), 0.11394854824644542810, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 1, -10.0, &r), 0.0006715506365396127863, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 1, -100.0, &r), -4.208138537480269868e-32, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 50, -1.0, &r), 0.820006196079380, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, -10.0, &r), 0.38378859043466243, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, -100.0, &r), 0.0008460143401464189061, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, -500.0, &r), 1.1090822141973655929e-08, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (10, 100, -10000.0, &r), 5.173783508088272292e-21, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (50, 1, -90.0, &r), -1.6624258547648311554e-21, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (50, 1, -100.0, &r), 4.069661775122048204e-24, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (50, 1, -110.0, &r), 1.0072444993946236025e-25, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 10, -100.0, &r), -2.7819353611733941962e-37, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 1, -90.0, &r), 7.501705041159802854e-22, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 1, -100.0, &r), 6.305128893152291187e-25, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 1, -110.0, &r), -7.007122115422439755e-26, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (100, 10, -100.0, &r), -2.7819353611733941962e-37, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (200, 50, -1.0, &r), 0.016087060191732290813, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (200, 50, -300.0, &r), -4.294975979706421471e-121, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (200, 100, -1.0, &r), 0.13397521083325179687, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (200, 100, -10.0, &r), 5.835134393749807387e-10, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (200, 100, -100.0, &r), 4.888460453078914804e-74, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (200, 100, -500.0, &r), -1.4478509059582015053e-195, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-1, 1, 2.0, &r), -1.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-1, -2, 2.0, &r), 2.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-2, -3, 2.0, &r), 3.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, 1, 1.0, &r), 0.4189459325396825397, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, 1, 10.0, &r), 27.984126984126984127, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, 1, 100.0, &r), 9.051283795429571429e+12, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-100, 20, 1.0, &r), 0.0020203016320697069566, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -20, 1.0, &r), 1.6379141878548080173, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -20, 10.0, &r), 78.65202404521289970, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -20, 100.0, &r), 4.416169713262624315e+08, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -100, 1.0, &r), 1.1046713999681950919, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -100, 10.0, &r), 2.6035952191039006838, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -100, 100.0, &r), 1151.6852040836932392, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-100, -200, 1.0, &r), 1.6476859702535324743, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-100, -200, 10.0, &r), 139.38026829540687270, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-100, -200, 100.0, &r), 1.1669433576237933752e+19, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -20, -1.0, &r), 0.6025549561148035735, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -20, -10.0, &r), 0.00357079636732993491, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -20, -100.0, &r), 1.64284868563391159e-35, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -100, -1.0, &r), 0.90442397250313899, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -100, -10.0, &r), 0.35061515251367215, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-10, -100, -100.0, &r), 8.19512187960476424e-09, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-100, -200, -1.0, &r), 0.6061497939628952629, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-100, -200, -10.0, &r), 0.0063278543908877674, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_int_e, (-100, -200, -100.0, &r), 4.34111795007336552e-25, TEST_TOL2, GSL_SUCCESS); /* 1F1 */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, 1, &r), 2.0300784692787049755, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, 10, &r), 6172.859561078406855, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, 100, &r), 2.3822817898485692114e+42, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, 500, &r), 5.562895351723513581e+215, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1.5, 2.5, 1, &r), 1.8834451238277954398, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1.5, 2.5, 10, &r), 3128.7352996840916381, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, 1, &r), 110.17623733873889579, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, 10, &r), 6.146657975268385438e+09, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, 100, &r), 9.331833897230312331e+55, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, 500, &r), 4.519403368795715843e+235, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 50.1, 2, &r), 1.5001295507968071788, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 50.1, 10, &r), 8.713385849265044908, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 50.1, 100, &r), 5.909423932273380330e+18, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 50.1, 500, &r), 9.740060618457198900e+165, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, 1, &r), 5.183531067116809033e+07, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, 10, &r), 1.6032649110096979462e+28, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, 100, &r), 1.1045151213192280064e+110, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 50.1, 1, &r), 7.222953133216603757, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 50.1, 10, &r), 1.0998696410887171538e+08, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 50.1, 100, &r), 7.235304862322283251e+63, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, -1, &r), 0.5380795069127684191, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, -10, &r), 0.05303758099290164485, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, -100, &r), 0.005025384718759852803, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, -500, &r), 0.0010010030151059555322, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.1, -500, &r), 0.00020036137599690208265, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, -1, &r), 0.07227645648935938168, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, -10, &r), 0.0003192415409695588126, TEST_TOL1, GSL_SUCCESS); /* sensitive to the pair_ratio hack in hyperg_1F1.c TEST_SF_RLX(s, gsl_sf_hyperg_1F1_e, (10, 1.1, -100, &r), -8.293425316123158950e-16, 50.0*TEST_SNGL, GSL_SUCCESS); */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, -500, &r), -3.400379216707701408e-23, TEST_TOL2, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_1F1_e, (50, 1.1, -90, &r), -7.843129411802921440e-22, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (50, 1.1, -100, &r), 4.632883869540640460e-24, TEST_SQRT_TOL0, GSL_SUCCESS); /* FIXME: tolerance is poor, but is consistent within reported error */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (50, 1.1, -110.0, &r), 5.642684651305310023e-26, 0.03, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -1, &r), 0.0811637344096042096, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -10, &r), 0.00025945610092231574387, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -50, &r), 2.4284830988994084452e-13, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -90, &r), 2.4468224638378426461e-22, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -99, &r), 1.0507096272617608461e-23, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -100, &r), 1.8315497474210138602e-24, TEST_TOL2, GSL_SUCCESS); /* FIXME: Reported error is too small. TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -101, &r), -2.3916306291344452490e-24, 0.04, GSL_SUCCESS); */ /* FIXME: Reported error is too small. // TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -110, &r), -4.517581986037732280e-26, TEST_TOL0, GSL_SUCCESS); */ /* FIXME: Result is terrible, but reported error is very large, so consistent. // TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 10.1, -220, &r), -4.296130300021696573e-64, TEST_TOL1, GSL_SUCCESS); */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -10.1, 10.0, &r), 10959.603204633058116, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -10.1, 1000.0, &r), 2.0942691895502242831e+23, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -100.1, 10.0, &r), 2.6012036337980078062, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-1000, -1000.1, 10.0, &r), 22004.341698908631636, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-1000, -1000.1, 200.0, &r), 7.066514294896245043e+86, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-8.1, -10.1, -10.0, &r), 0.00018469685276347199258, TEST_TOL0, GSL_SUCCESS); /* TEST_SF(s, gsl_sf_hyperg_1F1_e, (-8.1, -1000.1, -10.0, &r), 0.9218280185080036020, TEST_TOL0, GSL_SUCCESS); */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -5.1, 1, &r), 16.936141866089601635, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -5.1, 10, &r), 771534.0349543820541, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -5.1, 100, &r), 2.2733956505084964469e+17, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, -1, &r), 0.13854540373629275583, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, -10, &r), -9.142260314353376284e+19, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, -100, &r), -1.7437371339223929259e+87, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, 1, &r), 7.516831748170351173, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, 10, &r), 1.0551632286359671976e+11, TEST_SQRT_TOL0, GSL_SUCCESS); /* These come out way off. On the other hand, the error estimates are also very large; so much so that the answers are consistent within the reported error. Something will need to be done about this eventually // TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, 50, &r), -7.564755600940346649e+36, TEST_TOL3, GSL_SUCCESS); // TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, 100, &r), 4.218776962675977e+55, TEST_TOL3, GSL_SUCCESS); */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10.5, -8.1, 0.1, &r), 1.1387201443786421724, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10.5, -11.1, 1, &r), 2.5682766147138452362, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100.5, -80.1, 10, &r), 355145.4517305220603, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100.5, -102.1, 10, &r), 18678.558725244365016, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100.5, -500.1, 10, &r), 7.342209011101454, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100.5, -500.1, 100, &r), 1.2077443075367177662e+8, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-500.5, -80.1, 2, &r), 774057.8541325341699, TEST_TOL4, GSL_SUCCESS); /* UNIMPL TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, 1, &r), -2.1213846338338567395e+12, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, 10, &r), -6.624849346145112398e+39, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, 100, &r), -1.2413466759089171904e+129, TEST_TOL0, GSL_SUCCESS); */ /* UNIMPL // TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, -1, &r), 34456.29405305551691, TEST_TOL0, GSL_SUCCESS); // TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, -10, &r), -7.809224251467710833e+07, TEST_TOL0, GSL_SUCCESS); // TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, -100, &r), -5.214065452753988395e-07, TEST_TOL0, GSL_SUCCESS); */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, 1, &r), 0.21519810496314438414, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, 10, &r), 8.196123715597869948, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, 100, &r), -1.4612966715976530293e+20, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 20.1, 1, &r), 0.0021267655527278456412, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 20.1, 10, &r), 2.0908665169032186979e-11, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 20.1, 100, &r), -0.04159447537001340412, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, -1, &r), 2.1214770215694685282e+07, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, -10, &r), 1.0258848879387572642e+24, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, -100, &r), 1.1811367147091759910e+67, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 50.1, -1, &r), 6.965259317271427390, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 50.1, -10, &r), 1.0690052487716998389e+07, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 50.1, -100, &r), 6.889644435777096248e+36, TEST_TOL3, GSL_SUCCESS); /* Bug report from Fernando Pilotto */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (-2.05, 1.0, 5.05, &r), 3.79393389516785e+00, TEST_TOL3, GSL_SUCCESS); /* Bug reports from Ivan Liu */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (-26, 2.0, 100.0, &r), 1.444786781107436954e+19, TEST_TOL3, GSL_SUCCESS); #if 0 /* This one is computed with a huge error, there is loss of precision but the error estimate flags the problem (assuming the user looks at it). We should probably trap any return with err>|val| and signal loss of precision */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (-26.1, 2.0, 100.0, &r), 1.341557199575986995e+19, TEST_TOL3, GSL_SUCCESS); #endif /* Bug report H.Moseby */ TEST_SF(s, gsl_sf_hyperg_1F1_e, (1.2, 1.1e-15, 1.5, &r), 8254503159672429.02, TEST_TOL3, GSL_SUCCESS); // TEST_SF(s, gsl_sf_hyperg_1F1_e, (1.0, 1000000.5, 0.8e6 + 0.5, &r), 4.999922505099443804e+00, TEST_TOL3, GSL_SUCCESS); // TEST_SF(s, gsl_sf_hyperg_1F1_e, (1.0, 1000000.5, 1001000.5, &r), 3480.3699557431856166, TEST_TOL4, GSL_SUCCESS); #if 0 /* FIX THESE NEXT RELEASE */ // TEST_SF(s, gsl_sf_hyperg_1F1_e, (1.1, 1000000.5, 1001000.5, &r), 7304.6126942641350122, TEST_TOL3, GSL_SUCCESS); // TEST_SF(s, gsl_sf_hyperg_1F1_e, (0.9, 1000000.5, 1001000.5, &r), 1645.4879293475410982, TEST_TOL3, GSL_SUCCESS); #endif TEST_SF(s, gsl_sf_hyperg_1F1_e, (-1.1, 1000000.5, 1001000.5, &r), -5.30066488697455e-04, TEST_TOL3, GSL_SUCCESS); // TEST_SF(s, gsl_sf_hyperg_1F1_e, (1.5, 1000000.5, 0.8e6 + 0.5, &r), 11.18001288977894650469927615, TEST_TOL4, GSL_SUCCESS); /* U for integer parameters */ TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 0.0001, &r), 8.634088070212725330, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 0.01, &r), 4.078511443456425847, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 0.5, &r), 0.9229106324837304688, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 2.0, &r), 0.3613286168882225847, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 100, &r), 0.009901942286733018406, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 1000, &r), 0.0009990019940238807150, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 0.01, &r), 7.272361203006010000e+16, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 1, &r), 1957.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 5, &r), 1.042496, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 8, &r), 0.3207168579101562500, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 50, &r), 0.022660399001600000000, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 100, &r), 0.010631236727200000000, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 1000, &r), 0.0010060301203607207200, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 20, 1, &r), 1.7403456103284421000e+16, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 20, 20, &r), 0.22597813610531052969, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 50, 1, &r), 3.374452117521520758e+61, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 50, 50, &r), 0.15394136814987651785, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 0.1, &r), 1.0418325171990852858e+253, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 1, &r), 2.5624945006073464385e+154, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 50, &r), 3.0978624160896431391e+07, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 100, &r), 0.11323192555773717475, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 200, &r), 0.009715680951406713589, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 1000, &r), 0.0011085142546061528661, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1000, 2000, &r), 0.0009970168547036318206, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -1, 1, &r), 0.29817368116159703717, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -1, 10, &r), 0.07816669698940409380, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -10, 1, &r), 0.08271753756946041959, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -10, 5, &r), 0.06127757419425055261, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -10, 10, &r), 0.04656199948873187212, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -10, 20, &r), 0.031606421847946077709, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 0.01, &r), 0.009900000099999796950, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 1, &r), 0.009802970197050404429, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 10, &r), 0.009001648897173103447, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 20, &r), 0.008253126487166557546, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 50, &r), 0.006607993916432051008, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 90, &r), 0.005222713769726871937, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 110, &r), 0.004727658137692606210, TEST_TOL2, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_U_int_e, (1, -1000, 1, &r), 0.0009980029970019970050, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -1000, 1010, &r), 0.0004971408839859245170, TEST_TOL4, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 1, 0.001, &r), 0.0007505359326875706975, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 1, 0.5, &r), 6.449509938973479986e-06, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 1, 8, &r), 6.190694573035761284e-10, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 1, 20, &r), 3.647213845460374016e-12, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 8, 1, &r), 0.12289755012652317578, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 8, 10, &r), 5.687710359507564272e-09, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 8, 20, &r), 2.8175404594901039724e-11, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (100, 100, 0.01, &r), 1.0099979491941914867e+196, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (100, 100, 0.1, &r), 1.0090713562719862833e+97, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (100, 100, 1, &r), 0.009998990209084729106, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (100, 100, 20, &r), 1.3239363905866130603e-131, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 1, 0.01, &r), 3.274012540759009536e+06, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 1, 1, &r), 1.5202710000000000000e+06, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 1, 10, &r), 1.0154880000000000000e+08, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 1, 100, &r), 3.284529863685482880e+19, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 10, 1, &r), 1.1043089864100000000e+11, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 100, 1, &r), 1.3991152402448957897e+20, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 100, 10, &r), 5.364469916567136000e+19, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 100, 100, &r), 3.909797568000000000e+12, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 100, 500, &r), 8.082625576697984130e+25, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 1, 0.01, &r), 1.6973422555823855798e+64, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 1, 1, &r), 7.086160198304780325e+63, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 1, 10, &r), 5.332862895528712200e+65, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 10, 1, &r), -7.106713471565790573e+71, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 100, 1, &r), 2.4661377199407186476e+104, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 10, 10, &r), 5.687538583671241287e+68, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 100, 10, &r), 1.7880761664553373445e+102, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 1, 0.01, &r), 4.185245354032917715e+137, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 1, 0.1, &r), 2.4234043408007841358e+137, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 1, 10, &r), -1.8987677149221888807e+139, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 10, 10, &r), -5.682999988842066677e+143, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 100, 10, &r), 2.3410029853990624280e+189, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 1000, 10, &r), 1.9799451517572225316e+271, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, -1, 10, &r), -9.083195466262584149e+64, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, -10, 10, &r), -1.4418257327071634407e+62, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, -100, 0.01, &r), 3.0838993811468983931e+93, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, -100, 10, &r), 4.014552630378340665e+95, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-100, -100, 10, &r), 2.0556466922347982030e+162, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-100, -200, 10, &r), 1.1778399522973555582e+219, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_int_e, (-100, -200, 100, &r), 9.861313408898201873e+235, TEST_TOL3, GSL_SUCCESS); /* U */ TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 0.0001, 0.0001, &r), 1.0000576350699863577, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 0.0001, 1.0, &r), 0.9999403679233247536, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 0.0001, 100.0, &r), 0.9995385992657260887, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 1, 0.0001, &r), 1.0009210608660065989, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 1.0, 1.0, &r), 0.9999999925484179084, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 10, 1, &r), 13.567851006281412726, TEST_TOL3, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.0001, 10, 5, &r), 1.0006265020064596364, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 10, 10, &r), 0.9999244381454633265, TEST_TOL0, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.0001, 100, 1, &r), 2.5890615708804247881e+150, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.0001, 100, 10, &r), 2.3127845417739661466e+55, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.0001, 100, 50, &r), 6402.818715083582554, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 100, 98, &r), 0.9998517867411840044, TEST_TOL2, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.0001, 1000, 300, &r), 2.5389557274938010716e+213, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 1000, 999, &r), 0.9997195294193261604, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 1000, 1100, &r), 0.9995342990014584713, TEST_TOL1, GSL_SUCCESS); TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.5, 1000, 300, &r), 1.1977955438214207486e+217, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.5, 1000, 800, &r), 9.103916020464797207e+08, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.5, 1000, 998, &r), 0.21970269691801966806, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (0.5, 0.5, 1.0, &r), 0.7578721561413121060, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (1, 0.0001, 0.0001, &r), 0.9992361337764090785, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (1, 0.0001, 1, &r), 0.4036664068111504538, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (1, 0.0001, 100, &r), 0.009805780851264329587, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (1, 1.2, 2.0, &r), 0.3835044780075602550, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (1, -0.0001, 1, &r), 0.4036388693605999482, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (8, 10.5, 1, &r), 27.981926466707438538, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (8, 10.5, 10, &r), 2.4370135607662056809e-8, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (8, 10.5, 100, &r), 1.1226567526311488330e-16, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (10, -2.5, 10, &r), 6.734690720346560349e-14, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (10, 2.5, 10, &r), 6.787780794037971638e-13, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (10, 2.5, 50, &r), 2.4098720076596087125e-18, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 1, &r), -3.990841457734147e+6, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 10, &r), 1.307472052129343e+8, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 50, &r), 3.661978424114088e+16, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 90, &r), 8.09469542130868e+19, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 99, &r), 2.546328328942063e+20, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 100, &r), 2.870463201832814e+20, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 200, &r), 8.05143453769373e+23, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 10.1, 0.1, &r), -3.043016255306515e+20, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 10.1, 1, &r), -3.194745265896115e+12, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 10.1, 4, &r), -6.764203430361954e+07, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 10.1, 10, &r), -2.067399425480545e+09, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 10.1, 50, &r), 4.661837330822824e+14, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 100.4, 10, &r), -6.805460513724838e+66, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 100.4, 50, &r), -2.081052558162805e+18, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 100.4, 80, &r), 2.034113191014443e+14, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 100.4, 100, &r), 6.85047268436107e+13, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 100.4, 200, &r), 1.430815706105649e+20, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-19.5, 82.1, 10, &r), 5.464313196201917432e+60, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-50.5, 100.1, 10, &r), -5.5740216266953e+126, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-50.5, 100.1, 40, &r), 5.937463786613894e+91, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-50.5, 100.1, 50, &r), -1.631898534447233e+89, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-50.5, 100.1, 70, &r), 3.249026971618851e+84, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_U_e, (-50.5, 100.1, 100, &r), 1.003401902126641e+85, TEST_TOL1, GSL_SUCCESS); /* 2F1 */ TEST_SF(s, gsl_sf_hyperg_2F1_e, (1, 1, 1, 0.5, &r), 2.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, 8, 1, 0.5, &r), 12451584.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, -8, 1, 0.5, &r), 0.13671875, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, -8.1, 1, 0.5, &r), 0.14147385378899930422, TEST_TOL4, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, -8, 1, -0.5, &r), 4945.136718750000000, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, -8, -5.5, 0.5, &r), -906.6363636363636364, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, -8, -5.5, -0.5, &r), 24565.363636363636364, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, 8, 1, -0.5, &r), -0.006476312098196747669, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, 8, 5, 0.5, &r), 4205.714285714285714, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, 8, 5, -0.5, &r), 0.0028489656290296436616, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, 1, 0.99, &r), 1.2363536673577259280e+38 , TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -1.5, 0.99, &r), 3.796186436458346579e+46, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -1.5, -0.99, &r), 0.14733409946001025146, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -8.5, 0.99, &r), -1.1301780432998743440e+65, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -8.5, -0.99, &r), -8.856462606575344483, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -21.5, 0.99, &r), 2.0712920991876073253e+95, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -21.5, -0.99, &r), -74.30517015382249216, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -100.5, 0.99, &r), -3.186778061428268980e+262, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -100.5, -0.99, &r), 2.4454358338375677520, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (25, 25, 1, -0.5, &r), -2.9995530823639545027e-06, TEST_SQRT_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, 1.0-1.0/64.0, &r), 3.17175539044729373926, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, 1.0-1.0/128.0, &r), 3.59937243502024563424, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, 1.0-1.0/256.0, &r), 4.03259299524392504369, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, 1.0-1.0/1024.0, &r), 4.90784159359675398250, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, 1.0-1.0/65536.0, &r), 7.552266033399683914, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, 1.0-1.0/16777216.0, &r), 11.08235454026043830363, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, -1.0+1.0/1024.0, &r), 0.762910940909954974527, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, -1.0+1.0/65536.0, &r), 0.762762124908845424449, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 2.0, -1.0+1.0/1048576.0, &r), 0.762759911089064738044, TEST_TOL0, GSL_SUCCESS); /* added special handling with x == 1.0 , Richard J. Mathar, 2008-01-09 */ TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, 0.5, 3.0, 1.0, &r), 1.6976527263135502482014268 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (1.5, -4.2, 3.0, 1.0, &r), .15583601560025710649555254 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (-7.4, 0.7, -1.5, 1.0, &r), -.34478866959246584996859 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_e, (0.1, -2.7, -1.5, 1.0, &r), 1.059766766063610122925 , TEST_TOL0, GSL_SUCCESS); /* 2F1 conj */ TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (1, 1, 1, 0.5, &r), 3.352857095662929028, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (8, 8, 1, 0.5, &r), 1.7078067538891293983e+09, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (8, 8, 5, 0.5, &r), 285767.15696901140627, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (8, 8, 1, -0.5, &r), 0.007248196261471276276, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (8, 8, 5, -0.5, &r), 0.00023301916814505902809, TEST_TOL3, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (25, 25, 1, -0.5, &r), 5.1696944096e-06, TEST_SQRT_TOL0, GSL_SUCCESS); /* updated correct values, testing enabled, Richard J. Mathar, 2008-01-09 */ TEST_SF(s, gsl_sf_hyperg_2F0_e, (0.01, 1.0, -0.02, &r), .99980388665511730901180717 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F0_e, (0.1, 0.5, -0.02, &r), .99901595171179281891589794 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F0_e, (1, 1, -0.02, &r), .98075549650574351826538049000 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F0_e, (8, 8, -0.02, &r), .32990592849626965538692141 , TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F0_e, (50, 50, -0.02, &r), .2688995263772964415245902e-12 , TEST_TOL0, GSL_SUCCESS); /* 2F1 renorm */ TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (1, 1, 1, 0.5, &r), 2.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, 8, 1, 0.5, &r), 12451584.0, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, -8, 1, 0.5, &r), 0.13671875, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, -8, 1, -0.5, &r), 4945.13671875, TEST_TOL0, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, -8, -5.5, 0.5, &r), -83081.19167659493609, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, -8, -5.5, -0.5, &r), 2.2510895952730178518e+06, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, 8, 5, 0.5, &r), 175.2380952380952381, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (9, 9, -1.5, 0.99, &r), 1.6063266334913066551e+46, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (9, 9, -1.5, -0.99, &r), 0.06234327316254516616, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (5, 5, -1, 0.5, &r), 4949760.0, TEST_TOL1, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (5, 5, -10, 0.5, &r), 139408493229637632000.0, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (5, 5, -100, 0.5, &r), 3.0200107544594411315e+206, TEST_TOL3, GSL_SUCCESS); /* 2F1 conj renorm */ TEST_SF(s, gsl_sf_hyperg_2F1_conj_renorm_e, (9, 9, -1.5, 0.99, &r), 5.912269095984229412e+49, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_renorm_e, (9, 9, -1.5, -0.99, &r), 0.10834020229476124874, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_renorm_e, (5, 5, -1, 0.5, &r), 1.4885106335357933625e+08, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_renorm_e, (5, 5, -10, 0.5, &r), 7.968479361426355095e+21, TEST_TOL2, GSL_SUCCESS); TEST_SF(s, gsl_sf_hyperg_2F1_conj_renorm_e, (5, 5, -100, 0.5, &r), 3.1113180227052313057e+208, TEST_TOL3, GSL_SUCCESS); return s; } gsl-1.0.8/src/configure.base0000644000175000017500000002313311201030403013501 0ustar shshdnl The configure script is generated by autogen.sh from configure.base dnl and the various configure.add files in the source tree. Edit dnl configure.base and reprocess rather than modifying ./configure. dnl autoconf 2.13 certainly doesn't work! What is the minimum requirement? AC_PREREQ(2.2) AC_INIT(configure.base) PACKAGE=octave-forge MAJOR_VERSION=0 MINOR_VERSION=1 PATCH_LEVEL=0 dnl Kill caching --- this ought to be the default define([AC_CACHE_LOAD], )dnl define([AC_CACHE_SAVE], )dnl dnl uncomment to put support files in another directory dnl AC_CONFIG_AUX_DIR(admin) VERSION=$MAJOR_VERSION.$MINOR_VERSION.$PATCH_LEVEL AC_SUBST(PACKAGE) AC_SUBST(VERSION) dnl need to find admin files, so keep track of the top dir. TOPDIR=`pwd` AC_SUBST(TOPDIR) dnl if mkoctfile doesn't work, then we need the following: dnl AC_PROG_CXX dnl AC_PROG_F77 dnl Need C compiler regardless so define it in a way that dnl makes autoconf happy and we can override whatever we dnl need with mkoctfile -p. dnl XXX FIXME XXX should use mkoctfile to get CC and CFLAGS AC_PROG_CC dnl XXX FIXME XXX need tests for -p -c -s in mkoctfile. dnl ******************************************************************* dnl Sort out mkoctfile version number and install paths dnl XXX FIXME XXX latest octave has octave-config so we don't dnl need to discover things here. Doesn't have --exe-site-dir dnl but defines --oct-site-dir and --m-site-dir dnl Check for mkoctfile AC_CHECK_PROG(MKOCTFILE,mkoctfile,mkoctfile) test -z "$MKOCTFILE" && AC_MSG_WARN([no mkoctfile found on path]) AC_SUBST(ver) AC_SUBST(subver) AC_SUBST(mpath) AC_SUBST(opath) AC_SUBST(xpath) AC_SUBST(altpath) AC_SUBST(altmpath) AC_SUBST(altopath) AC_ARG_WITH(path, [ --with-path install path prefix], [ path=$withval ]) AC_ARG_WITH(mpath, [ --with-mpath override path for m-files], [mpath=$withval]) AC_ARG_WITH(opath, [ --with-opath override path for oct-files], [opath=$withval]) AC_ARG_WITH(xpath, [ --with-xpath override path for executables], [xpath=$withval]) AC_ARG_WITH(altpath, [ --with-altpath alternative functions install path prefix], [ altpath=$withval ]) AC_ARG_WITH(altmpath, [ --with-altmpath override path for alternative m-files], [altmpath=$withval]) AC_ARG_WITH(altopath, [ --with-altopath override path for alternative oct-files], [altopath=$withval]) if test -n "$path" ; then test -z "$mpath" && mpath=$path test -z "$opath" && opath=$path/oct test -z "$xpath" && xpath=$path/bin test -z "$altpath" && altpath=$path-alternatives fi if test -n "$altpath" ; then test -z "$altmpath" && altmpath=$altpath test -z "$altopath" && altopath=$altpath/oct fi dnl Don't query if path/ver are given in the configure environment #if test -z "$mpath" || test -z "$opath" || test -z "$xpath" || test -z "$altmpath" || test -z "$altopath" || test -z "$ver" ; then if test -z "$mpath" || test -z "$opath" || test -z "$xpath" || test -z "$ver" ; then dnl Construct program to get mkoctfile version and local install paths cat > conftest.cc < #include #include #define INFOV "\nINFOV=" OCTAVE_VERSION "\n" #define INFOH "\nINFOH=" OCTAVE_CANONICAL_HOST_TYPE "\n" #ifdef OCTAVE_LOCALVERFCNFILEDIR # define INFOM "\nINFOM=" OCTAVE_LOCALVERFCNFILEDIR "\n" #else # define INFOM "\nINFOM=" OCTAVE_LOCALFCNFILEPATH "\n" #endif #ifdef OCTAVE_LOCALVEROCTFILEDIR # define INFOO "\nINFOO=" OCTAVE_LOCALVEROCTFILEDIR "\n" #else # define INFOO "\nINFOO=" OCTAVE_LOCALOCTFILEPATH "\n" #endif #ifdef OCTAVE_LOCALVERARCHLIBDIR # define INFOX "\nINFOX=" OCTAVE_LOCALVERARCHLIBDIR "\n" #else # define INFOX "\nINFOX=" OCTAVE_LOCALARCHLIBDIR "\n" #endif const char *infom = INFOM; const char *infoo = INFOO; const char *infox = INFOX; const char *infoh = INFOH; const char *infov = INFOV; EOF dnl Compile program perhaps with a special version of mkoctfile $MKOCTFILE conftest.cc || AC_MSG_ERROR(Could not run $MKOCTFILE) dnl Strip the config info from the compiled file eval `strings conftest.o | grep "^INFO.=" | sed -e "s,//.*$,,"` rm -rf conftest* dnl set the appropriate variables if they are not already set ver=`echo $INFOV | sed -e "s/\.//" -e "s/\..*$//"` subver=`echo $INFOV | sed -e "[s/^[^.]*[.][^.]*[.]//]"` alt_mbase=`echo $INFOM | sed -e "[s,\/[^\/]*$,,]"` alt_obase=`echo $INFOO | sed -e "[s,/site.*$,/site,]"` test -z "$mpath" && mpath=$INFOM/octave-forge test -z "$opath" && opath=$INFOO/octave-forge test -z "$xpath" && xpath=$INFOX test -z "$altmpath" && altmpath=$alt_mbase/octave-forge-alternatives/m test -z "$altopath" && altopath=$alt_obase/octave-forge-alternatives/oct/$INFOH fi dnl ******************************************************************* dnl XXX FIXME XXX Should we allow the user to override these? dnl Do we even need them? The individual makefiles can call mkoctfile -p dnl themselves, so the only reason to keep them is for configure, and dnl for those things which are not built using mkoctfile (e.g., aurecord) dnl but it is not clear we should be using octave compile flags for those. dnl C compiler and flags AC_MSG_RESULT([retrieving compile and link flags from $MKOCTFILE]) CC=`$MKOCTFILE -p CC` CFLAGS=`$MKOCTFILE -p CFLAGS` CPPFLAGS=`$MKOCTFILE -p CPPFLAGS` CPICFLAG=`$MKOCTFILE -p CPICFLAG` LDFLAGS=`$MKOCTFILE -p LDFLAGS` LIBS=`$MKOCTFILE -p LIBS` AC_SUBST(CC) AC_SUBST(CFLAGS) AC_SUBST(CPPFLAGS) AC_SUBST(CPICFLAG) dnl Fortran compiler and flags F77=`$MKOCTFILE -p F77` FFLAGS=`$MKOCTFILE -p FFLAGS` FPICFLAG=`$MKOCTFILE -p FPICFLAG` AC_SUBST(F77) AC_SUBST(FFLAGS) AC_SUBST(FPICFLAG) dnl C++ compiler and flags CXX=`$MKOCTFILE -p CXX` CXXFLAGS=`$MKOCTFILE -p CXXFLAGS` CXXPICFLAG=`$MKOCTFILE -p CXXPICFLAG` AC_SUBST(CXX) AC_SUBST(CXXFLAGS) AC_SUBST(CXXPICFLAG) dnl ******************************************************************* dnl Check for features of your version of mkoctfile. dnl All checks should be designed so that the default dnl action if the tests are not performed is to do whatever dnl is appropriate for the most recent version of Octave. dnl Define the following macro: dnl OF_CHECK_LIB(lib,fn,true,false,helpers) dnl This is just like AC_CHECK_LIB, but it doesn't update LIBS AC_DEFUN(OF_CHECK_LIB, [save_LIBS="$LIBS" AC_CHECK_LIB($1,$2,$3,$4,$5) LIBS="$save_LIBS" ]) dnl Define the following macro: dnl TRY_MKOCTFILE(msg,program,action_if_true,action_if_false) dnl AC_DEFUN(TRY_MKOCTFILE, [AC_MSG_CHECKING($1) cat > conftest.cc << EOF #include $2 EOF ac_try="$MKOCTFILE -c conftest.cc" if AC_TRY_EVAL(ac_try) ; then AC_MSG_RESULT(yes) $3 else AC_MSG_RESULT(no) $4 fi ]) dnl dnl Check if F77_FUNC works with MKOCTFILE dnl TRY_MKOCTFILE([for F77_FUNC], [int F77_FUNC (hello, HELLO) (const int &n);],, [MKOCTFILE="$MKOCTFILE -DF77_FUNC=F77_FCN"]) dnl ********************************************************** dnl Evaluate an expression in octave dnl dnl OCTAVE_EVAL(expr,var) -> var=expr dnl AC_DEFUN(OCTAVE_EVAL, [AC_MSG_CHECKING([for $1 in Octave]) $2=`echo "disp($1)" | $OCTAVE -qf` AC_MSG_RESULT($$2) AC_SUBST($2) ]) dnl Check status of an octave variable dnl dnl OCTAVE_CHECK_EXIST(variable,action_if_true,action_if_false) dnl AC_DEFUN(OCTAVE_CHECK_EXIST, [AC_MSG_CHECKING([for $1 in Octave]) if test `echo 'disp(exist("$1"))' | $OCTAVE -qf`X != 0X ; then AC_MSG_RESULT(yes) $2 else AC_MSG_RESULT(no) $3 fi ]) dnl should check that $(OCTAVE) --version matches $(MKOCTFILE) --version AC_CHECK_PROG(OCTAVE,octave,octave) OCTAVE_EVAL(OCTAVE_VERSION,OCTAVE_VERSION) dnl grab canonical host type so we can write system specific install stuff OCTAVE_EVAL(octave_config_info('canonical_host_type'),canonical_host_type) dnl grab SHLEXT from octave config OCTAVE_EVAL(octave_config_info('SHLEXT'),SHLEXT) AC_PROG_LN_S AC_PROG_RANLIB dnl Use $(COPY_FLAGS) to set options for cp when installing .oct files. COPY_FLAGS="-Rfp" case "$canonical_host_type" in *-*-linux*) COPY_FLAGS="-fdp" ;; esac AC_SUBST(COPY_FLAGS) dnl Use $(STRIP) in the makefile to strip executables. If not found, dnl STRIP expands to ':', which in the makefile does nothing. dnl Don't need this for .oct files since mkoctfile handles them directly STRIP=${STRIP-strip} AC_CHECK_PROG(STRIP,$STRIP,$STRIP,:) dnl Strip on windows, don't strip on Mac OS/X or IRIX dnl For the rest, you can force strip using MKOCTFILE="mkoctfile -s" dnl or avoid strip using STRIP=: before ./configure case "$canonical_host_type" in powerpc-apple-darwin*|*-sgi-*) STRIP=: ;; *-cygwin-*|*-mingw-*) MKOCTFILE="$MKOCTFILE -s" ;; esac dnl Checking if the GSL library exists. AC_SUBST(HAVE_GSL) AC_SUBST(GSL_MISSING) OF_CHECK_LIB(gsl, gsl_message, HAVE_GSL=yes,HAVE_GSL=no,-lgslcblas) dnl If have GSL, check for newer GSL functions. if test $HAVE_GSL = yes ; then OF_CHECK_LIB(gsl, gsl_sf_hazard,,GSL_MISSING="$GSL_MISSING hazard",-lgslcblas) OF_CHECK_LIB(gsl, gsl_sf_gamma_inc,,GSL_MISSING="$GSL_MISSING gamma_inc",-lgslcblas) if test -z $GSL_MISSING; then GSLSTATUS=yes else GSLSTATUS="using old version of GSL" fi else GSLSTATUS=no fi CONFIGURE_OUTPUTS="Makeconf" STATUS_MSG=" octave commands will install into the following directories: m-files: $mpath oct-files: $opath binaries: $xpath alternatives: m-files: $altmpath oct-files: $altopath shell commands will install into the following directories: binaries: $bindir man pages: $mandir libraries: $libdir headers: $includedir octave-forge is configured with octave: $OCTAVE (version $OCTAVE_VERSION) mkoctfile: $MKOCTFILE for Octave $subver GSL toolbox: $GSLSTATUS" gsl-1.0.8/src/legendre_sphPlm_array.cc0000644000175000017500000000476411201030403015512 0ustar shsh/* Copyright (C) 2004 Teemu Ikonen This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; If not, see . Changes: 6/18/2008 R. Rogers Removed unsed variable i */ #include #include #include #include void octave_gsl_errorhandler (const char * reason, const char * file, int line, int gsl_errno) { error("GSL error %d at %s, line %d: %s\n", gsl_errno, file, line, reason); } DEFUN_DLD(legendre_sphPlm_array, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} legendre_sphPlm_array (@var{lmax}, @var{m}, @var{x})\n\ \n\ This function computes an array of normalized associated Legendre functions\n\ @iftex\n\ @tex\n\ $\\sqrt{(2l+1)/(4\\pi)} \\sqrt{(l-m)!/(l+m)!} P_l^m(x)$\n\ for $m >= 0, l = |m|, ..., lmax, |x| <= 1.0$\n\ @end tex\n\ @end iftex\n\ @ifinfo\n\ sqrt((2l+1)/(4*pi)) * sqrt((l-m)!/(l+m)!) Plm (x)\n\ for m >= 0, l = |m|, ..., lmax, |x| <= 1.0\n\ @end ifinfo\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn") { gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 3) { print_usage (); return octave_value_list(); } if(!args(0).is_real_type() || !args(1).is_real_type() || !args(2).is_real_type() || !args(0).is_scalar_type() || !args(1).is_scalar_type() || !args(2).is_scalar_type()) { error("The arguments must be real scalars."); print_usage (); return octave_value_list(); } int lmax = static_cast(args(0).scalar_value()); int m = static_cast(args(1).scalar_value()); double x = args(2).scalar_value(); RowVector *y = new RowVector(gsl_sf_legendre_array_size (lmax, m)); double *yd = y->fortran_vec(); gsl_sf_legendre_sphPlm_array (lmax, m, x, yd); return octave_value_list(octave_value(*y)); } gsl-1.0.8/src/buildgsl_sf.sh0000644000175000017500000010576411201030403013530 0ustar shsh## Copyright (C) 2004 Teemu Ikonen ## ## This program is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 2 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; if not, see . # list of missing functions surrounded by spaces # # # R. Rogers 4/23/2008 Added Confluent hypergeometric entries replace "'s" # "\'s" for descriptions; in other cases removed. If you have # with this blame the klutz (me). # R. Rogers 6/18/2008 Added some ellint documentation. # missing=" $* " cat <gsl_sf.cc // *** DO NOT EDIT *** this file is generated by buildgsl_sf.sh EOF cat precode.cc.template >> gsl_sf.cc # double to double export octave_name=clausen export funcname=gsl_sf_clausen cat << \EOF > docstring.txt The Clausen function is defined by the following integral, Cl_2(x) = - \int_0^x dt \log(2 \sin(t/2)) It is related to the dilogarithm by Cl_2(\theta) = \Im Li_2(\exp(i \theta)). EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=dawson export funcname=gsl_sf_dawson cat << \EOF > docstring.txt The Dawson integral is defined by \exp(-x^2) \int_0^x dt \exp(t^2). A table of Dawson integral can be found in Abramowitz & Stegun, Table 7.5. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=debye_1 export funcname=gsl_sf_debye_1 cat << \EOF > docstring.txt The Debye functions are defined by the integral D_n(x) = n/x^n \int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=debye_2 export funcname=gsl_sf_debye_2 cat << \EOF > docstring.txt The Debye functions are defined by the integral D_n(x) = n/x^n \int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=debye_3 export funcname=gsl_sf_debye_3 cat << \EOF > docstring.txt The Debye functions are defined by the integral D_n(x) = n/x^n \int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=debye_4 export funcname=gsl_sf_debye_4 cat << \EOF > docstring.txt The Debye functions are defined by the integral D_n(x) = n/x^n \int_0^x dt (t^n/(e^t - 1)). For further information see Abramowitz & Stegun, Section 27.1. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=erf_gsl export funcname=gsl_sf_erf cat << \EOF > docstring.txt These routines compute the error function erf(x) = (2/\sqrt(\pi)) \int_0^x dt \exp(-t^2). EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=erfc_gsl export funcname=gsl_sf_erfc cat << \EOF > docstring.txt These routines compute the complementary error function erfc(x) = 1 - erf(x) = (2/\sqrt(\pi)) \int_x^\infty \exp(-t^2). EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=log_erfc export funcname=gsl_sf_log_erfc cat << \EOF > docstring.txt These routines compute the logarithm of the complementary error function \log(\erfc(x)). EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=erf_Z export funcname=gsl_sf_erf_Z cat << \EOF > docstring.txt These routines compute the Gaussian probability function Z(x) = (1/(2\pi)) \exp(-x^2/2). EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=erf_Q export funcname=gsl_sf_erf_Q cat << \EOF > docstring.txt These routines compute the upper tail of the Gaussian probability function Q(x) = (1/(2\pi)) \int_x^\infty dt \exp(-t^2/2). EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc if test -n "${missing##* hazard *}"; then export octave_name=hazard export funcname=gsl_sf_hazard cat << \EOF > docstring.txt The hazard function for the normal distrbution, also known as the inverse Mill\'s ratio, is defined as h(x) = Z(x)/Q(x) = \sqrt@{2/\pi \exp(-x^2 / 2) / \erfc(x/\sqrt 2)@}. It decreases rapidly as x approaches -\infty and asymptotes to h(x) \sim x as x approaches +\infty. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc fi export octave_name=expm1 export funcname=gsl_sf_expm1 cat << \EOF > docstring.txt These routines compute the quantity \exp(x)-1 using an algorithm that is accurate for small x. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=exprel export funcname=gsl_sf_exprel cat << \EOF > docstring.txt These routines compute the quantity (\exp(x)-1)/x using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion (\exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \dots. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=exprel_2 export funcname=gsl_sf_exprel_2 cat << \EOF > docstring.txt These routines compute the quantity 2(\exp(x)-1-x)/x^2 using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion 2(\exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \dots. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=expint_E1 export funcname=gsl_sf_expint_E1 cat << \EOF > docstring.txt These routines compute the exponential integral E_1(x), E_1(x) := Re \int_1^\infty dt \exp(-xt)/t. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=expint_E2 export funcname=gsl_sf_expint_E2 cat << \EOF > docstring.txt These routines compute the second-order exponential integral E_2(x), E_2(x) := \Re \int_1^\infty dt \exp(-xt)/t^2. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=expint_Ei export funcname=gsl_sf_expint_Ei cat << \EOF > docstring.txt These routines compute the exponential integral E_i(x), Ei(x) := - PV(\int_@{-x@}^\infty dt \exp(-t)/t) where PV denotes the principal value of the integral. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=Shi export funcname=gsl_sf_Shi cat << \EOF > docstring.txt These routines compute the integral Shi(x) = \int_0^x dt \sinh(t)/t. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=Chi export funcname=gsl_sf_Chi cat << \EOF > docstring.txt These routines compute the integral Chi(x) := Re[ \gamma_E + \log(x) + \int_0^x dt (\cosh[t]-1)/t] , where \gamma_E is the Euler constant. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=expint_3 export funcname=gsl_sf_expint_3 cat << \EOF > docstring.txt These routines compute the exponential integral Ei_3(x) = \int_0^x dt \exp(-t^3) for x >= 0. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=Si export funcname=gsl_sf_Si cat << \EOF > docstring.txt These routines compute the Sine integral Si(x) = \int_0^x dt \sin(t)/t. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=Ci export funcname=gsl_sf_Ci cat << \EOF > docstring.txt These routines compute the Cosine integral Ci(x) = -\int_x^\infty dt \cos(t)/t for x > 0. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=atanint export funcname=gsl_sf_atanint cat << \EOF > docstring.txt These routines compute the Arctangent integral AtanInt(x) = \int_0^x dt \arctan(t)/t. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=fermi_dirac_mhalf export funcname=gsl_sf_fermi_dirac_mhalf cat << \EOF > docstring.txt These routines compute the complete Fermi-Dirac integral F_@{-1/2@}(x). EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=fermi_dirac_half export funcname=gsl_sf_fermi_dirac_half cat << \EOF > docstring.txt These routines compute the complete Fermi-Dirac integral F_@{1/2@}(x). EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=fermi_dirac_3half export funcname=gsl_sf_fermi_dirac_3half cat << \EOF > docstring.txt These routines compute the complete Fermi-Dirac integral F_@{3/2@}(x). EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=gamma_gsl export funcname=gsl_sf_gamma cat << \EOF > docstring.txt These routines compute the Gamma function \Gamma(x), subject to x not being a negative integer. The function is computed using the real Lanczos method. The maximum value of x such that \Gamma(x) is not considered an overflow is given by the macro GSL_SF_GAMMA_XMAX and is 171.0. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=lngamma_gsl export funcname=gsl_sf_lngamma cat << \EOF > docstring.txt These routines compute the logarithm of the Gamma function, \log(\Gamma(x)), subject to x not a being negative integer. For x<0 the real part of \log(\Gamma(x)) is returned, which is equivalent to \log(|\Gamma(x)|). The function is computed using the real Lanczos method. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=gammastar export funcname=gsl_sf_gammastar cat << \EOF > docstring.txt These routines compute the regulated Gamma Function \Gamma^*(x) for x > 0. The regulated gamma function is given by, \Gamma^*(x) = \Gamma(x)/(\sqrt@{2\pi@} x^@{(x-1/2)@} \exp(-x)) = (1 + (1/12x) + ...) for x \to \infty and is a useful suggestion of Temme. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=gammainv_gsl export funcname=gsl_sf_gammainv cat << \EOF > docstring.txt These routines compute the reciprocal of the gamma function, 1/\Gamma(x) using the real Lanczos method. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=lambert_W0 export funcname=gsl_sf_lambert_W0 cat << \EOF > docstring.txt These compute the principal branch of the Lambert W function, W_0(x). Lambert\'s W functions, W(x), are defined to be solutions of the equation W(x) \exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@{-1@}(x) to be the other real branch, where W < -1 for x < 0. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=lambert_Wm1 export funcname=gsl_sf_lambert_Wm1 cat << \EOF > docstring.txt These compute the secondary real-valued branch of the Lambert W function, W_@{-1@}(x). Lambert\'s W functions, W(x), are defined to be solutions of the equation W(x) \exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_@{-1@}(x) to be the other real branch, where W < -1 for x < 0. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=log_1plusx export funcname=gsl_sf_log_1plusx cat << \EOF > docstring.txt These routines compute \log(1 + x) for x > -1 using an algorithm that is accurate for small x. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=log_1plusx_mx export funcname=gsl_sf_log_1plusx_mx cat << \EOF > docstring.txt These routines compute \log(1 + x) - x for x > -1 using an algorithm that is accurate for small x. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=psi export funcname=gsl_sf_psi cat << \EOF > docstring.txt These routines compute the digamma function \psi(x) for general x, x \ne 0. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=psi_1piy export funcname=gsl_sf_psi_1piy cat << \EOF > docstring.txt These routines compute the real part of the digamma function on the line 1+i y, Re[\psi(1 + i y)]. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=synchrotron_1 export funcname=gsl_sf_synchrotron_1 cat << \EOF > docstring.txt These routines compute the first synchrotron function x \int_x^\infty dt K_@{5/3@}(t) for x >= 0. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=synchrotron_2 export funcname=gsl_sf_synchrotron_2 cat << \EOF > docstring.txt These routines compute the second synchrotron function x K_@{2/3@}(x) for x >= 0. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=transport_2 export funcname=gsl_sf_transport_2 cat << \EOF > docstring.txt These routines compute the transport function J(2,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \int_0^x dt t^n e^t /(e^t - 1)^2. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=transport_3 export funcname=gsl_sf_transport_3 cat << \EOF > docstring.txt These routines compute the transport function J(3,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \int_0^x dt t^n e^t /(e^t - 1)^2. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=transport_4 export funcname=gsl_sf_transport_4 cat << \EOF > docstring.txt These routines compute the transport function J(4,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \int_0^x dt t^n e^t /(e^t - 1)^2. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=transport_5 export funcname=gsl_sf_transport_5 cat << \EOF > docstring.txt These routines compute the transport function J(5,x). The transport functions J(n,x) are defined by the integral representations J(n,x) := \int_0^x dt t^n e^t /(e^t - 1)^2. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=sinc_gsl export funcname=gsl_sf_sinc cat << \EOF > docstring.txt These routines compute \sinc(x) = \sin(\pi x) / (\pi x) for any value of x. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=lnsinh export funcname=gsl_sf_lnsinh cat << \EOF > docstring.txt These routines compute \log(\sinh(x)) for x > 0. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=lncosh export funcname=gsl_sf_lncosh cat << \EOF > docstring.txt These routines compute \log(\cosh(x)) for any x. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=zeta export funcname=gsl_sf_zeta cat << \EOF > docstring.txt These routines compute the Riemann zeta function \zeta(s) for arbitrary s, s \ne 1. The Riemann zeta function is defined by the infinite sum \zeta(s) = \sum_@{k=1@}^\infty k^@{-s@}. EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc export octave_name=eta export funcname=gsl_sf_eta cat << \EOF > docstring.txt These routines compute the eta function \eta(s) for arbitrary s. The eta function is defined by \eta(s) = (1-2^@{1-s@}) \zeta(s). EOF ./replace_template.sh double_to_double.cc.template >> gsl_sf.cc # (int, double) to double export octave_name=bessel_Jn export funcname=gsl_sf_bessel_Jn cat << \EOF > docstring.txt These routines compute the regular cylindrical Bessel function of order n, J_n(x). EOF ./replace_template.sh int_double_to_double.cc.template >> gsl_sf.cc export octave_name=bessel_Yn export funcname=gsl_sf_bessel_Yn cat << \EOF > docstring.txt These routines compute the irregular cylindrical Bessel function of order n, Y_n(x), for x>0. EOF ./replace_template.sh int_double_to_double.cc.template >> gsl_sf.cc export octave_name=bessel_In export funcname=gsl_sf_bessel_In cat << \EOF > docstring.txt These routines compute the regular modified cylindrical Bessel function of order n, I_n(x). EOF ./replace_template.sh int_double_to_double.cc.template >> gsl_sf.cc export octave_name=bessel_In_scaled export funcname=gsl_sf_bessel_In_scaled cat << \EOF > docstring.txt These routines compute the scaled regular modified cylindrical Bessel function of order n, \exp(-|x|) I_n(x) EOF ./replace_template.sh int_double_to_double.cc.template >> gsl_sf.cc export octave_name=bessel_Kn export funcname=gsl_sf_bessel_Kn cat << \EOF > docstring.txt These routines compute the irregular modified cylindrical Bessel function of order n, K_n(x), for x > 0. EOF ./replace_template.sh int_double_to_double.cc.template >> gsl_sf.cc export octave_name=bessel_Kn_scaled export funcname=gsl_sf_bessel_Kn_scaled cat << \EOF > docstring.txt EOF ./replace_template.sh int_double_to_double.cc.template >> gsl_sf.cc export octave_name=bessel_jl export funcname=gsl_sf_bessel_jl cat << \EOF > docstring.txt These routines compute the regular spherical Bessel function of order l, j_l(x), for l >= 0 and x >= 0. EOF ./replace_template.sh int_double_to_double.cc.template >> gsl_sf.cc export octave_name=bessel_yl export funcname=gsl_sf_bessel_yl cat << \EOF > docstring.txt These routines compute the irregular spherical Bessel function of order l, y_l(x), for l >= 0. EOF ./replace_template.sh int_double_to_double.cc.template >> gsl_sf.cc export octave_name=bessel_il_scaled export funcname=gsl_sf_bessel_il_scaled cat << \EOF > docstring.txt These routines compute the scaled regular modified spherical Bessel function of order l, \exp(-|x|) i_l(x) EOF ./replace_template.sh int_double_to_double.cc.template >> gsl_sf.cc export octave_name=bessel_kl_scaled export funcname=gsl_sf_bessel_kl_scaled cat << \EOF > docstring.txt These routines compute the scaled irregular modified spherical Bessel function of order l, \exp(x) k_l(x), for x>0. EOF ./replace_template.sh int_double_to_double.cc.template >> gsl_sf.cc export octave_name=exprel_n export funcname=gsl_sf_exprel_n cat << \EOF > docstring.txt These routines compute the N-relative exponential, which is the n-th generalization of the functions gsl_sf_exprel and gsl_sf_exprel2. The N-relative exponential is given by, exprel_N(x) = N!/x^N (\exp(x) - \sum_@{k=0@}^@{N-1@} x^k/k!) = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ... = 1F1 (1,1+N,x) EOF ./replace_template.sh int_double_to_double.cc.template >> gsl_sf.cc export octave_name=fermi_dirac_int export funcname=gsl_sf_fermi_dirac_int cat << \EOF > docstring.txt These routines compute the complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/\Gamma(j+1)) \int_0^\infty dt (t^j /(\exp(t-x)+1)). EOF ./replace_template.sh int_double_to_double.cc.template >> gsl_sf.cc export octave_name=taylorcoeff export funcname=gsl_sf_taylorcoeff cat << \EOF > docstring.txt These routines compute the Taylor coefficient x^n / n! for x >= 0, n >= 0. EOF ./replace_template.sh int_double_to_double.cc.template >> gsl_sf.cc export octave_name=legendre_Pl export funcname=gsl_sf_legendre_Pl cat << \EOF > docstring.txt These functions evaluate the Legendre polynomial P_l(x) for a specific value of l, x subject to l >= 0, |x| <= 1 EOF ./replace_template.sh int_double_to_double.cc.template >> gsl_sf.cc export octave_name=legendre_Ql export funcname=gsl_sf_legendre_Ql cat << \EOF > docstring.txt These routines compute the Legendre function Q_l(x) for x > -1, x != 1 and l >= 0. EOF ./replace_template.sh int_double_to_double.cc.template >> gsl_sf.cc export octave_name=psi_n export funcname=gsl_sf_psi_n cat << \EOF > docstring.txt These routines compute the polygamma function \psi^@{(m)@}(x) for m >= 0, x > 0. EOF ./replace_template.sh int_double_to_double.cc.template >> gsl_sf.cc # (double, double) to double export octave_name=bessel_Jnu export funcname=gsl_sf_bessel_Jnu cat << \EOF > docstring.txt These routines compute the regular cylindrical Bessel function of fractional order nu, J_\nu(x). EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc export octave_name=bessel_Ynu export funcname=gsl_sf_bessel_Ynu cat << \EOF > docstring.txt These routines compute the irregular cylindrical Bessel function of fractional order nu, Y_\nu(x). EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc export octave_name=bessel_Inu export funcname=gsl_sf_bessel_Inu cat << \EOF > docstring.txt These routines compute the regular modified Bessel function of fractional order nu, I_\nu(x) for x>0, \nu>0. EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc export octave_name=bessel_Inu_scaled export funcname=gsl_sf_bessel_Inu_scaled cat << \EOF > docstring.txt These routines compute the scaled regular modified Bessel function of fractional order nu, \exp(-|x|)I_\nu(x) for x>0, \nu>0. EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc export octave_name=bessel_Knu export funcname=gsl_sf_bessel_Knu cat << \EOF > docstring.txt These routines compute the irregular modified Bessel function of fractional order nu, K_\nu(x) for x>0, \nu>0. EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc export octave_name=bessel_lnKnu export funcname=gsl_sf_bessel_lnKnu cat << \EOF > docstring.txt These routines compute the logarithm of the irregular modified Bessel function of fractional order nu, \ln(K_\nu(x)) for x>0, \nu>0. EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc export octave_name=bessel_Knu_scaled export funcname=gsl_sf_bessel_Knu_scaled cat << \EOF > docstring.txt These routines compute the scaled irregular modified Bessel function of fractional order nu, \exp(+|x|) K_\nu(x) for x>0, \nu>0. EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc export octave_name=exp_mult export funcname=gsl_sf_exp_mult cat << \EOF > docstring.txt These routines exponentiate x and multiply by the factor y to return the product y \exp(x). EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc export octave_name=fermi_dirac_inc_0 export funcname=gsl_sf_fermi_dirac_inc_0 cat << \EOF > docstring.txt These routines compute the incomplete Fermi-Dirac integral with an index of zero, F_0(x,b) = \ln(1 + e^@{b-x@}) - (b-x). EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc export octave_name=poch export funcname=gsl_sf_poch cat << \EOF > docstring.txt These routines compute the Pochhammer symbol (a)_x := \Gamma(a + x)/\Gamma(a), subject to a and a+x not being negative integers. The Pochhammer symbol is also known as the Apell symbol. EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc export octave_name=lnpoch export funcname=gsl_sf_lnpoch cat << \EOF > docstring.txt These routines compute the logarithm of the Pochhammer symbol, \log((a)_x) = \log(\Gamma(a + x)/\Gamma(a)) for a > 0, a+x > 0. EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc export octave_name=pochrel export funcname=gsl_sf_pochrel cat << \EOF > docstring.txt These routines compute the relative Pochhammer symbol ((a,x) - 1)/x where (a,x) = (a)_x := \Gamma(a + x)/\Gamma(a). EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc export octave_name=gamma_inc_Q export funcname=gsl_sf_gamma_inc_Q cat << \EOF > docstring.txt These routines compute the normalized incomplete Gamma Function Q(a,x) = 1/\Gamma(a) \int_x\infty dt t^@{a-1@} \exp(-t) for a > 0, x >= 0. EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc export octave_name=gamma_inc_P export funcname=gsl_sf_gamma_inc_P cat << \EOF > docstring.txt These routines compute the complementary normalized incomplete Gamma Function P(a,x) = 1/\Gamma(a) \int_0^x dt t^@{a-1@} \exp(-t) for a > 0, x >= 0. EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc if test -n "${missing##* gamma_inc *@}"; then export octave_name=gamma_inc export funcname=gsl_sf_gamma_inc cat << \EOF > docstring.txt These functions compute the incomplete Gamma Function the normalization factor included in the previously defined functions: \Gamma(a,x) = \int_x\infty dt t^@{a-1@} \exp(-t) for a real and x >= 0. EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc fi export octave_name=beta_gsl export funcname=gsl_sf_beta cat << \EOF > docstring.txt These routines compute the Beta Function, B(a,b) = \Gamma(a)\Gamma(b)/\Gamma(a+b) for a > 0, b > 0. EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc export octave_name=lnbeta export funcname=gsl_sf_lnbeta cat << \EOF > docstring.txt These routines compute the logarithm of the Beta Function, \log(B(a,b)) for a > 0, b > 0. EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc export octave_name=hyperg_0F1 export funcname=gsl_sf_hyperg_0F1 cat << \EOF > docstring.txt These routines compute the hypergeometric function 0F1(c,x). EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc export octave_name=conicalP_half export funcname=gsl_sf_conicalP_half cat << \EOF > docstring.txt These routines compute the irregular Spherical Conical Function P^@{1/2@}_@{-1/2 + i \lambda@}(x) for x > -1. EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc export octave_name=conicalP_mhalf export funcname=gsl_sf_conicalP_mhalf cat << \EOF > docstring.txt These routines compute the regular Spherical Conical Function P^@{-1/2@}_@{-1/2 + i \lambda@}(x) for x > -1. EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc export octave_name=conicalP_0 export funcname=gsl_sf_conicalP_0 cat << \EOF > docstring.txt These routines compute the conical function P^0_@{-1/2 + i \lambda@}(x) for x > -1. EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc export octave_name=conicalP_1 export funcname=gsl_sf_conicalP_1 cat << \EOF > docstring.txt These routines compute the conical function P^1_@{-1/2 + i \lambda@}(x) for x > -1. EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc export octave_name=hzeta export funcname=gsl_sf_hzeta cat << \EOF > docstring.txt These routines compute the Hurwitz zeta function \zeta(s,q) for s > 1, q > 0. EOF ./replace_template.sh double_double_to_double.cc.template >> gsl_sf.cc # (double, mode) to double export octave_name=airy_Ai export funcname=gsl_sf_airy_Ai cat << \EOF > docstring.txt These routines compute the Airy function Ai(x) with an accuracy specified by mode. EOF ./replace_template.sh double_mode_to_double.cc.template >> gsl_sf.cc export octave_name=airy_Bi export funcname=gsl_sf_airy_Bi cat << \EOF > docstring.txt These routines compute the Airy function Bi(x) with an accuracy specified by mode. EOF ./replace_template.sh double_mode_to_double.cc.template >> gsl_sf.cc export octave_name=airy_Ai_scaled export funcname=gsl_sf_airy_Ai_scaled cat << \EOF > docstring.txt These routines compute a scaled version of the Airy function S_A(x) Ai(x). For x>0 the scaling factor S_A(x) is \exp(+(2/3) x^(3/2)), and is 1 for x<0. EOF ./replace_template.sh double_mode_to_double.cc.template >> gsl_sf.cc export octave_name=airy_Bi_scaled export funcname=gsl_sf_airy_Bi_scaled cat << \EOF > docstring.txt These routines compute a scaled version of the Airy function S_B(x) Bi(x). For x>0 the scaling factor S_B(x) is exp(-(2/3) x^(3/2)), and is 1 for x<0. EOF ./replace_template.sh double_mode_to_double.cc.template >> gsl_sf.cc export octave_name=airy_Ai_deriv export funcname=gsl_sf_airy_Ai_deriv cat << \EOF > docstring.txt These routines compute the Airy function derivative Ai'(x) with an accuracy specified by mode. EOF ./replace_template.sh double_mode_to_double.cc.template >> gsl_sf.cc export octave_name=airy_Bi_deriv export funcname=gsl_sf_airy_Bi_deriv cat << \EOF > docstring.txt These routines compute the Airy function derivative Bi'(x) with an accuracy specified by mode. EOF ./replace_template.sh double_mode_to_double.cc.template >> gsl_sf.cc export octave_name=airy_Ai_deriv_scaled export funcname=gsl_sf_airy_Ai_deriv_scaled cat << \EOF > docstring.txt These routines compute the derivative of the scaled Airy function S_A(x) Ai(x). EOF ./replace_template.sh double_mode_to_double.cc.template >> gsl_sf.cc export octave_name=airy_Bi_deriv_scaled export funcname=gsl_sf_airy_Bi_deriv_scaled cat << \EOF > docstring.txt These routines compute the derivative of the scaled Airy function S_B(x) Bi(x). EOF ./replace_template.sh double_mode_to_double.cc.template >> gsl_sf.cc export octave_name=ellint_Kcomp export funcname=gsl_sf_ellint_Kcomp cat << \EOF > docstring.txt These routines compute the complete elliptic integral K(k) @tex \beforedisplay $$ \eqalign{ K(k) &= \int_0^{\pi/2} {dt \over \sqrt{(1 - k^2 \sin^2(t))}} \cr } $$ \afterdisplay See also: @end tex @ifinfo @group @example pi --- 2 / | 1 ellint_Kcomp(k) = | ------------------- dt | 2 2 / sqrt(1 - k sin (t)) 0 @end example @end group @end ifinfo @ifhtml @group @example pi --- 2 / | 1 ellint_Kcomp(k) = | ------------------- dt | 2 2 / sqrt(1 - k sin (t)) 0 @end example @end group @end ifhtml @seealso{ellipj, ellipke} The notation used here is based on Carlson, @cite{Numerische Mathematik} 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter @math{m = k^2}. EOF ./replace_template.sh double_mode_to_double.cc.template >> gsl_sf.cc export octave_name=ellint_Ecomp export funcname=gsl_sf_ellint_Ecomp cat << \EOF > docstring.txt These routines compute the complete elliptic integral E(k) to the accuracy specified by the mode variable mode. @tex \beforedisplay $$ \eqalign{ E(k) &= \int_0^{\pi/2} \sqrt{(1 - k^2 \sin^2(t))} dt \cr } $$ \afterdisplay See also: @end tex @ifinfo @group @example pi --- 2 / | 2 2 ellint_Ecomp(k) = | sqrt(1 - k sin (t)) dt | / 0 @end example @end group @end ifinfo @ifhtml @group @example pi --- 2 / | 2 2 ellint_Ecomp(k) = | sqrt(1 - k sin (t)) dt | / 0 @end example @end group @end ifhtml @seealso{ellipj, ellipke} The notation used here is based on Carlson, @cite{Numerische Mathematik} 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter @math{m = k^2}. EOF ./replace_template.sh double_mode_to_double.cc.template >> gsl_sf.cc # int to double export octave_name=airy_zero_Ai export funcname=gsl_sf_airy_zero_Ai cat << \EOF > docstring.txt These routines compute the location of the s-th zero of the Airy function Ai(x). EOF ./replace_template.sh int_to_double.cc.template >> gsl_sf.cc export octave_name=airy_zero_Bi export funcname=gsl_sf_airy_zero_Bi cat << \EOF > docstring.txt These routines compute the location of the s-th zero of the Airy function Bi(x). EOF ./replace_template.sh int_to_double.cc.template >> gsl_sf.cc export octave_name=airy_zero_Ai_deriv export funcname=gsl_sf_airy_zero_Ai_deriv cat << \EOF > docstring.txt These routines compute the location of the s-th zero of the Airy function derivative Ai(x). EOF ./replace_template.sh int_to_double.cc.template >> gsl_sf.cc export octave_name=airy_zero_Bi_deriv export funcname=gsl_sf_airy_zero_Bi_deriv cat << \EOF > docstring.txt These routines compute the location of the s-th zero of the Airy function derivative Bi(x). EOF ./replace_template.sh int_to_double.cc.template >> gsl_sf.cc export octave_name=bessel_zero_J0 export funcname=gsl_sf_bessel_zero_J0 cat << \EOF > docstring.txt These routines compute the location of the s-th positive zero of the Bessel function J_0(x). EOF ./replace_template.sh int_to_double.cc.template >> gsl_sf.cc export octave_name=bessel_zero_J1 export funcname=gsl_sf_bessel_zero_J1 cat << \EOF > docstring.txt These routines compute the location of the s-th positive zero of the Bessel function J_1(x). EOF ./replace_template.sh int_to_double.cc.template >> gsl_sf.cc export octave_name=psi_1_int export funcname=gsl_sf_psi_1_int cat << \EOF > docstring.txt These routines compute the Trigamma function \psi(n) for positive integer n. EOF ./replace_template.sh int_to_double.cc.template >> gsl_sf.cc export octave_name=zeta_int export funcname=gsl_sf_zeta_int cat << \EOF > docstring.txt These routines compute the Riemann zeta function \zeta(n) for integer n, n \ne 1. EOF ./replace_template.sh int_to_double.cc.template >> gsl_sf.cc export octave_name=eta_int export funcname=gsl_sf_eta_int cat << \EOF > docstring.txt These routines compute the eta function \eta(n) for integer n. EOF ./replace_template.sh int_to_double.cc.template >> gsl_sf.cc # (int, int, double) to double export octave_name=legendre_Plm export funcname=gsl_sf_legendre_Plm cat << \EOF > docstring.txt These routines compute the associated Legendre polynomial P_l^m(x) for m >= 0, l >= m, |x| <= 1. EOF ./replace_template.sh int_int_double_to_double.cc.template >> gsl_sf.cc export octave_name=legendre_sphPlm export funcname=gsl_sf_legendre_sphPlm cat << \EOF > docstring.txt These routines compute the normalized associated Legendre polynomial $\sqrt@{(2l+1)/(4\pi)@} \sqrt@{(l-m)!/(l+m)!@} P_l^m(x)$ suitable for use in spherical harmonics. The parameters must satisfy m >= 0, l >= m, |x| <= 1. Theses routines avoid the overflows that occur for the standard normalization of P_l^m(x). EOF ./replace_template.sh int_int_double_to_double.cc.template >> gsl_sf.cc export octave_name=hyperg_U export funcname=gsl_sf_hyperg_U cat << \EOF > docstring.txt Secondary Confluent Hypergoemetric U function A&E 13.1.3 All inputs are double as is the output. EOF ./replace_template.sh DDD_to_D.cc.template >> gsl_sf.cc export octave_name=hyperg_1F1 export funcname=gsl_sf_hyperg_1F1 cat << \EOF > docstring.txt Primary Confluent Hypergoemetric U function A&E 13.1.3 All inputs are double as is the output. EOF ./replace_template.sh DDD_to_D.cc.template >> gsl_sf.cc gsl-1.0.8/src/double_to_double.cc.template0000644000175000017500000000265111201030403016315 0ustar shshDEFUN_DLD(GSL_OCTAVE_NAME, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} GSL_OCTAVE_NAME (@var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} GSL_OCTAVE_NAME (@dots{})\n\ \n\ GSL_FUNC_DOCSTRING \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 1) { print_usage (); return octave_value(); } if(!args(0).is_real_type()) { error("The argument must be real."); print_usage (); return octave_value(); } NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); // printf("length: %d\n", lx); // printf("nargout: %d\n", nargout); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = GSL_FUNC_NAME (x.xelem(i)); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { GSL_FUNC_NAME_e (x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ gsl-1.0.8/src/autogen.sh0000755000175000017500000000132211201030403012661 0ustar shsh#! 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It's necessary to write '\x00'==0 to get something that's true only with -std. */ int osf4_cc_array ['\x00' == 0 ? 1 : -1]; /* IBM C 6 for AIX is almost-ANSI by default, but it replaces macro parameters inside strings and character constants. */ #define FOO(x) 'x' int xlc6_cc_array[FOO(a) == 'x' ? 1 : -1]; int test (int i, double x); struct s1 {int (*f) (int a);}; struct s2 {int (*f) (double a);}; int pairnames (int, char **, FILE *(*)(struct buf *, struct stat *, int), int, int); int argc; char **argv; int main () { return f (e, argv, 0) != argv[0] || f (e, argv, 1) != argv[1]; ; return 0; } _ACEOF for ac_arg in '' -qlanglvl=extc89 -qlanglvl=ansi -std \ -Ae "-Aa -D_HPUX_SOURCE" "-Xc -D__EXTENSIONS__" do CC="$ac_save_CC $ac_arg" rm -f conftest.$ac_objext if { (ac_try="$ac_compile" case "(($ac_try" in *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;; *) ac_try_echo=$ac_try;; esac eval ac_try_echo="\"\$as_me:$LINENO: $ac_try_echo\"" $as_echo "$ac_try_echo") >&5 (eval "$ac_compile") 2>conftest.er1 ac_status=$? grep -v '^ *+' conftest.er1 >conftest.err rm -f conftest.er1 cat conftest.err >&5 $as_echo "$as_me:$LINENO: \$? = $ac_status" >&5 (exit $ac_status); } && { test -z "$ac_c_werror_flag" || test ! -s conftest.err } && test -s conftest.$ac_objext; then ac_cv_prog_cc_c89=$ac_arg else $as_echo "$as_me: failed program was:" >&5 sed 's/^/| /' conftest.$ac_ext >&5 fi rm -f core conftest.err conftest.$ac_objext test "x$ac_cv_prog_cc_c89" != "xno" && break done rm -f conftest.$ac_ext CC=$ac_save_CC fi # AC_CACHE_VAL case "x$ac_cv_prog_cc_c89" in x) { $as_echo "$as_me:$LINENO: result: none needed" >&5 $as_echo "none needed" >&6; } ;; xno) { $as_echo "$as_me:$LINENO: result: unsupported" >&5 $as_echo "unsupported" >&6; } ;; *) CC="$CC $ac_cv_prog_cc_c89" { $as_echo "$as_me:$LINENO: result: $ac_cv_prog_cc_c89" >&5 $as_echo "$ac_cv_prog_cc_c89" >&6; } ;; esac ac_ext=c ac_cpp='$CPP $CPPFLAGS' ac_compile='$CC -c $CFLAGS $CPPFLAGS conftest.$ac_ext >&5' ac_link='$CC -o conftest$ac_exeext $CFLAGS $CPPFLAGS $LDFLAGS conftest.$ac_ext $LIBS >&5' ac_compiler_gnu=$ac_cv_c_compiler_gnu # Extract the first word of "mkoctfile", so it can be a program name with args. set dummy mkoctfile; ac_word=$2 { $as_echo "$as_me:$LINENO: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_MKOCTFILE+set}" = set; then $as_echo_n "(cached) " >&6 else if test -n "$MKOCTFILE"; then ac_cv_prog_MKOCTFILE="$MKOCTFILE" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_MKOCTFILE="mkoctfile" $as_echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi MKOCTFILE=$ac_cv_prog_MKOCTFILE if test -n "$MKOCTFILE"; then { $as_echo "$as_me:$LINENO: result: $MKOCTFILE" >&5 $as_echo "$MKOCTFILE" >&6; } else { $as_echo "$as_me:$LINENO: result: no" >&5 $as_echo "no" >&6; } fi test -z "$MKOCTFILE" && { $as_echo "$as_me:$LINENO: WARNING: no mkoctfile found on path" >&5 $as_echo "$as_me: WARNING: no mkoctfile found on path" >&2;} # Check whether --with-path was given. if test "${with_path+set}" = set; then withval=$with_path; path=$withval fi # Check whether --with-mpath was given. if test "${with_mpath+set}" = set; then withval=$with_mpath; mpath=$withval fi # Check whether --with-opath was given. if test "${with_opath+set}" = set; then withval=$with_opath; opath=$withval fi # Check whether --with-xpath was given. if test "${with_xpath+set}" = set; then withval=$with_xpath; xpath=$withval fi # Check whether --with-altpath was given. if test "${with_altpath+set}" = set; then withval=$with_altpath; altpath=$withval fi # Check whether --with-altmpath was given. if test "${with_altmpath+set}" = set; then withval=$with_altmpath; altmpath=$withval fi # Check whether --with-altopath was given. if test "${with_altopath+set}" = set; then withval=$with_altopath; altopath=$withval fi if test -n "$path" ; then test -z "$mpath" && mpath=$path test -z "$opath" && opath=$path/oct test -z "$xpath" && xpath=$path/bin test -z "$altpath" && altpath=$path-alternatives fi if test -n "$altpath" ; then test -z "$altmpath" && altmpath=$altpath test -z "$altopath" && altopath=$altpath/oct fi #if test -z "$mpath" || test -z "$opath" || test -z "$xpath" || test -z "$altmpath" || test -z "$altopath" || test -z "$ver" ; then if test -z "$mpath" || test -z "$opath" || test -z "$xpath" || test -z "$ver" ; then cat > conftest.cc < #include #include #define INFOV "\nINFOV=" OCTAVE_VERSION "\n" #define INFOH "\nINFOH=" OCTAVE_CANONICAL_HOST_TYPE "\n" #ifdef OCTAVE_LOCALVERFCNFILEDIR # define INFOM "\nINFOM=" OCTAVE_LOCALVERFCNFILEDIR "\n" #else # define INFOM "\nINFOM=" OCTAVE_LOCALFCNFILEPATH "\n" #endif #ifdef OCTAVE_LOCALVEROCTFILEDIR # define INFOO "\nINFOO=" OCTAVE_LOCALVEROCTFILEDIR "\n" #else # define INFOO "\nINFOO=" OCTAVE_LOCALOCTFILEPATH "\n" #endif #ifdef OCTAVE_LOCALVERARCHLIBDIR # define INFOX "\nINFOX=" OCTAVE_LOCALVERARCHLIBDIR "\n" #else # define INFOX "\nINFOX=" OCTAVE_LOCALARCHLIBDIR "\n" #endif const char *infom = INFOM; const char *infoo = INFOO; const char *infox = INFOX; const char *infoh = INFOH; const char *infov = INFOV; EOF $MKOCTFILE conftest.cc || { { $as_echo "$as_me:$LINENO: error: Could not run $MKOCTFILE" >&5 $as_echo "$as_me: error: Could not run $MKOCTFILE" >&2;} { (exit 1); exit 1; }; } eval `strings conftest.o | grep "^INFO.=" | sed -e "s,//.*$,,"` rm -rf conftest* ver=`echo $INFOV | sed -e "s/\.//" -e "s/\..*$//"` subver=`echo $INFOV | sed -e "s/^[^.]*[.][^.]*[.]//"` alt_mbase=`echo $INFOM | sed -e "s,\/[^\/]*$,,"` alt_obase=`echo $INFOO | sed -e "s,/site.*$,/site,"` test -z "$mpath" && mpath=$INFOM/octave-forge test -z "$opath" && opath=$INFOO/octave-forge test -z "$xpath" && xpath=$INFOX test -z "$altmpath" && altmpath=$alt_mbase/octave-forge-alternatives/m test -z "$altopath" && altopath=$alt_obase/octave-forge-alternatives/oct/$INFOH fi { $as_echo "$as_me:$LINENO: result: retrieving compile and link flags from $MKOCTFILE" >&5 $as_echo "retrieving compile and link flags from $MKOCTFILE" >&6; } CC=`$MKOCTFILE -p CC` CFLAGS=`$MKOCTFILE -p CFLAGS` CPPFLAGS=`$MKOCTFILE -p CPPFLAGS` CPICFLAG=`$MKOCTFILE -p CPICFLAG` LDFLAGS=`$MKOCTFILE -p LDFLAGS` LIBS=`$MKOCTFILE -p LIBS` F77=`$MKOCTFILE -p F77` FFLAGS=`$MKOCTFILE -p FFLAGS` FPICFLAG=`$MKOCTFILE -p FPICFLAG` CXX=`$MKOCTFILE -p CXX` CXXFLAGS=`$MKOCTFILE -p CXXFLAGS` CXXPICFLAG=`$MKOCTFILE -p CXXPICFLAG` { $as_echo "$as_me:$LINENO: checking for F77_FUNC" >&5 $as_echo_n "checking for F77_FUNC... " >&6; } cat > conftest.cc << EOF #include int F77_FUNC (hello, HELLO) (const int &n); EOF ac_try="$MKOCTFILE -c conftest.cc" if { (eval echo "$as_me:$LINENO: \"$ac_try\"") >&5 (eval $ac_try) 2>&5 ac_status=$? $as_echo "$as_me:$LINENO: \$? = $ac_status" >&5 (exit $ac_status); } ; then { $as_echo "$as_me:$LINENO: result: yes" >&5 $as_echo "yes" >&6; } else { $as_echo "$as_me:$LINENO: result: no" >&5 $as_echo "no" >&6; } MKOCTFILE="$MKOCTFILE -DF77_FUNC=F77_FCN" fi # Extract the first word of "octave", so it can be a program name with args. set dummy octave; ac_word=$2 { $as_echo "$as_me:$LINENO: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_OCTAVE+set}" = set; then $as_echo_n "(cached) " >&6 else if test -n "$OCTAVE"; then ac_cv_prog_OCTAVE="$OCTAVE" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_OCTAVE="octave" $as_echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi OCTAVE=$ac_cv_prog_OCTAVE if test -n "$OCTAVE"; then { $as_echo "$as_me:$LINENO: result: $OCTAVE" >&5 $as_echo "$OCTAVE" >&6; } else { $as_echo "$as_me:$LINENO: result: no" >&5 $as_echo "no" >&6; } fi { $as_echo "$as_me:$LINENO: checking for OCTAVE_VERSION in Octave" >&5 $as_echo_n "checking for OCTAVE_VERSION in Octave... " >&6; } OCTAVE_VERSION=`echo "disp(OCTAVE_VERSION)" | $OCTAVE -qf` { $as_echo "$as_me:$LINENO: result: $OCTAVE_VERSION" >&5 $as_echo "$OCTAVE_VERSION" >&6; } { $as_echo "$as_me:$LINENO: checking for octave_config_info('canonical_host_type') in Octave" >&5 $as_echo_n "checking for octave_config_info('canonical_host_type') in Octave... " >&6; } canonical_host_type=`echo "disp(octave_config_info('canonical_host_type'))" | $OCTAVE -qf` { $as_echo "$as_me:$LINENO: result: $canonical_host_type" >&5 $as_echo "$canonical_host_type" >&6; } { $as_echo "$as_me:$LINENO: checking for octave_config_info('SHLEXT') in Octave" >&5 $as_echo_n "checking for octave_config_info('SHLEXT') in Octave... " >&6; } SHLEXT=`echo "disp(octave_config_info('SHLEXT'))" | $OCTAVE -qf` { $as_echo "$as_me:$LINENO: result: $SHLEXT" >&5 $as_echo "$SHLEXT" >&6; } { $as_echo "$as_me:$LINENO: checking whether ln -s works" >&5 $as_echo_n "checking whether ln -s works... " >&6; } LN_S=$as_ln_s if test "$LN_S" = "ln -s"; then { $as_echo "$as_me:$LINENO: result: yes" >&5 $as_echo "yes" >&6; } else { $as_echo "$as_me:$LINENO: result: no, using $LN_S" >&5 $as_echo "no, using $LN_S" >&6; } fi if test -n "$ac_tool_prefix"; then # Extract the first word of "${ac_tool_prefix}ranlib", so it can be a program name with args. set dummy ${ac_tool_prefix}ranlib; ac_word=$2 { $as_echo "$as_me:$LINENO: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_RANLIB+set}" = set; then $as_echo_n "(cached) " >&6 else if test -n "$RANLIB"; then ac_cv_prog_RANLIB="$RANLIB" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_RANLIB="${ac_tool_prefix}ranlib" $as_echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi RANLIB=$ac_cv_prog_RANLIB if test -n "$RANLIB"; then { $as_echo "$as_me:$LINENO: result: $RANLIB" >&5 $as_echo "$RANLIB" >&6; } else { $as_echo "$as_me:$LINENO: result: no" >&5 $as_echo "no" >&6; } fi fi if test -z "$ac_cv_prog_RANLIB"; then ac_ct_RANLIB=$RANLIB # Extract the first word of "ranlib", so it can be a program name with args. set dummy ranlib; ac_word=$2 { $as_echo "$as_me:$LINENO: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_ac_ct_RANLIB+set}" = set; then $as_echo_n "(cached) " >&6 else if test -n "$ac_ct_RANLIB"; then ac_cv_prog_ac_ct_RANLIB="$ac_ct_RANLIB" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_ac_ct_RANLIB="ranlib" $as_echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi ac_ct_RANLIB=$ac_cv_prog_ac_ct_RANLIB if test -n "$ac_ct_RANLIB"; then { $as_echo "$as_me:$LINENO: result: $ac_ct_RANLIB" >&5 $as_echo "$ac_ct_RANLIB" >&6; } else { $as_echo "$as_me:$LINENO: result: no" >&5 $as_echo "no" >&6; } fi if test "x$ac_ct_RANLIB" = x; then RANLIB=":" else case $cross_compiling:$ac_tool_warned in yes:) { $as_echo "$as_me:$LINENO: WARNING: using cross tools not prefixed with host triplet" >&5 $as_echo "$as_me: WARNING: using cross tools not prefixed with host triplet" >&2;} ac_tool_warned=yes ;; esac RANLIB=$ac_ct_RANLIB fi else RANLIB="$ac_cv_prog_RANLIB" fi COPY_FLAGS="-Rfp" case "$canonical_host_type" in *-*-linux*) COPY_FLAGS="-fdp" ;; esac STRIP=${STRIP-strip} # Extract the first word of "$STRIP", so it can be a program name with args. set dummy $STRIP; ac_word=$2 { $as_echo "$as_me:$LINENO: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_STRIP+set}" = set; then $as_echo_n "(cached) " >&6 else if test -n "$STRIP"; then ac_cv_prog_STRIP="$STRIP" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_STRIP="$STRIP" $as_echo "$as_me:$LINENO: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS test -z "$ac_cv_prog_STRIP" && ac_cv_prog_STRIP=":" fi fi STRIP=$ac_cv_prog_STRIP if test -n "$STRIP"; then { $as_echo "$as_me:$LINENO: result: $STRIP" >&5 $as_echo "$STRIP" >&6; } else { $as_echo "$as_me:$LINENO: result: no" >&5 $as_echo "no" >&6; } fi case "$canonical_host_type" in powerpc-apple-darwin*|*-sgi-*) STRIP=: ;; *-cygwin-*|*-mingw-*) MKOCTFILE="$MKOCTFILE -s" ;; esac save_LIBS="$LIBS" { $as_echo "$as_me:$LINENO: checking for gsl_message in -lgsl" >&5 $as_echo_n "checking for gsl_message in -lgsl... " >&6; } if test "${ac_cv_lib_gsl_gsl_message+set}" = set; then $as_echo_n "(cached) " >&6 else ac_check_lib_save_LIBS=$LIBS LIBS="-lgsl -lgslcblas $LIBS" cat >conftest.$ac_ext <<_ACEOF /* confdefs.h. */ _ACEOF cat confdefs.h >>conftest.$ac_ext cat >>conftest.$ac_ext <<_ACEOF /* end confdefs.h. */ /* Override any GCC internal prototype to avoid an error. Use char because int might match the return type of a GCC builtin and then its argument prototype would still apply. */ #ifdef __cplusplus extern "C" #endif char gsl_message (); int main () { return gsl_message (); ; return 0; } _ACEOF rm -f conftest.$ac_objext conftest$ac_exeext if { (ac_try="$ac_link" case "(($ac_try" in *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;; *) ac_try_echo=$ac_try;; esac eval ac_try_echo="\"\$as_me:$LINENO: $ac_try_echo\"" $as_echo "$ac_try_echo") >&5 (eval "$ac_link") 2>conftest.er1 ac_status=$? grep -v '^ *+' conftest.er1 >conftest.err rm -f conftest.er1 cat conftest.err >&5 $as_echo "$as_me:$LINENO: \$? = $ac_status" >&5 (exit $ac_status); } && { test -z "$ac_c_werror_flag" || test ! -s conftest.err } && test -s conftest$ac_exeext && { test "$cross_compiling" = yes || $as_test_x conftest$ac_exeext }; then ac_cv_lib_gsl_gsl_message=yes else $as_echo "$as_me: failed program was:" >&5 sed 's/^/| /' conftest.$ac_ext >&5 ac_cv_lib_gsl_gsl_message=no fi rm -rf conftest.dSYM rm -f core conftest.err conftest.$ac_objext conftest_ipa8_conftest.oo \ conftest$ac_exeext conftest.$ac_ext LIBS=$ac_check_lib_save_LIBS fi { $as_echo "$as_me:$LINENO: result: $ac_cv_lib_gsl_gsl_message" >&5 $as_echo "$ac_cv_lib_gsl_gsl_message" >&6; } if test "x$ac_cv_lib_gsl_gsl_message" = x""yes; then HAVE_GSL=yes else HAVE_GSL=no fi LIBS="$save_LIBS" if test $HAVE_GSL = yes ; then save_LIBS="$LIBS" { $as_echo "$as_me:$LINENO: checking for gsl_sf_hazard in -lgsl" >&5 $as_echo_n "checking for gsl_sf_hazard in -lgsl... " >&6; } if test "${ac_cv_lib_gsl_gsl_sf_hazard+set}" = set; then $as_echo_n "(cached) " >&6 else ac_check_lib_save_LIBS=$LIBS LIBS="-lgsl -lgslcblas $LIBS" cat >conftest.$ac_ext <<_ACEOF /* confdefs.h. */ _ACEOF cat confdefs.h >>conftest.$ac_ext cat >>conftest.$ac_ext <<_ACEOF /* end confdefs.h. */ /* Override any GCC internal prototype to avoid an error. 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Rogers 4/21/2008 // Version 1 Expanded to three argument input and added maintainence hints // { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); // Check number of arguments here if((args.length() != 3 )|| (nargout > 2)) { print_usage (); return octave_value(); } // Check argument types here if(!args(0).is_real_type() || !args(1).is_real_type()|| !args(2).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here // Generate internal variables NDArray x0 = args(0).array_value(); NDArray x1 = args(1).array_value(); NDArray x2 = args(2).array_value(); // // Case one; all inputs the same length A A A if((x0.length() == x1.length() )&& (x0.length()==x2.length())) { dv = x0.dims(); NDArray out(dv); int len = x0.length(); // One output argument if(nargout < 2) { for(i = 0; i < len; i++) { out.xelem(i) = GSL_FUNC_NAME (x0.xelem(i), x1.xelem(i),x2.xelem(i)); } return octave_value(out); // Two arguments } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { GSL_FUNC_NAME_e (x0.xelem(i), x1.xelem(i), x2.xelem(i), &result); out.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(out); return retval; } // // Now we start on having only one array and two scalars, A S S } else if(( x0.length() != 1)&& (x1.length() == 1) && (x2.length()==1)) { dv = x0.dims(); NDArray out(dv); int len = x0.length(); // int x1_int = static_cast(x1.xelem(0)); // int x2_int = static_cast(x2.xelem(0)); double x1_real = x1.xelem(0); double x2_real = x2.xelem(0); // One output argument if(nargout < 2) { for(i = 0; i < len; i++) { out.xelem(i) = GSL_FUNC_NAME (x0.xelem(i),x1_real,x2_real); } return octave_value(out); // Two output argument } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { GSL_FUNC_NAME_e (x0.xelem(i),x1_real,x2_real, &result); out.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(out); return retval; } // S A S input form } else if((x0.length() == 1)&& ( x1.length() != 1) && (x2.length()==1)) { dv = x1.dims(); NDArray out(dv); int len = x1.length(); // int x0_int = static_cast(x0.xelem(0)); // int x2_int = static_cast(x2.xelem(0)); double x0_real = x0.xelem(0); double x2_real = x2.xelem(0); // One output argument if(nargout < 2) { for(i = 0; i < len; i++) { out.xelem(i) = GSL_FUNC_NAME (x0_real,x1.xelem(i),x2_real); } return octave_value(out); // Two output argument } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { GSL_FUNC_NAME_e (x0_real,x1.xelem(i),x2_real, &result); out.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(out); return retval; } // S S A input form } else if((x0.length() == 1)&& ( x1.length() == 1) && ( x2.length()!=1)) { dv = x2.dims(); NDArray out(dv); int len = x2.length(); // int x0_int = static_cast(x0.xelem(0)); // int x1_int = static_cast(x1.xelem(0)); double x0_real = x0.xelem(0); double x1_real = x1.xelem(0); // One output argument if(nargout < 2) { for(i = 0; i < len; i++) { out.xelem(i) = GSL_FUNC_NAME (x0_real,x1_real,x2.xelem(i)); } return octave_value(out); // Two output argument } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { GSL_FUNC_NAME_e (x0_real,x1_real,x2.xelem(i), &result); out.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(out); return retval; } } else { error("First, second, and third argument must either have the same size, or two of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ gsl-1.0.8/src/replace_template.sh0000755000175000017500000000037111201030403014530 0ustar shsh#!/bin/sh sed -e 's/\\/\\\\/g;s/$/\\n\\/g' < docstring.txt > docstring2.txt sed -e "s/GSL_OCTAVE_NAME/$octave_name/g;s/GSL_FUNC_NAME/$funcname/g;/GSL_FUNC_DOCSTRING/r docstring2.txt" -e "/GSL_FUNC_DOCSTRING/d" $1 rm -f docstring.txt docstring2.txt gsl-1.0.8/src/Makeconf.in0000644000175000017500000000310311201030403012732 0ustar shsh ## Makeconf is automatically generated from Makeconf.base and Makeconf.add ## in the various subdirectories. To regenerate, use ./autogen.sh to ## create a new ./Makeconf.in, then use ./configure to generate a new ## Makeconf. OCTAVE_FORGE = 1 SHELL = @SHELL@ canonical_host_type = @canonical_host_type@ prefix = @prefix@ exec_prefix = @exec_prefix@ bindir = @bindir@ mandir = @mandir@ libdir = @libdir@ datadir = @datadir@ infodir = @infodir@ includedir = @includedir@ datarootdir = @datarootdir@ INSTALL = @INSTALL@ INSTALL_PROGRAM = @INSTALL_PROGRAM@ INSTALL_SCRIPT = @INSTALL_SCRIPT@ INSTALL_DATA = @INSTALL_DATA@ INSTALLOCT=octinst.sh DESTDIR = RANLIB = @RANLIB@ STRIP = @STRIP@ LN_S = @LN_S@ AWK = @AWK@ # Most octave programs will be compiled with $(MKOCTFILE). Those which # cannot use mkoctfile directly can request the flags that mkoctfile # would use as follows: # FLAG = $(shell $(MKOCTFILE) -p FLAG) # The following flags are for compiling programs that are independent # of Octave. How confusing. CC = @CC@ CFLAGS = @CFLAGS@ CPPFLAGS = @CPPFLAGS@ CPICFLAG = @CPICFLAG@ CXX = @CXX@ CXXFLAGS = @CXXFLAGS@ CXXPICFLAG = @CXXPICFLAG@ F77 = @F77@ FFLAGS = @FFLAGS@ FPICFLAG = @FPICFLAG@ OCTAVE = @OCTAVE@ OCTAVE_VERSION = @OCTAVE_VERSION@ MKOCTFILE = @MKOCTFILE@ -DHAVE_OCTAVE_$(ver) -v SHLEXT = @SHLEXT@ ver = @ver@ MPATH = @mpath@ OPATH = @opath@ XPATH = @xpath@ ALTMPATH = @altmpath@ ALTOPATH = @altopath@ HAVE_GSL=@HAVE_GSL@ GSL_MISSING=@GSL_MISSING@ %.o: %.c ; $(MKOCTFILE) -c $< %.o: %.f ; $(MKOCTFILE) -c $< %.o: %.cc ; $(MKOCTFILE) -c $< %.oct: %.cc ; $(MKOCTFILE) $< gsl-1.0.8/src/int_int_double_to_double.cc.template0000644000175000017500000000664411201030403020047 0ustar shshDEFUN_DLD(GSL_OCTAVE_NAME, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} GSL_OCTAVE_NAME (@var{n}, @var{m}, @var{x})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} GSL_OCTAVE_NAME (@dots{})\n\ \n\ GSL_FUNC_DOCSTRING \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; dim_vector dv; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 3) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type() || !args(2).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } // Nice combinatorial explosion here NDArray n = args(0).array_value(); NDArray m = args(1).array_value(); if(n.length() != m.length()) { error("Two first arguments must have the same size."); print_usage (); return octave_value(); } NDArray x = args(2).array_value(); if(n.length() == x.length()) { dv = x.dims(); NDArray y(dv); int len = x.length(); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = GSL_FUNC_NAME (static_cast(n.xelem(i)), static_cast(m.xelem(i)), x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { GSL_FUNC_NAME_e (static_cast(n.xelem(i)), static_cast(m.xelem(i)), x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(n.length() == 1) { dv = x.dims(); NDArray y(dv); int len = x.length(); int nint = static_cast(n.xelem(0)); int mint = static_cast(m.xelem(0)); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = GSL_FUNC_NAME (nint, mint, x.xelem(i)); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { GSL_FUNC_NAME_e (nint, mint, x.xelem(i), &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else if(x.length() == 1) { dv = n.dims(); NDArray y(dv); int len = n.length(); double xdouble = x.xelem(0); if(nargout < 2) { for(i = 0; i < len; i++) { y.xelem(i) = GSL_FUNC_NAME (static_cast(n.xelem(i)), static_cast(m.xelem(i)), xdouble); } return octave_value(y); } else { NDArray err(dv); gsl_sf_result result; octave_value_list retval; for(i = 0; i < len; i++) { GSL_FUNC_NAME_e (static_cast(n.xelem(i)), static_cast(m.xelem(i)), xdouble, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } } else { error("The two first and the third argument must either have the same size, or one of them must be scalar."); print_usage (); } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ gsl-1.0.8/src/double_mode_to_double.cc.template0000644000175000017500000000410611201030403017316 0ustar shshDEFUN_DLD(GSL_OCTAVE_NAME, args, nargout, "\ -*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{y} =} GSL_OCTAVE_NAME (@var{x}, @var{mode})\n\ @deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} GSL_OCTAVE_NAME (@dots{})\n\ \n\ GSL_FUNC_DOCSTRING \n\ The second argument @var{mode} must be an integer corresponding to\n\ \n\ @table @asis\n\ @item 0 = GSL_PREC_DOUBLE\n\ Double-precision, a relative accuracy of approximately @code{2 * 10^-16}.\n\ @item 1 = GSL_PREC_SINGLE\n\ Single-precision, a relative accuracy of approximately @code{10^-7}.\n\ @item 2 = GSL_PREC_APPROX\n\ Approximate values, a relative accuracy of approximately @code{5 * 10^-4}.\n\ @end table\n\ \n\ @var{err} contains an estimate of the absolute error in the value @var{y}.\n\ \n\ This function is from the GNU Scientific Library,\n\ see @url{http://www.gnu.org/software/gsl/} for documentation.\n\ @end deftypefn\n\ ") { int i; gsl_set_error_handler (octave_gsl_errorhandler); if(args.length() != 2) { print_usage (); return octave_value(); } if(!args(0).is_real_type() || !args(1).is_real_type()) { error("The arguments must be real."); print_usage (); return octave_value(); } if(!args(1).is_scalar_type()) { error("The mode must be scalar."); print_usage (); return octave_value(); } int mode = static_cast((args(1).array_value())(0)); if(mode < 0) mode = 0; else if(mode > 2) mode = 2; NDArray x = args(0).array_value(); NDArray y(x.dims()); int lx = x.length(); if(nargout < 2) { for(i = 0; i < lx; i++) { y.xelem(i) = GSL_FUNC_NAME (x.xelem(i), mode); } return octave_value(y); } else { NDArray err(x.dims()); gsl_sf_result result; octave_value_list retval; for(i = 0; i < lx; i++) { GSL_FUNC_NAME_e (x.xelem(i), mode, &result); y.xelem(i) = result.val; err.xelem(i) = result.err; } retval(1) = octave_value(err); retval(0) = octave_value(y); return retval; } return octave_value(); } /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */ gsl-1.0.8/INDEX0000644000175000017500000000263111201030403010667 0ustar shshmath >> Mathematics Special functions Chi Ci Shi Si airy_Ai airy_Ai_deriv airy_Ai_deriv_scaled airy_Ai_scaled airy_Bi airy_Bi_deriv airy_Bi_deriv_scaled airy_Bi_scaled airy_zero_Ai airy_zero_Ai_deriv airy_zero_Bi airy_zero_Bi_deriv atanint bessel_In bessel_In_scaled bessel_Inu bessel_Inu_scaled bessel_Jn bessel_Jnu bessel_Kn bessel_Kn_scaled bessel_Knu bessel_Knu_scaled bessel_Yn bessel_Ynu bessel_il_scaled bessel_jl bessel_kl_scaled bessel_lnKnu bessel_yl bessel_zero_J0 bessel_zero_J1 beta_gsl clausen conicalP_0 conicalP_1 conicalP_half conicalP_mhalf coupling_3j coupling_6j coupling_9j dawson debye_1 debye_2 debye_3 debye_4 ellint_Ecomp ellint_Kcomp erf_Q erf_Z erf_gsl erfc_gsl eta eta_int exp_mult expint_3 expint_E1 expint_E2 expint_Ei expm1 exprel exprel_2 exprel_n fermi_dirac_3half fermi_dirac_half fermi_dirac_inc_0 fermi_dirac_int fermi_dirac_mhalf gamma_gsl gamma_inc gamma_inc_P gamma_inc_Q gammainv_gsl gammastar hazard hyperg_0F1 hyperg_1F1 hyperg_U hzeta lambert_W0 lambert_Wm1 legendre_Pl legendre_Plm legendre_Ql legendre_sphPlm legendre_sphPlm_array lnbeta lncosh lngamma_gsl lnpoch lnsinh log_1plusx log_1plusx_mx log_erfc poch pochrel psi psi_1_int psi_1piy psi_n sinc_gsl synchrotron_1 synchrotron_2 taylorcoeff transport_2 transport_3 transport_4 transport_5 zeta zeta_int Support gsl_sf gsl-1.0.8/configure0000755000175000017500000000011311201031723012003 0ustar shsh#! /bin/sh -f if [ -e src/configure ]; then cd src ./configure $* fi gsl-1.0.8/ChangeLog0000644000175000017500000055235011201031723011665 0ustar shsh# Automatically generated file --- DO NOT EDIT 2009-05-04 16:59 hauberg * trunk/octave-forge/extra/NaN/DESCRIPTION, trunk/octave-forge/extra/Windows/DESCRIPTION, trunk/octave-forge/extra/ad/DESCRIPTION, trunk/octave-forge/extra/engine/DESCRIPTION, trunk/octave-forge/extra/integration/DESCRIPTION, trunk/octave-forge/extra/java/DESCRIPTION, trunk/octave-forge/extra/jhandles/DESCRIPTION, trunk/octave-forge/extra/soctcl/DESCRIPTION, trunk/octave-forge/extra/tsa/DESCRIPTION, trunk/octave-forge/main/audio/DESCRIPTION, trunk/octave-forge/main/comm/DESCRIPTION, trunk/octave-forge/main/econometrics/DESCRIPTION, trunk/octave-forge/main/fixed/DESCRIPTION, DESCRIPTION, trunk/octave-forge/main/image/DESCRIPTION, trunk/octave-forge/main/info-theory/DESCRIPTION, trunk/octave-forge/main/linear-algebra/DESCRIPTION, trunk/octave-forge/main/miscellaneous/DESCRIPTION, trunk/octave-forge/main/optiminterp/DESCRIPTION, trunk/octave-forge/main/signal/DESCRIPTION, trunk/octave-forge/main/specfun/DESCRIPTION, trunk/octave-forge/main/statistics/DESCRIPTION, trunk/octave-forge/main/strings/DESCRIPTION, trunk/octave-forge/main/struct/DESCRIPTION, trunk/octave-forge/main/symbolic/DESCRIPTION, trunk/octave-forge/main/time/DESCRIPTION, trunk/octave-forge/main/video/DESCRIPTION, trunk/octave-forge/nonfree/arpack/DESCRIPTION, trunk/octave-forge/nonfree/spline-gsvspl/DESCRIPTION: Update version number 2008-12-09 19:58 thomas-weber * inst/test_hyperg.m: Remove svn:executable property from test_hyperg.m 2008-06-20 21:10 rrogers * doc, doc/.cc, doc/.doc, doc/.dvi, doc/.log, doc/.ps, doc/.texi, doc/DOSCSTRINGS.old, doc/RCS, doc/RCS/#mktexi#,v, doc/RCS/DOSCSTRINGS.old,v, doc/RCS/README,v, doc/RCS/README~,v, doc/RCS/gsl.cc,v, doc/RCS/gsl.doc,v, doc/RCS/gsl.dvi,v, doc/RCS/gsl.info,v, doc/RCS/gsl.log,v, doc/RCS/gsl.pdf,v, doc/RCS/gsl.ps,v, doc/RCS/gsl.texi,v, doc/RCS/make.lst,v, doc/RCS/make_index,v, doc/RCS/mk.tgz,v, doc/RCS/mk_pdf_dvi,v, doc/RCS/mk_pdf_dvi~,v, doc/RCS/mkdoc,v, doc/RCS/mktexi,v, doc/RCS/mktexi_inc,v, doc/RCS/mktexi_inc~,v, doc/RCS/mktexi~,v, doc/RCS/texinfo.tex,v, doc/RCS/texinfo.tex.max,v, doc/RCS/texput.log,v, doc/RCS/txt2latex,v, doc/README, doc/gsl_sf.cc, doc/gsl_sf.doc, doc/gsl_sf.dvi, doc/gsl_sf.log, doc/gsl_sf.pdf, doc/gsl_sf.ps, doc/gsl_sf.texi, doc/gsl_sf_a.ps, doc/make.lst, doc/mk.tgz, doc/mk_pdf_dvi, doc/mkdoc, doc/mktexi, doc/mktexi_inc, doc/texinfo.tex, doc/texinfo.tex.max, doc/txt2latex, inst, inst/test_ellint.m, inst/test_hyperg.m, inst/test_hyperg_corr.c, inst/test_sf.c, svn-commit.tmp: 2008-06-20 21:07 rrogers * DESCRIPTION, Makefile, src/DDD_to_D.cc.template, src/buildgsl_sf.sh, src/legendre_sphPlm_array.cc: 2008-04-29 18:02 hauberg * src/Makeconf: remove autogenerated file from SVN 2008-04-29 18:00 hauberg * src/Makeconf, src/gsl_sf.cc: remove autogenerated file from SVN 2008-04-29 17:48 hauberg * RCS, src/#buildgsl_sf.sh.old#, src/RCS, src/autom4te.cache, src/buildgsl_sf.sh.old, src/config.log, src/config.status, src/configure: Remove autogenerated files from SVN 2008-04-29 15:45 rrogers * RCS, RCS/PKG_ADD,v: Version 1.0.6 R.Rogers Add hyperg_1F1, hyperg_U (KummerM, KummerU) and DDD_to_D template 2008-04-29 15:20 rrogers * src/#buildgsl_sf.sh.old#, src/DDD_to_D.cc.template, src/Makeconf, src/RCS, src/RCS/buildgsl_sf.sh,v, src/autom4te.cache, src/autom4te.cache/output.0, src/autom4te.cache/requests, src/autom4te.cache/traces.0, src/buildgsl_sf.sh.old, src/config.log, src/config.status, src/configure, src/test, src/test/check.m, src/test/test_hyperg.c, src/test/test_hyperg_cor.c: Added hyperg_1F1, hyperg_U (KummerM,KummerU) only double inputs 2008-04-29 15:13 rrogers * DESCRIPTION, INDEX, PKG_ADD, src/buildgsl_sf.sh, src/gsl_sf.cc: 1.0.6 Added hyperg_1F1, hyperg_U (KummerM, KummerU). It only handles doubles for input. 2008-04-06 23:36 adb014 * trunk/octave-forge/extra/NaN/DESCRIPTION, trunk/octave-forge/extra/Windows/DESCRIPTION, trunk/octave-forge/extra/ad/DESCRIPTION, trunk/octave-forge/extra/bim/DESCRIPTION, trunk/octave-forge/extra/civil/DESCRIPTION, trunk/octave-forge/extra/engine/DESCRIPTION, trunk/octave-forge/extra/fpl/DESCRIPTION, trunk/octave-forge/extra/graceplot/DESCRIPTION, trunk/octave-forge/extra/integration/DESCRIPTION, trunk/octave-forge/extra/java/DESCRIPTION, trunk/octave-forge/extra/jhandles/DESCRIPTION, trunk/octave-forge/extra/mapping/DESCRIPTION, trunk/octave-forge/extra/msh/DESCRIPTION, trunk/octave-forge/extra/multicore/DESCRIPTION, trunk/octave-forge/extra/pdb/DESCRIPTION, trunk/octave-forge/extra/secs1d/DESCRIPTION, trunk/octave-forge/extra/secs2d/DESCRIPTION, trunk/octave-forge/extra/soctcl/DESCRIPTION, trunk/octave-forge/extra/symband/DESCRIPTION, trunk/octave-forge/extra/triangular/DESCRIPTION, trunk/octave-forge/extra/tsa/DESCRIPTION, 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trunk/octave-forge/main/outliers/DESCRIPTION, trunk/octave-forge/main/parallel/DESCRIPTION, trunk/octave-forge/main/physical-constants/DESCRIPTION, trunk/octave-forge/main/plot/DESCRIPTION, trunk/octave-forge/main/signal/DESCRIPTION, trunk/octave-forge/main/statistics/DESCRIPTION, trunk/octave-forge/main/strings/DESCRIPTION, trunk/octave-forge/main/struct/DESCRIPTION, trunk/octave-forge/main/symbolic/DESCRIPTION, trunk/octave-forge/main/time/DESCRIPTION, trunk/octave-forge/main/vrml/DESCRIPTION, trunk/octave-forge/main/zenity/DESCRIPTION, trunk/octave-forge/nonfree/arpack/DESCRIPTION, trunk/octave-forge/nonfree/spline-gsvspl/DESCRIPTION: Update version numbers, release dates, and news in preparation for release 2008-03-03 11:04 cdf * trunk/octave-forge/extra/msh/inst/MSH2Mjigglemesh.m, src/gsl_sf.cc, trunk/octave-forge/main/splines/INDEX: Catmull-Rom spline inerpolation 2008-02-04 13:47 adb014 * trunk/octave-forge/COPYING.GPL, 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trunk/octave-forge/nonfree/gpc/src/gpc_get.cc, trunk/octave-forge/nonfree/gpc/src/gpc_is_polygon.cc, trunk/octave-forge/nonfree/gpc/src/gpc_read.cc, trunk/octave-forge/nonfree/gpc/src/gpc_tristrip.cc, trunk/octave-forge/nonfree/gpc/src/gpc_write.cc, trunk/octave-forge/nonfree/gpc/src/octave-gpc.cc, trunk/octave-forge/nonfree/gpc/src/octave-gpc.h, trunk/octave-forge/texinfo.tex: More copyright updates 2008-01-31 19:44 hauberg * trunk/octave-forge/main/audio/DESCRIPTION, trunk/octave-forge/main/combinatorics/DESCRIPTION, trunk/octave-forge/main/comm/DESCRIPTION, trunk/octave-forge/main/control/DESCRIPTION, trunk/octave-forge/main/econometrics/DESCRIPTION, trunk/octave-forge/main/fixed/DESCRIPTION, trunk/octave-forge/main/general/DESCRIPTION, DESCRIPTION, trunk/octave-forge/main/ident/DESCRIPTION, trunk/octave-forge/main/image/DESCRIPTION, trunk/octave-forge/main/image/INDEX, trunk/octave-forge/main/info-theory/DESCRIPTION, trunk/octave-forge/main/io/DESCRIPTION, trunk/octave-forge/main/irsa/DESCRIPTION, trunk/octave-forge/main/linear-algebra/DESCRIPTION, trunk/octave-forge/main/miscellaneous/DESCRIPTION, trunk/octave-forge/main/miscellaneous/inst/inz.m, trunk/octave-forge/main/nnet/DESCRIPTION, trunk/octave-forge/main/octcdf/DESCRIPTION, trunk/octave-forge/main/odebvp/DESCRIPTION, trunk/octave-forge/main/odepkg/DESCRIPTION, trunk/octave-forge/main/optim/DESCRIPTION, trunk/octave-forge/main/optiminterp/DESCRIPTION, trunk/octave-forge/main/outliers/DESCRIPTION, trunk/octave-forge/main/parallel/DESCRIPTION, trunk/octave-forge/main/physical-constants/DESCRIPTION, trunk/octave-forge/main/plot/DESCRIPTION, trunk/octave-forge/main/signal/DESCRIPTION, trunk/octave-forge/main/signal/INDEX, trunk/octave-forge/main/sockets/DESCRIPTION, trunk/octave-forge/main/specfun/DESCRIPTION, trunk/octave-forge/main/special-matrix/DESCRIPTION, trunk/octave-forge/main/splines/DESCRIPTION, trunk/octave-forge/main/statistics/DESCRIPTION, trunk/octave-forge/main/statistics/INDEX, trunk/octave-forge/main/statistics/inst/nanvar.m, trunk/octave-forge/main/strings/DESCRIPTION, trunk/octave-forge/main/struct/DESCRIPTION, trunk/octave-forge/main/symbolic/DESCRIPTION, trunk/octave-forge/main/time/DESCRIPTION, trunk/octave-forge/main/vrml/DESCRIPTION, trunk/octave-forge/main/zenity/DESCRIPTION: Update version numbers 2008-01-29 21:05 hauberg * trunk/octave-forge/extra/MacOSX/src/autogen.sh, trunk/octave-forge/extra/Windows/src/autogen.sh, trunk/octave-forge/extra/ad/src/autogen.sh, trunk/octave-forge/extra/engine/src/autogen.sh, trunk/octave-forge/extra/java/src/autogen.sh, trunk/octave-forge/extra/jhandles/src/autogen.sh, trunk/octave-forge/extra/tk_octave/src/autogen.sh, trunk/octave-forge/main/audio/src/autogen.sh, trunk/octave-forge/main/comm/src/autogen.sh, trunk/octave-forge/main/fixed/src/autogen.sh, src/autogen.sh, trunk/octave-forge/main/image/src/autogen.sh, trunk/octave-forge/main/linear-algebra/src/autogen.sh, trunk/octave-forge/main/miscellaneous/src/autogen.sh, trunk/octave-forge/main/octcdf/src/autogen.sh, trunk/octave-forge/main/odepkg/src/autogen.sh, trunk/octave-forge/main/optiminterp/src/autogen.sh, trunk/octave-forge/main/plot/src/autogen.sh, trunk/octave-forge/main/strings/src/autogen.sh, trunk/octave-forge/main/symbolic/src/autogen.sh, trunk/octave-forge/nonfree/arpack/src/autogen.sh, trunk/octave-forge/nonfree/gpc/src/autogen.sh, trunk/octave-forge/nonfree/splines/src/autogen.sh: Remove bashism from autogen.sh files 2007-12-17 12:33 adb014 * trunk/octave-forge/doc/htdocs/NEWS.in, trunk/octave-forge/doc/htdocs/index.in, trunk/octave-forge/doc/htdocs/packages.in, trunk/octave-forge/extra/MacOSX/src/Makeconf.in, trunk/octave-forge/extra/Windows/src/Makeconf.in, trunk/octave-forge/extra/engine/src/Makeconf.in, trunk/octave-forge/extra/java/src/Makeconf.in, trunk/octave-forge/extra/jhandles/src/Makeconf.in, trunk/octave-forge/extra/tk_octave/src/Makeconf.in, trunk/octave-forge/main/audio/src/Makeconf.in, trunk/octave-forge/main/comm/src/Makeconf.in, trunk/octave-forge/main/fixed/src/Makeconf.in, src/Makeconf.in, trunk/octave-forge/main/image/src/Makeconf.in, trunk/octave-forge/main/linear-algebra/src/Makeconf.in, trunk/octave-forge/main/miscellaneous/src/Makeconf.in, trunk/octave-forge/main/octcdf/src/Makeconf.in, trunk/octave-forge/main/odepkg/src/Makeconf.in, trunk/octave-forge/main/optiminterp/src/Makeconf.in, trunk/octave-forge/main/plot/src/Makeconf.in, trunk/octave-forge/main/strings/src/Makeconf.in, trunk/octave-forge/main/symbolic/src/Makeconf.in, trunk/octave-forge/nonfree/arpack/src/Makeconf.in, trunk/octave-forge/nonfree/splines/src/Makeconf.in: Get rid of spurious warnings about --datarootdir. Small doc update 2007-12-05 16:24 adb014 * trunk/octave-forge/extra/MacOSX/DESCRIPTION, trunk/octave-forge/extra/NaN/DESCRIPTION, trunk/octave-forge/extra/Windows/DESCRIPTION, trunk/octave-forge/extra/bim/DESCRIPTION, trunk/octave-forge/extra/civil/DESCRIPTION, trunk/octave-forge/extra/engine/DESCRIPTION, trunk/octave-forge/extra/fpl/DESCRIPTION, trunk/octave-forge/extra/graceplot/DESCRIPTION, trunk/octave-forge/extra/integration/DESCRIPTION, trunk/octave-forge/extra/java/DESCRIPTION, trunk/octave-forge/extra/jhandles/DESCRIPTION, trunk/octave-forge/extra/mapping/DESCRIPTION, trunk/octave-forge/extra/msh/DESCRIPTION, trunk/octave-forge/extra/pdb/DESCRIPTION, trunk/octave-forge/extra/secs1d/DESCRIPTION, trunk/octave-forge/extra/secs2d/DESCRIPTION, trunk/octave-forge/extra/soctcl/DESCRIPTION, trunk/octave-forge/extra/symband/DESCRIPTION, trunk/octave-forge/extra/triangular/DESCRIPTION, trunk/octave-forge/extra/tsa/DESCRIPTION, trunk/octave-forge/extra/xraylib/DESCRIPTION, trunk/octave-forge/language/pt_BR/DESCRIPTION, trunk/octave-forge/main/audio/DESCRIPTION, trunk/octave-forge/main/combinatorics/DESCRIPTION, trunk/octave-forge/main/comm/DESCRIPTION, trunk/octave-forge/main/control/DESCRIPTION, trunk/octave-forge/main/econometrics/DESCRIPTION, trunk/octave-forge/main/fixed/DESCRIPTION, trunk/octave-forge/main/fixed/doc/configure.add, trunk/octave-forge/main/fixed/src/configure.base, trunk/octave-forge/main/general/DESCRIPTION, DESCRIPTION, trunk/octave-forge/main/ident/DESCRIPTION, trunk/octave-forge/main/image/DESCRIPTION, trunk/octave-forge/main/info-theory/DESCRIPTION, trunk/octave-forge/main/io/DESCRIPTION, trunk/octave-forge/main/irsa/DESCRIPTION, trunk/octave-forge/main/linear-algebra/DESCRIPTION, trunk/octave-forge/main/nnet/DESCRIPTION, trunk/octave-forge/main/odebvp/DESCRIPTION, trunk/octave-forge/main/optiminterp/DESCRIPTION, trunk/octave-forge/main/outliers/DESCRIPTION, trunk/octave-forge/main/parallel/DESCRIPTION, trunk/octave-forge/main/physical-constants/DESCRIPTION, trunk/octave-forge/main/plot/DESCRIPTION, trunk/octave-forge/main/signal/DESCRIPTION, trunk/octave-forge/main/specfun/DESCRIPTION, trunk/octave-forge/main/special-matrix/DESCRIPTION, trunk/octave-forge/main/splines/DESCRIPTION, trunk/octave-forge/main/statistics/DESCRIPTION, trunk/octave-forge/main/strings/DESCRIPTION, trunk/octave-forge/main/struct/DESCRIPTION, trunk/octave-forge/main/symbolic/DESCRIPTION, trunk/octave-forge/main/time/DESCRIPTION, trunk/octave-forge/main/vrml/DESCRIPTION, trunk/octave-forge/main/zenity/DESCRIPTION, trunk/octave-forge/nonfree/arpack/DESCRIPTION, trunk/octave-forge/nonfree/splines/DESCRIPTION: Update the version numbers. All packages need new version numbers due to package differences in the CVS to SVN transition 2007-10-22 23:26 adb014 * trunk/octave-forge/.cvsignore, trunk/octave-forge/.svnignore, trunk/octave-forge/admin/Windows/.cvsignore, trunk/octave-forge/admin/Windows/.svnignore, trunk/octave-forge/admin/Windows/msvc/.cvsignore, trunk/octave-forge/admin/Windows/msvc/.svnignore, trunk/octave-forge/doc/.cvsignore, trunk/octave-forge/doc/.svnignore, trunk/octave-forge/doc/coda/.cvsignore, trunk/octave-forge/doc/coda/.svnignore, trunk/octave-forge/doc/coda/out/.cvsignore, trunk/octave-forge/doc/coda/out/.svnignore, trunk/octave-forge/doc/htdocs/.cvsignore, trunk/octave-forge/doc/htdocs/.svnignore, trunk/octave-forge/extra/MacOSX/doc/.cvsignore, trunk/octave-forge/extra/MacOSX/doc/.svnignore, trunk/octave-forge/extra/MacOSX/src/.cvsignore, trunk/octave-forge/extra/MacOSX/src/.svnignore, trunk/octave-forge/extra/Windows/src/.cvsignore, trunk/octave-forge/extra/Windows/src/.svnignore, trunk/octave-forge/extra/engine/src/.cvsignore, trunk/octave-forge/extra/engine/src/.svnignore, trunk/octave-forge/extra/graceplot/inst/.cvsignore, trunk/octave-forge/extra/graceplot/inst/.svnignore, trunk/octave-forge/extra/java/src/.cvsignore, trunk/octave-forge/extra/java/src/.svnignore, trunk/octave-forge/extra/java/src/org/octave/.cvsignore, trunk/octave-forge/extra/java/src/org/octave/.svnignore, trunk/octave-forge/extra/jhandles/src/.cvsignore, trunk/octave-forge/extra/jhandles/src/.svnignore, trunk/octave-forge/extra/jhandles/src/org/octave/graphics/.cvsignore, trunk/octave-forge/extra/jhandles/src/org/octave/graphics/.svnignore, trunk/octave-forge/extra/symband/doc/.cvsignore, trunk/octave-forge/extra/symband/doc/.svnignore, trunk/octave-forge/extra/triangular/doc/.cvsignore, trunk/octave-forge/extra/triangular/doc/.svnignore, trunk/octave-forge/main/audio/src/.cvsignore, trunk/octave-forge/main/audio/src/.svnignore, trunk/octave-forge/main/comm/doc/.cvsignore, trunk/octave-forge/main/comm/doc/.svnignore, trunk/octave-forge/main/comm/inst/.cvsignore, trunk/octave-forge/main/comm/inst/.svnignore, trunk/octave-forge/main/comm/src/.cvsignore, trunk/octave-forge/main/comm/src/.svnignore, trunk/octave-forge/main/fixed/doc/.cvsignore, trunk/octave-forge/main/fixed/doc/.svnignore, trunk/octave-forge/main/fixed/examples/.cvsignore, trunk/octave-forge/main/fixed/examples/.svnignore, trunk/octave-forge/main/fixed/inst/.cvsignore, trunk/octave-forge/main/fixed/inst/.svnignore, trunk/octave-forge/main/fixed/src/.cvsignore, trunk/octave-forge/main/fixed/src/.svnignore, trunk/octave-forge/main/general/inst/.cvsignore, trunk/octave-forge/main/general/inst/.svnignore, trunk/octave-forge/main/general/src/.cvsignore, trunk/octave-forge/main/general/src/.svnignore, src/.cvsignore, src/.svnignore, trunk/octave-forge/main/image/inst/.cvsignore, trunk/octave-forge/main/image/inst/.svnignore, trunk/octave-forge/main/image/src/.cvsignore, trunk/octave-forge/main/image/src/.svnignore, trunk/octave-forge/main/io/.cvsignore, trunk/octave-forge/main/io/.svnignore, trunk/octave-forge/main/io/inst/.cvsignore, trunk/octave-forge/main/io/inst/.svnignore, trunk/octave-forge/main/io/src/.cvsignore, trunk/octave-forge/main/io/src/.svnignore, trunk/octave-forge/main/linear-algebra/inst/.cvsignore, trunk/octave-forge/main/linear-algebra/inst/.svnignore, trunk/octave-forge/main/linear-algebra/src/.cvsignore, trunk/octave-forge/main/linear-algebra/src/.svnignore, trunk/octave-forge/main/miscellaneous/inst/.cvsignore, trunk/octave-forge/main/miscellaneous/inst/.svnignore, trunk/octave-forge/main/miscellaneous/src/.cvsignore, trunk/octave-forge/main/miscellaneous/src/.svnignore, trunk/octave-forge/main/octcdf/inst/.cvsignore, trunk/octave-forge/main/octcdf/inst/.svnignore, trunk/octave-forge/main/octcdf/src/.cvsignore, trunk/octave-forge/main/octcdf/src/.svnignore, trunk/octave-forge/main/odepkg/doc/.cvsignore, trunk/octave-forge/main/odepkg/doc/.svnignore, trunk/octave-forge/main/odepkg/inst/.cvsignore, trunk/octave-forge/main/odepkg/inst/.svnignore, trunk/octave-forge/main/odepkg/src/.cvsignore, trunk/octave-forge/main/odepkg/src/.svnignore, trunk/octave-forge/main/optim/doc/.cvsignore, trunk/octave-forge/main/optim/doc/.svnignore, trunk/octave-forge/main/optim/inst/.cvsignore, trunk/octave-forge/main/optim/inst/.svnignore, trunk/octave-forge/main/optim/src/.cvsignore, trunk/octave-forge/main/optim/src/.svnignore, trunk/octave-forge/main/optiminterp/inst/.cvsignore, trunk/octave-forge/main/optiminterp/inst/.svnignore, trunk/octave-forge/main/optiminterp/src/.cvsignore, trunk/octave-forge/main/optiminterp/src/.svnignore, trunk/octave-forge/main/plot/inst/.cvsignore, trunk/octave-forge/main/plot/inst/.svnignore, trunk/octave-forge/main/plot/src/.cvsignore, trunk/octave-forge/main/plot/src/.svnignore, trunk/octave-forge/main/signal/inst/.cvsignore, trunk/octave-forge/main/signal/inst/.svnignore, trunk/octave-forge/main/signal/src/.cvsignore, trunk/octave-forge/main/signal/src/.svnignore, trunk/octave-forge/main/specfun/inst/.cvsignore, trunk/octave-forge/main/specfun/inst/.svnignore, trunk/octave-forge/main/specfun/src/.cvsignore, trunk/octave-forge/main/specfun/src/.svnignore, trunk/octave-forge/main/splines/inst/.cvsignore, trunk/octave-forge/main/splines/inst/.svnignore, trunk/octave-forge/main/strings/inst/.cvsignore, trunk/octave-forge/main/strings/inst/.svnignore, trunk/octave-forge/main/strings/src/.cvsignore, trunk/octave-forge/main/strings/src/.svnignore, trunk/octave-forge/main/struct/.cvsignore, trunk/octave-forge/main/struct/.svnignore, trunk/octave-forge/main/struct/inst/.cvsignore, trunk/octave-forge/main/struct/inst/.svnignore, trunk/octave-forge/main/symbolic/inst/.cvsignore, trunk/octave-forge/main/symbolic/inst/.svnignore, trunk/octave-forge/main/symbolic/src/.cvsignore, trunk/octave-forge/main/symbolic/src/.svnignore, trunk/octave-forge/main/vrml/doc/.cvsignore, trunk/octave-forge/main/vrml/doc/.svnignore, trunk/octave-forge/nonfree/arpack/src/.cvsignore, trunk/octave-forge/nonfree/arpack/src/.svnignore, trunk/octave-forge/nonfree/gpc/src/.cvsignore, trunk/octave-forge/nonfree/gpc/src/.svnignore, trunk/octave-forge/nonfree/splines/src/.cvsignore, trunk/octave-forge/nonfree/splines/src/.svnignore, trunk/octave-forge/packages/.cvsignore, trunk/octave-forge/packages/.svnignore: Move the cvsignore files to svnignore 2007-09-24 23:38 adb014 * trunk/octave-forge/extra/MacOSX/DESCRIPTION, trunk/octave-forge/extra/Windows/DESCRIPTION, trunk/octave-forge/extra/civil/DESCRIPTION, trunk/octave-forge/extra/engine/DESCRIPTION, trunk/octave-forge/extra/fpl/DESCRIPTION, trunk/octave-forge/extra/graceplot/DESCRIPTION, trunk/octave-forge/extra/integration/DESCRIPTION, trunk/octave-forge/extra/mapping/DESCRIPTION, trunk/octave-forge/extra/msh/DESCRIPTION, trunk/octave-forge/extra/pdb/DESCRIPTION, trunk/octave-forge/extra/secs1d/DESCRIPTION, trunk/octave-forge/extra/secs2d/DESCRIPTION, trunk/octave-forge/extra/soctcl/DESCRIPTION, trunk/octave-forge/extra/symband/DESCRIPTION, trunk/octave-forge/extra/triangular/DESCRIPTION, trunk/octave-forge/extra/xraylib/DESCRIPTION, trunk/octave-forge/language/pt_BR/DESCRIPTION, trunk/octave-forge/main/audio/DESCRIPTION, trunk/octave-forge/main/combinatorics/DESCRIPTION, trunk/octave-forge/main/comm/DESCRIPTION, trunk/octave-forge/main/control/DESCRIPTION, trunk/octave-forge/main/econometrics/DESCRIPTION, trunk/octave-forge/main/fixed/DESCRIPTION, trunk/octave-forge/main/fixed/src/configure.base, trunk/octave-forge/main/general/DESCRIPTION, DESCRIPTION, trunk/octave-forge/main/ident/DESCRIPTION, trunk/octave-forge/main/image/DESCRIPTION, trunk/octave-forge/main/info-theory/DESCRIPTION, trunk/octave-forge/main/io/DESCRIPTION, trunk/octave-forge/main/irsa/DESCRIPTION, trunk/octave-forge/main/miscellaneous/DESCRIPTION, trunk/octave-forge/main/nnet/DESCRIPTION, trunk/octave-forge/main/outliers/DESCRIPTION, trunk/octave-forge/main/parallel/DESCRIPTION, trunk/octave-forge/main/physical-constants/DESCRIPTION, trunk/octave-forge/main/sockets/DESCRIPTION, trunk/octave-forge/main/specfun/DESCRIPTION, trunk/octave-forge/main/special-matrix/DESCRIPTION, trunk/octave-forge/main/splines/DESCRIPTION, trunk/octave-forge/main/strings/DESCRIPTION, trunk/octave-forge/main/struct/DESCRIPTION, trunk/octave-forge/main/symbolic/DESCRIPTION, trunk/octave-forge/main/time/DESCRIPTION, trunk/octave-forge/main/vrml/DESCRIPTION, trunk/octave-forge/main/zenity/DESCRIPTION, trunk/octave-forge/nonfree/splines/DESCRIPTION: Update version numbers for modified packages 2007-09-24 15:15 opoplawski * trunk/octave-forge/Makefile, trunk/octave-forge/doc/Makefile, trunk/octave-forge/extra/MacOSX/Makefile, trunk/octave-forge/extra/secs1d/src/Makefile, trunk/octave-forge/extra/secs2d/src/Makefile, trunk/octave-forge/extra/symband/Makefile, trunk/octave-forge/extra/triangular/Makefile, trunk/octave-forge/extra/xraylib/src/Makefile, trunk/octave-forge/main/comm/Makefile, trunk/octave-forge/main/fixed/Makefile, Makefile, trunk/octave-forge/main/octcdf/Makefile, trunk/octave-forge/main/odepkg/Makefile, trunk/octave-forge/main/optim/Makefile, trunk/octave-forge/main/vrml/Makefile, trunk/octave-forge/packages/package_Makefile.in: Call make with $(MAKE) instead of make 2007-07-24 20:04 adb014 * trunk/octave-forge/extra/NaN/DESCRIPTION, trunk/octave-forge/extra/Windows/DESCRIPTION, trunk/octave-forge/extra/civil/DESCRIPTION, trunk/octave-forge/extra/engine/DESCRIPTION, trunk/octave-forge/extra/graceplot/DESCRIPTION, trunk/octave-forge/extra/integration/DESCRIPTION, trunk/octave-forge/extra/mapping/DESCRIPTION, trunk/octave-forge/extra/pdb/DESCRIPTION, trunk/octave-forge/extra/secs1d/DESCRIPTION, trunk/octave-forge/extra/soctcl/DESCRIPTION, trunk/octave-forge/extra/tsa/DESCRIPTION, trunk/octave-forge/extra/xraylib/DESCRIPTION, trunk/octave-forge/main/audio/DESCRIPTION, trunk/octave-forge/main/combinatorics/DESCRIPTION, trunk/octave-forge/main/control/DESCRIPTION, trunk/octave-forge/main/general/DESCRIPTION, DESCRIPTION, trunk/octave-forge/main/ident/DESCRIPTION, trunk/octave-forge/main/info-theory/DESCRIPTION, trunk/octave-forge/main/io/DESCRIPTION, trunk/octave-forge/main/irsa/DESCRIPTION, trunk/octave-forge/main/linear-algebra/DESCRIPTION, trunk/octave-forge/main/miscellaneous/DESCRIPTION, trunk/octave-forge/main/octcdf/DESCRIPTION, trunk/octave-forge/main/outliers/DESCRIPTION, trunk/octave-forge/main/parallel/DESCRIPTION, trunk/octave-forge/main/physical-constants/DESCRIPTION, trunk/octave-forge/main/plot/DESCRIPTION, trunk/octave-forge/main/polynomial/DESCRIPTION, trunk/octave-forge/main/sockets/DESCRIPTION, trunk/octave-forge/main/specfun/DESCRIPTION, trunk/octave-forge/main/special-matrix/DESCRIPTION, trunk/octave-forge/main/splines/DESCRIPTION, trunk/octave-forge/main/strings/DESCRIPTION, trunk/octave-forge/main/struct/DESCRIPTION, trunk/octave-forge/main/symbolic/DESCRIPTION, trunk/octave-forge/main/time/DESCRIPTION, trunk/octave-forge/main/zenity/DESCRIPTION, trunk/octave-forge/nonfree/splines/DESCRIPTION: Version numbering changes of all packages needed due to inclusion of generic Makefile/configure in all packages 2007-03-28 18:54 adb014 * trunk/octave-forge/Makefile, trunk/octave-forge/TODO, trunk/octave-forge/main/geometry/DESCRIPTION, DESCRIPTION, trunk/octave-forge/main/image/DESCRIPTION, trunk/octave-forge/main/miscellaneous/DESCRIPTION, trunk/octave-forge/main/plot/DESCRIPTION, trunk/octave-forge/main/strings/DESCRIPTION, trunk/octave-forge/main/symbolic/DESCRIPTION: Update for the external dependencies 2007-03-23 16:14 adb014 * trunk/octave-forge/admin/Windows/msvc/ar-msvc, trunk/octave-forge/admin/Windows/msvc/build_atlas_dll, trunk/octave-forge/admin/Windows/msvc/cc-msvc.cc, trunk/octave-forge/admin/Windows/msvc/ranlib-msvc, trunk/octave-forge/admin/make_index, trunk/octave-forge/admin/template.ndev, trunk/octave-forge/doc/coda/appendices/examples.sgml, trunk/octave-forge/doc/coda/appendices/gnufdl.sgml, trunk/octave-forge/doc/coda/appendices/gnugpl.sgml, trunk/octave-forge/doc/coda/coda.sgml, trunk/octave-forge/doc/coda/oct/advanced.sgml, trunk/octave-forge/doc/coda/oct/oct.sgml, trunk/octave-forge/doc/coda/oct/quickref.sgml, trunk/octave-forge/doc/coda/oct/tut-basic.sgml, trunk/octave-forge/doc/coda/oct/tut-interm.sgml, trunk/octave-forge/doc/coda/oct/tut-intro.sgml, trunk/octave-forge/doc/coda/oct/tutorial.sgml, trunk/octave-forge/doc/coda/standalone/standalone.sgml, trunk/octave-forge/extra/MacOSX/src/image.m.in, trunk/octave-forge/extra/NaN/doc/README.TXT, trunk/octave-forge/extra/NaN/inst/center.m, trunk/octave-forge/extra/NaN/inst/coefficient_of_variation.m, trunk/octave-forge/extra/NaN/inst/conv2nan.m, trunk/octave-forge/extra/NaN/inst/cor.m, trunk/octave-forge/extra/NaN/inst/corrcoef.m, trunk/octave-forge/extra/NaN/inst/cov.m, trunk/octave-forge/extra/NaN/inst/covm.m, trunk/octave-forge/extra/NaN/inst/detrend.m, trunk/octave-forge/extra/NaN/inst/flag_implicit_significance.m, trunk/octave-forge/extra/NaN/inst/geomean.m, trunk/octave-forge/extra/NaN/inst/harmmean.m, trunk/octave-forge/extra/NaN/inst/kurtosis.m, trunk/octave-forge/extra/NaN/inst/mad.m, trunk/octave-forge/extra/NaN/inst/mean.m, trunk/octave-forge/extra/NaN/inst/meandev.m, trunk/octave-forge/extra/NaN/inst/meansq.m, trunk/octave-forge/extra/NaN/inst/median.m, trunk/octave-forge/extra/NaN/inst/mod.m, trunk/octave-forge/extra/NaN/inst/moment.m, trunk/octave-forge/extra/NaN/inst/naninsttest.m, trunk/octave-forge/extra/NaN/inst/nanstd.m, trunk/octave-forge/extra/NaN/inst/nansum.m, trunk/octave-forge/extra/NaN/inst/nantest.m, trunk/octave-forge/extra/NaN/inst/normcdf.m, trunk/octave-forge/extra/NaN/inst/norminv.m, trunk/octave-forge/extra/NaN/inst/normpdf.m, trunk/octave-forge/extra/NaN/inst/rankcorr.m, trunk/octave-forge/extra/NaN/inst/ranks.m, trunk/octave-forge/extra/NaN/inst/rem.m, trunk/octave-forge/extra/NaN/inst/rms.m, trunk/octave-forge/extra/NaN/inst/sem.m, trunk/octave-forge/extra/NaN/inst/skewness.m, trunk/octave-forge/extra/NaN/inst/spearman.m, trunk/octave-forge/extra/NaN/inst/statistic.m, trunk/octave-forge/extra/NaN/inst/std.m, trunk/octave-forge/extra/NaN/inst/sumskipnan.m, trunk/octave-forge/extra/NaN/inst/tcdf.m, trunk/octave-forge/extra/NaN/inst/tinv.m, trunk/octave-forge/extra/NaN/inst/tpdf.m, trunk/octave-forge/extra/NaN/inst/trimean.m, trunk/octave-forge/extra/NaN/inst/var.m, trunk/octave-forge/extra/NaN/inst/xcovf.m, trunk/octave-forge/extra/NaN/inst/zscore.m, trunk/octave-forge/extra/NaN/src/sumskipnan.cc, trunk/octave-forge/extra/NaN/src/sumskipnan.cpp, trunk/octave-forge/extra/Windows/examples/mat2xls.m, trunk/octave-forge/extra/Windows/src/__COM__.cc, trunk/octave-forge/extra/Windows/src/image.m.in, trunk/octave-forge/extra/civil/inst/__nlnewmark_fcn__.m, trunk/octave-forge/extra/civil/inst/newmark.m, trunk/octave-forge/extra/civil/inst/nlnewmark.m, trunk/octave-forge/extra/graceplot/inst/alternatives/__errcomm__.m, trunk/octave-forge/extra/graceplot/inst/alternatives/__errplot__.m, trunk/octave-forge/extra/graceplot/inst/alternatives/__grpltfmt__.m, trunk/octave-forge/extra/graceplot/inst/alternatives/__plr1__.m, trunk/octave-forge/extra/graceplot/inst/alternatives/__plr2__.m, trunk/octave-forge/extra/graceplot/inst/alternatives/__plr__.m, trunk/octave-forge/extra/graceplot/inst/alternatives/__plt1__.m, trunk/octave-forge/extra/graceplot/inst/alternatives/__plt2__.m, trunk/octave-forge/extra/graceplot/inst/alternatives/__plt2mm__.m, trunk/octave-forge/extra/graceplot/inst/alternatives/__plt2mv__.m, trunk/octave-forge/extra/graceplot/inst/alternatives/__plt2ss__.m, trunk/octave-forge/extra/graceplot/inst/alternatives/__plt2vm__.m, trunk/octave-forge/extra/graceplot/inst/alternatives/__plt2vv__.m, trunk/octave-forge/extra/graceplot/inst/alternatives/__plt__.m, trunk/octave-forge/extra/graceplot/inst/alternatives/__pltopt1__.m, trunk/octave-forge/extra/graceplot/inst/alternatives/__pltopt__.m, trunk/octave-forge/extra/graceplot/inst/alternatives/axis.m, trunk/octave-forge/extra/graceplot/inst/alternatives/bar.m, trunk/octave-forge/extra/graceplot/inst/alternatives/cla.m, trunk/octave-forge/extra/graceplot/inst/alternatives/clf.m, trunk/octave-forge/extra/graceplot/inst/alternatives/errorbar.m, trunk/octave-forge/extra/graceplot/inst/alternatives/figure.m, trunk/octave-forge/extra/graceplot/inst/alternatives/hold.m, trunk/octave-forge/extra/graceplot/inst/alternatives/ishold.m, trunk/octave-forge/extra/graceplot/inst/alternatives/legend.m, trunk/octave-forge/extra/graceplot/inst/alternatives/mplot.m, trunk/octave-forge/extra/graceplot/inst/alternatives/multiplot.m, trunk/octave-forge/extra/graceplot/inst/alternatives/oneplot.m, trunk/octave-forge/extra/graceplot/inst/alternatives/plot.m, trunk/octave-forge/extra/graceplot/inst/alternatives/polar.m, trunk/octave-forge/extra/graceplot/inst/alternatives/print.m, trunk/octave-forge/extra/graceplot/inst/alternatives/semilogx.m, trunk/octave-forge/extra/graceplot/inst/alternatives/semilogxerr.m, trunk/octave-forge/extra/graceplot/inst/alternatives/semilogy.m, trunk/octave-forge/extra/graceplot/inst/alternatives/semilogyerr.m, trunk/octave-forge/extra/graceplot/inst/alternatives/subplot.m, trunk/octave-forge/extra/graceplot/inst/alternatives/subtitle.m, trunk/octave-forge/extra/graceplot/inst/alternatives/subwindow.m, trunk/octave-forge/extra/graceplot/inst/alternatives/title.m, trunk/octave-forge/extra/graceplot/inst/alternatives/xlabel.m, trunk/octave-forge/extra/graceplot/inst/alternatives/ylabel.m, 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trunk/octave-forge/main/zenity/inst/zenity_progress.m, trunk/octave-forge/main/zenity/inst/zenity_scale.m, trunk/octave-forge/main/zenity/inst/zenity_text_info.m, trunk/octave-forge/nonfree/gpc/inst/gpc_plot.m, trunk/octave-forge/nonfree/gpc/src/Makefile.am, trunk/octave-forge/nonfree/gpc/src/acinclude.m4, trunk/octave-forge/nonfree/gpc/src/configure.in, trunk/octave-forge/nonfree/gpc/src/gpc_clip.cc, trunk/octave-forge/nonfree/gpc/src/gpc_create.cc, trunk/octave-forge/nonfree/gpc/src/gpc_get.cc, trunk/octave-forge/nonfree/gpc/src/gpc_is_polygon.cc, trunk/octave-forge/nonfree/gpc/src/gpc_read.cc, trunk/octave-forge/nonfree/gpc/src/gpc_tristrip.cc, trunk/octave-forge/nonfree/gpc/src/gpc_write.cc, trunk/octave-forge/nonfree/gpc/src/octave-gpc.cc, trunk/octave-forge/nonfree/gpc/src/octave-gpc.h, trunk/octave-forge/texinfo.tex: Update the FSF address 2007-03-20 22:17 adb014 * trunk/octave-forge/extra/MacOSX/src/autogen.sh, trunk/octave-forge/extra/Windows/src/autogen.sh, trunk/octave-forge/extra/engine/src/autogen.sh, trunk/octave-forge/extra/java/src/autogen.sh, trunk/octave-forge/extra/tk_octave/src/autogen.sh, trunk/octave-forge/main/audio/src/autogen.sh, trunk/octave-forge/main/comm/src/autogen.sh, trunk/octave-forge/main/fixed/src/autogen.sh, trunk/octave-forge/main/geometry/src/autogen.sh, src/autogen.sh, trunk/octave-forge/main/image/src/autogen.sh, trunk/octave-forge/main/linear-algebra/src/autogen.sh, trunk/octave-forge/main/miscellaneous/src/autogen.sh, trunk/octave-forge/main/octcdf/src/autogen.sh, trunk/octave-forge/main/odepkg/src/autogen.sh, trunk/octave-forge/main/optiminterp/src/autogen.sh, trunk/octave-forge/main/plot/src/autogen.sh, trunk/octave-forge/main/strings/src/autogen.sh, trunk/octave-forge/main/symbolic/src/autogen.sh, trunk/octave-forge/nonfree/arpack/src/autogen.sh, trunk/octave-forge/nonfree/gpc/src/autogen.sh, trunk/octave-forge/nonfree/splines/src/autogen.sh: Ensure that configure script is executable 2007-03-07 20:20 adb014 * trunk/octave-forge/extra/MacOSX/src/autogen.sh, trunk/octave-forge/extra/Windows/src/autogen.sh, trunk/octave-forge/extra/engine/src/autogen.sh, trunk/octave-forge/extra/java/src/autogen.sh, trunk/octave-forge/extra/tk_octave/src/autogen.sh, trunk/octave-forge/main/audio/src/autogen.sh, trunk/octave-forge/main/comm/src/autogen.sh, trunk/octave-forge/main/fixed/src/autogen.sh, trunk/octave-forge/main/geometry/src/autogen.sh, src/autogen.sh, trunk/octave-forge/main/image/src/autogen.sh, trunk/octave-forge/main/linear-algebra/src/autogen.sh, trunk/octave-forge/main/miscellaneous/src/autogen.sh, trunk/octave-forge/main/octcdf/src/autogen.sh, trunk/octave-forge/main/odepkg/src/autogen.sh, trunk/octave-forge/main/optiminterp/src/autogen.sh, trunk/octave-forge/main/plot/src/autogen.sh, trunk/octave-forge/main/strings/src/autogen.sh, trunk/octave-forge/main/symbolic/src/autogen.sh, trunk/octave-forge/nonfree/arpack/src/autogen.sh, trunk/octave-forge/nonfree/gpc/src/autogen.sh, trunk/octave-forge/nonfree/splines/src/autogen.sh: Conditional build of configure file 2007-03-05 13:19 adb014 * trunk/octave-forge/extra/Windows/PKG_ADD, trunk/octave-forge/extra/graceplot/PKG_ADD, trunk/octave-forge/extra/java/PKG_ADD, trunk/octave-forge/extra/symband/PKG_ADD, trunk/octave-forge/extra/tk_octave/PKG_ADD, trunk/octave-forge/extra/xraylib/PKG_ADD, trunk/octave-forge/main/combinatorics/PKG_ADD, trunk/octave-forge/main/comm/PKG_ADD, trunk/octave-forge/main/fixed/PKG_ADD, PKG_ADD, trunk/octave-forge/main/octcdf/PKG_ADD, trunk/octave-forge/main/symbolic/PKG_ADD: Don't use which in autoload, but a command that identifies a function that coexists with the PKG_ADD file in which the autoload is found 2007-03-02 21:00 adb014 * trunk/octave-forge/Makeconf.base, trunk/octave-forge/doc/htdocs/packages.in, trunk/octave-forge/extra/MacOSX/Makefile, trunk/octave-forge/extra/symband/Makefile, trunk/octave-forge/main/comm/Makefile, trunk/octave-forge/main/fixed/Makefile, Makefile, trunk/octave-forge/main/octcdf/Makefile, trunk/octave-forge/main/odepkg/Makefile, trunk/octave-forge/main/optim/Makefile, trunk/octave-forge/main/vrml/Makefile: double-colon in pattern match rule is a termination, so remove pattern match from pre-pkg and post-pkg rules 2007-01-30 22:23 adb014 * trunk/octave-forge/main/audio/DESCRIPTION, trunk/octave-forge/main/combinatorics/DESCRIPTION, trunk/octave-forge/main/comm/DESCRIPTION, trunk/octave-forge/main/control/DESCRIPTION, trunk/octave-forge/main/econometrics/DESCRIPTION, trunk/octave-forge/main/fixed/DESCRIPTION, trunk/octave-forge/main/general/DESCRIPTION, trunk/octave-forge/main/geometry/DESCRIPTION, DESCRIPTION, trunk/octave-forge/main/ident/DESCRIPTION, trunk/octave-forge/main/image/DESCRIPTION, trunk/octave-forge/main/info-theory/DESCRIPTION, trunk/octave-forge/main/io/DESCRIPTION, trunk/octave-forge/main/irsa/DESCRIPTION, trunk/octave-forge/main/linear-algebra/DESCRIPTION, trunk/octave-forge/main/miscellaneous/DESCRIPTION, trunk/octave-forge/main/octcdf/DESCRIPTION, trunk/octave-forge/main/odepkg/DESCRIPTION, trunk/octave-forge/main/optim/DESCRIPTION, trunk/octave-forge/main/optiminterp/DESCRIPTION, trunk/octave-forge/main/parallel/DESCRIPTION, trunk/octave-forge/main/plot/DESCRIPTION, trunk/octave-forge/main/polynomial/DESCRIPTION, trunk/octave-forge/main/signal/DESCRIPTION, trunk/octave-forge/main/specfun/DESCRIPTION, trunk/octave-forge/main/special-matrix/DESCRIPTION, trunk/octave-forge/main/splines/DESCRIPTION, trunk/octave-forge/main/statistics/DESCRIPTION, trunk/octave-forge/main/strings/DESCRIPTION, trunk/octave-forge/main/struct/DESCRIPTION, trunk/octave-forge/main/symbolic/DESCRIPTION, trunk/octave-forge/main/time/DESCRIPTION, trunk/octave-forge/main/vrml/DESCRIPTION: Add Autoload field to DESCRIPTION of main/ packages 2007-01-27 16:32 adb014 * trunk/octave-forge/Makeconf.base, trunk/octave-forge/configure.base, trunk/octave-forge/extra/MacOSX/Makefile, trunk/octave-forge/extra/Makefile, trunk/octave-forge/extra/soctcl/Makefile, trunk/octave-forge/extra/symband/Makefile, trunk/octave-forge/extra/tk_octave/Makefile, trunk/octave-forge/main/Makefile, trunk/octave-forge/main/comm/Makefile, trunk/octave-forge/main/fixed/Makefile, Makefile, trunk/octave-forge/main/image/Makefile, trunk/octave-forge/main/optim/Makefile, trunk/octave-forge/main/vrml/Makefile, trunk/octave-forge/nonfree/Makefile, trunk/octave-forge/pkg.mk: Remove pkg.mk and incorporate in Makeconf.base. Update Makefiles accordingly. Use cvs2cl to create ChangeLog files for all of the packages if a ChangeLog file doesn't exist. Package build machine must therefore have access to the CVS 2007-01-17 10:14 goffioul * src/gsl_sf.cc: Add missing return statement to gsl_sf 2007-01-15 16:21 goffioul * trunk/octave-forge/ChangeLog, trunk/octave-forge/extra/MacOSX/doc/Makefile, src/Makefile, src/precode.cc.template, trunk/octave-forge/main/image/src/pngread.cc, trunk/octave-forge/main/io/src/textread.cc, trunk/octave-forge/main/octcdf/src/ov-ncatt.cc, trunk/octave-forge/main/octcdf/src/ov-ncvar.cc: *** empty log message *** 2007-01-08 20:18 adb014 * INDEX: index gdl_sf 2007-01-07 01:36 hauberg * trunk/octave-forge/admin/make_index, trunk/octave-forge/extra/xraylib/DESCRIPTION, src/gsl_sf.cc, trunk/octave-forge/main/zenity/DESCRIPTION: Dirt hack to remove spaces 2006-12-04 11:11 adb014 * src/precode.cc.template: Define dummy gsl_sf function, so that which('gsl_sf') will work correctly 2006-10-17 19:09 adb014 * src/buildgsl_sf.sh: trivial change to buildgsl_sf.sh so that its time stamp is later than gsl_sf.cc 2006-10-17 19:08 adb014 * src/gsl_sf.cc: Commit derived file gsl_sf.cc to the CVS so that the function help can find it 2006-10-17 19:07 adb014 * src, src/.cvsignore: Don't ignore gsl_sf.cc 2006-10-14 17:39 hauberg * trunk/octave-forge/extra/MacOSX/COPYING, trunk/octave-forge/extra/NaN/COPYING, trunk/octave-forge/extra/Windows/COPYING, trunk/octave-forge/extra/civil/COPYING, trunk/octave-forge/extra/engine/COPYING, trunk/octave-forge/extra/integration/COPYING, trunk/octave-forge/extra/mapping/COPYING, trunk/octave-forge/extra/ode/COPYING, trunk/octave-forge/extra/pdb/COPYING, trunk/octave-forge/extra/symband/COPYING, trunk/octave-forge/extra/tsa/COPYING, trunk/octave-forge/main/audio/COPYING, trunk/octave-forge/main/combinatorics/COPYING, trunk/octave-forge/main/comm/COPYING, trunk/octave-forge/main/control/COPYING, trunk/octave-forge/main/econometrics/COPYING, trunk/octave-forge/main/fixed/COPYING, trunk/octave-forge/main/general/COPYING, trunk/octave-forge/main/geometry/COPYING, COPYING, trunk/octave-forge/main/ident/COPYING, trunk/octave-forge/main/image/COPYING, trunk/octave-forge/main/io/COPYING, trunk/octave-forge/main/irsa/COPYING, trunk/octave-forge/main/linear-algebra/COPYING, trunk/octave-forge/main/miscellaneous/COPYING, trunk/octave-forge/main/octcdf/COPYING, trunk/octave-forge/main/optim/COPYING, trunk/octave-forge/main/parallel/COPYING, trunk/octave-forge/main/plot/COPYING, trunk/octave-forge/main/signal/COPYING, trunk/octave-forge/main/specfun/COPYING, trunk/octave-forge/main/splines/COPYING, trunk/octave-forge/main/struct/COPYING, trunk/octave-forge/main/symbolic/COPYING, trunk/octave-forge/main/time/COPYING, trunk/octave-forge/main/vrml/COPYING, trunk/octave-forge/nonfree/gpc/COPYING, trunk/octave-forge/www/build-www.py: Removed unvalid characters from all GPL licenses in the packages 2006-10-14 05:13 adb014 * trunk/octave-forge/extra/ode/INDEX, INDEX: Category name change in INDEX 2006-10-08 20:05 adb014 * src/double_mode_to_double.cc.template, src/legendre_sphPlm_array.cc: Add missing \\n\\ in texinfo strings. my fault 2006-10-07 17:59 adb014 * src/legendre_sphPlm_array.cc: trivial doc fix 2006-10-06 23:20 adb014 * src/buildgsl_sf.sh, src/double_double_to_double.cc.template, src/double_mode_to_double.cc.template, src/double_to_double.cc.template, src/int_double_to_double.cc.template, src/int_int_double_to_double.cc.template, src/int_to_double.cc.template: escape {} in help. 2006-10-06 22:54 adb014 * Makefile, src/Makefile, src/coupling_3j.cc, src/coupling_6j.cc, src/coupling_9j.cc, src/double_double_to_double.cc.template, src/double_mode_to_double.cc.template, src/double_to_double.cc.template, src/int_double_to_double.cc.template, src/int_int_double_to_double.cc.template, src/int_to_double.cc.template, src/legendre_sphPlm_array.cc: texinfo-fy gsl strings. Build gsl_sf.cc file on package build so that indexing can find the gsl functions 2006-10-03 12:56 hauberg * trunk/octave-forge/extra/NaN/INDEX, trunk/octave-forge/extra/civil/INDEX, trunk/octave-forge/extra/engine/DESCRIPTION, trunk/octave-forge/extra/integration/INDEX, trunk/octave-forge/extra/ode/INDEX, trunk/octave-forge/extra/pdb/INDEX, trunk/octave-forge/extra/soctcl/INDEX, trunk/octave-forge/extra/symband/INDEX, trunk/octave-forge/extra/tk_octave/INDEX, trunk/octave-forge/main/econometrics/INDEX, trunk/octave-forge/main/fixed/INDEX, INDEX, trunk/octave-forge/main/ident/INDEX, trunk/octave-forge/main/irsa/INDEX, trunk/octave-forge/main/miscellaneous/inst/edit.m, trunk/octave-forge/main/octcdf/INDEX, trunk/octave-forge/main/optim/INDEX, trunk/octave-forge/main/parallel/INDEX, trunk/octave-forge/nonfree/gpc/INDEX, trunk/octave-forge/www/build-www.py: Fixed various INDEX files 2006-10-02 19:47 adb014 * trunk/octave-forge/admin/template.ndev, trunk/octave-forge/doc/coda/coda.sgml, trunk/octave-forge/extra/civil/DESCRIPTION, trunk/octave-forge/extra/mapping/DESCRIPTION, trunk/octave-forge/extra/ode/DESCRIPTION, trunk/octave-forge/extra/symband/DESCRIPTION, trunk/octave-forge/main/audio/DESCRIPTION, trunk/octave-forge/main/combinatorics/DESCRIPTION, trunk/octave-forge/main/comm/DESCRIPTION, trunk/octave-forge/main/comm/doc, trunk/octave-forge/main/comm/doc/.cvsignore, trunk/octave-forge/main/comm/doc/Makefile, trunk/octave-forge/main/control/DESCRIPTION, trunk/octave-forge/main/econometrics/DESCRIPTION, trunk/octave-forge/main/fixed/DESCRIPTION, trunk/octave-forge/main/fixed/doc, trunk/octave-forge/main/fixed/doc/.cvsignore, trunk/octave-forge/main/fixed/doc/Makefile, trunk/octave-forge/main/general/DESCRIPTION, trunk/octave-forge/main/geometry/DESCRIPTION, DESCRIPTION, trunk/octave-forge/main/ident/DESCRIPTION, trunk/octave-forge/main/image/DESCRIPTION, trunk/octave-forge/main/info-theory/DESCRIPTION, trunk/octave-forge/main/io/DESCRIPTION, trunk/octave-forge/main/irsa/DESCRIPTION, trunk/octave-forge/main/linear-algebra/DESCRIPTION, trunk/octave-forge/main/miscellaneous/DESCRIPTION, trunk/octave-forge/main/odepkg/DESCRIPTION, trunk/octave-forge/main/optim/DESCRIPTION, trunk/octave-forge/main/parallel/DESCRIPTION, trunk/octave-forge/main/plot/DESCRIPTION, trunk/octave-forge/main/signal/DESCRIPTION, trunk/octave-forge/main/specfun/DESCRIPTION, trunk/octave-forge/main/special-matrix/DESCRIPTION, trunk/octave-forge/main/splines/DESCRIPTION, trunk/octave-forge/main/statistics/DESCRIPTION, trunk/octave-forge/main/strings/DESCRIPTION, trunk/octave-forge/main/struct/DESCRIPTION, trunk/octave-forge/main/symbolic/DESCRIPTION, trunk/octave-forge/main/time/DESCRIPTION, trunk/octave-forge/main/vrml/DESCRIPTION, trunk/octave-forge/www, trunk/octave-forge/www/.cvsignore, trunk/octave-forge/www/MIPS73-isoheaders.tar.gz, trunk/octave-forge/www/Makefile, trunk/octave-forge/www/build-www.py, trunk/octave-forge/www/docs.in, trunk/octave-forge/www/links.in, trunk/octave-forge/www/oct2mat.tar.gz, trunk/octave-forge/www/octave_embed.tar.gz, trunk/octave-forge/www/soctcl0.1.zip, trunk/octave-forge/www/texmacs.pdf, trunk/octave-forge/www/translation.in: Latest mega package manager update 2006-09-15 20:33 adb014 * trunk/octave-forge/README, trunk/octave-forge/admin/make_index, trunk/octave-forge/admin/make_rpm, trunk/octave-forge/admin/make_rpmmeta, trunk/octave-forge/admin/meta_template.in, trunk/octave-forge/admin/rpm_template.in, trunk/octave-forge/admin/template.ndev, trunk/octave-forge/extra/graceplot/DESCRIPTION, trunk/octave-forge/extra/soctcl/DESCRIPTION, trunk/octave-forge/main/geometry/DESCRIPTION, DESCRIPTION, trunk/octave-forge/main/image/DESCRIPTION, trunk/octave-forge/main/miscellaneous/DESCRIPTION, trunk/octave-forge/main/octcdf/DESCRIPTION, trunk/octave-forge/main/plot/DESCRIPTION, trunk/octave-forge/main/strings/DESCRIPTION, trunk/octave-forge/main/symbolic/DESCRIPTION, trunk/octave-forge/main/vrml/DESCRIPTION, trunk/octave-forge/packages/CONTENTS, trunk/octave-forge/packages/Makefile, trunk/octave-forge/packages/README, trunk/octave-forge/www/developers.in: Further automatic rpm build fixes 2006-08-28 20:06 adb014 * trunk/octave-forge/Makeconf.base, trunk/octave-forge/Makefile, trunk/octave-forge/configure.base, trunk/octave-forge/extra/Makefile, trunk/octave-forge/extra/graceplot, trunk/octave-forge/extra/graceplot/.cvsignore, trunk/octave-forge/extra/graceplot/PKG_ADD, trunk/octave-forge/extra/soctcl/Makefile, trunk/octave-forge/main/Makefile, trunk/octave-forge/main/combinatorics/.cvsignore, trunk/octave-forge/main/combinatorics/PKG_ADD, trunk/octave-forge/main/econometrics/Makefile, trunk/octave-forge/main/fixed/.cvsignore, trunk/octave-forge/main/fixed/PKG_ADD, trunk/octave-forge/main/general/.cvsignore, trunk/octave-forge/main/geometry/.cvsignore, trunk/octave-forge/main/geometry/AUTHORS, trunk/octave-forge/main/geometry/ChangeLog, trunk/octave-forge/main/geometry/Makefile, trunk/octave-forge/main/geometry/TODO, trunk/octave-forge/main/geometry/doc, trunk/octave-forge/main/geometry/doc/AUTHORS, trunk/octave-forge/main/geometry/doc/ChangeLog, trunk/octave-forge/main/geometry/doc/TODO, .cvsignore, trunk/octave-forge/main/image/.cvsignore, trunk/octave-forge/main/image/PKG_ADD, trunk/octave-forge/main/linear-algebra/.cvsignore, trunk/octave-forge/main/miscellaneous/.cvsignore, trunk/octave-forge/main/octcdf/.cvsignore, trunk/octave-forge/main/optim/.cvsignore, trunk/octave-forge/main/plot/.cvsignore, trunk/octave-forge/main/signal/.cvsignore, trunk/octave-forge/main/specfun/.cvsignore, trunk/octave-forge/main/splines/.cvsignore, trunk/octave-forge/main/strings/.cvsignore, trunk/octave-forge/main/symbolic/.cvsignore, trunk/octave-forge/nonfree/Makefile, trunk/octave-forge/nonfree/splines/src, trunk/octave-forge/nonfree/splines/src/.cvsignore, trunk/octave-forge/packages, trunk/octave-forge/packages/.cvsignore, trunk/octave-forge/packages/Makefile: More package manager stuff 2006-08-25 19:49 adb014 * trunk/octave-forge/extra/MacOSX/.cvsignore, trunk/octave-forge/extra/MacOSX/COPYING, trunk/octave-forge/extra/MacOSX/DESCRIPTION, trunk/octave-forge/extra/MacOSX/Makefile, trunk/octave-forge/extra/MacOSX/OFSndPlay.cc, trunk/octave-forge/extra/MacOSX/README, trunk/octave-forge/extra/MacOSX/bin, trunk/octave-forge/extra/MacOSX/bin/.keepme, trunk/octave-forge/extra/MacOSX/doc/README, trunk/octave-forge/extra/MacOSX/image.m, trunk/octave-forge/extra/MacOSX/src, trunk/octave-forge/extra/MacOSX/src/Makeconf.in, trunk/octave-forge/extra/MacOSX/src/Makefile, trunk/octave-forge/extra/MacOSX/src/OFSndPlay.cc, trunk/octave-forge/extra/MacOSX/src/autogen.sh, trunk/octave-forge/extra/MacOSX/src/configure.base, trunk/octave-forge/extra/MacOSX/src/image.m.in, trunk/octave-forge/extra/Makefile, trunk/octave-forge/extra/NaN/.cvsignore, trunk/octave-forge/extra/NaN/COPYING, trunk/octave-forge/extra/NaN/DESCRIPTION, trunk/octave-forge/extra/NaN/INSTALL, trunk/octave-forge/extra/NaN/NOINSTALL, trunk/octave-forge/extra/NaN/README.TXT, trunk/octave-forge/extra/NaN/center.m, trunk/octave-forge/extra/NaN/coefficient_of_variation.m, trunk/octave-forge/extra/NaN/conv2nan.m, trunk/octave-forge/extra/NaN/cor.m, trunk/octave-forge/extra/NaN/corrcoef.m, trunk/octave-forge/extra/NaN/cov.m, trunk/octave-forge/extra/NaN/covm.m, trunk/octave-forge/extra/NaN/detrend.m, trunk/octave-forge/extra/NaN/doc, trunk/octave-forge/extra/NaN/doc/INSTALL, trunk/octave-forge/extra/NaN/doc/README.TXT, trunk/octave-forge/extra/NaN/flag_implicit_significance.m, trunk/octave-forge/extra/NaN/geomean.m, trunk/octave-forge/extra/NaN/harmmean.m, trunk/octave-forge/extra/NaN/inst, trunk/octave-forge/extra/NaN/inst/center.m, trunk/octave-forge/extra/NaN/inst/coefficient_of_variation.m, trunk/octave-forge/extra/NaN/inst/conv2nan.m, trunk/octave-forge/extra/NaN/inst/cor.m, trunk/octave-forge/extra/NaN/inst/corrcoef.m, trunk/octave-forge/extra/NaN/inst/cov.m, trunk/octave-forge/extra/NaN/inst/covm.m, trunk/octave-forge/extra/NaN/inst/detrend.m, trunk/octave-forge/extra/NaN/inst/flag_implicit_significance.m, trunk/octave-forge/extra/NaN/inst/geomean.m, trunk/octave-forge/extra/NaN/inst/harmmean.m, trunk/octave-forge/extra/NaN/inst/kurtosis.m, trunk/octave-forge/extra/NaN/inst/mad.m, trunk/octave-forge/extra/NaN/inst/mean.m, trunk/octave-forge/extra/NaN/inst/meandev.m, trunk/octave-forge/extra/NaN/inst/meansq.m, trunk/octave-forge/extra/NaN/inst/median.m, trunk/octave-forge/extra/NaN/inst/mod.m, trunk/octave-forge/extra/NaN/inst/moment.m, trunk/octave-forge/extra/NaN/inst/naninsttest.m, trunk/octave-forge/extra/NaN/inst/nanstd.m, trunk/octave-forge/extra/NaN/inst/nansum.m, trunk/octave-forge/extra/NaN/inst/nantest.m, trunk/octave-forge/extra/NaN/inst/normcdf.m, trunk/octave-forge/extra/NaN/inst/norminv.m, trunk/octave-forge/extra/NaN/inst/normpdf.m, 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trunk/octave-forge/nonfree/gpc/README, trunk/octave-forge/nonfree/gpc/TODO, trunk/octave-forge/nonfree/gpc/acinclude.m4, trunk/octave-forge/nonfree/gpc/bootstrap.sh, trunk/octave-forge/nonfree/gpc/configure.in, trunk/octave-forge/nonfree/gpc/doc, trunk/octave-forge/nonfree/gpc/doc/AUTHORS, trunk/octave-forge/nonfree/gpc/doc/ChangeLog, trunk/octave-forge/nonfree/gpc/doc/NEWS, trunk/octave-forge/nonfree/gpc/doc/README, trunk/octave-forge/nonfree/gpc/gpc_clip.cc, trunk/octave-forge/nonfree/gpc/gpc_create.cc, trunk/octave-forge/nonfree/gpc/gpc_get.cc, trunk/octave-forge/nonfree/gpc/gpc_is_polygon.cc, trunk/octave-forge/nonfree/gpc/gpc_plot.m, trunk/octave-forge/nonfree/gpc/gpc_read.cc, trunk/octave-forge/nonfree/gpc/gpc_tristrip.cc, trunk/octave-forge/nonfree/gpc/gpc_write.cc, trunk/octave-forge/nonfree/gpc/inst, trunk/octave-forge/nonfree/gpc/inst/gpc_plot.m, trunk/octave-forge/nonfree/gpc/octave-gpc.cc, trunk/octave-forge/nonfree/gpc/octave-gpc.h, trunk/octave-forge/nonfree/gpc/src, trunk/octave-forge/nonfree/gpc/src/Makefile.am, trunk/octave-forge/nonfree/gpc/src/acinclude.m4, trunk/octave-forge/nonfree/gpc/src/autogen.sh, trunk/octave-forge/nonfree/gpc/src/configure.in, trunk/octave-forge/nonfree/gpc/src/gpc_clip.cc, trunk/octave-forge/nonfree/gpc/src/gpc_create.cc, trunk/octave-forge/nonfree/gpc/src/gpc_get.cc, trunk/octave-forge/nonfree/gpc/src/gpc_is_polygon.cc, trunk/octave-forge/nonfree/gpc/src/gpc_read.cc, trunk/octave-forge/nonfree/gpc/src/gpc_tristrip.cc, trunk/octave-forge/nonfree/gpc/src/gpc_write.cc, trunk/octave-forge/nonfree/gpc/src/octave-gpc.cc, trunk/octave-forge/nonfree/gpc/src/octave-gpc.h, trunk/octave-forge/packages/Makefile, trunk/octave-forge/pkg.mk: Latest package manager mega patch, but not the last 2006-08-23 23:07 adb014 * README, src, src/.cvsignore, src/Makeconf.add, src/Makeconf.base, src/Makeconf.in, src/Makefile, src/README, src/autogen.sh, src/configure.add, src/configure.base, src/double_double_to_double.cc.template, src/double_mode_to_double.cc.template, src/double_to_double.cc.template, src/int_double_to_double.cc.template, src/int_int_double_to_double.cc.template, src/int_to_double.cc.template: working gsl package. Clean-up print_usage warnings 2006-08-23 22:54 adb014 * src/admin: remove redundant admin directory 2006-08-23 22:15 adb014 * PKG_ADD: PKG_ADD for gsl package 2006-08-21 18:39 hauberg * trunk/octave-forge/main/comm/inst, trunk/octave-forge/main/comm/inst/.cvsignore, trunk/octave-forge/main/comm/src, trunk/octave-forge/main/comm/src/.cvsignore, trunk/octave-forge/main/fixed/inst, trunk/octave-forge/main/fixed/inst/.cvsignore, trunk/octave-forge/main/fixed/src, trunk/octave-forge/main/fixed/src/.cvsignore, trunk/octave-forge/main/general/inst, trunk/octave-forge/main/general/inst/.cvsignore, trunk/octave-forge/main/general/src, trunk/octave-forge/main/general/src/.cvsignore, trunk/octave-forge/main/geometry/inst, trunk/octave-forge/main/geometry/inst/.cvsignore, trunk/octave-forge/main/geometry/src, trunk/octave-forge/main/geometry/src/.cvsignore, src, src/.cvsignore, trunk/octave-forge/main/image/inst, trunk/octave-forge/main/image/inst/.cvsignore, trunk/octave-forge/main/image/src, trunk/octave-forge/main/image/src/.cvsignore, trunk/octave-forge/main/io/inst, trunk/octave-forge/main/io/inst/.cvsignore, trunk/octave-forge/main/io/src, trunk/octave-forge/main/io/src/.cvsignore, trunk/octave-forge/main/linear-algebra/inst, trunk/octave-forge/main/linear-algebra/inst/.cvsignore, trunk/octave-forge/main/linear-algebra/src, trunk/octave-forge/main/linear-algebra/src/.cvsignore, trunk/octave-forge/main/miscellaneous/inst, trunk/octave-forge/main/miscellaneous/inst/.cvsignore, trunk/octave-forge/main/miscellaneous/src, trunk/octave-forge/main/miscellaneous/src/.cvsignore, trunk/octave-forge/main/octcdf/inst, trunk/octave-forge/main/octcdf/inst/.cvsignore, trunk/octave-forge/main/octcdf/src, trunk/octave-forge/main/octcdf/src/.cvsignore, trunk/octave-forge/main/optim/inst, trunk/octave-forge/main/optim/inst/.cvsignore, trunk/octave-forge/main/optim/src, trunk/octave-forge/main/optim/src/.cvsignore, trunk/octave-forge/main/plot/inst, trunk/octave-forge/main/plot/inst/.cvsignore, trunk/octave-forge/main/plot/src, trunk/octave-forge/main/plot/src/.cvsignore, trunk/octave-forge/main/signal/inst, trunk/octave-forge/main/signal/inst/.cvsignore, trunk/octave-forge/main/signal/src, trunk/octave-forge/main/signal/src/.cvsignore, trunk/octave-forge/main/specfun/inst, trunk/octave-forge/main/specfun/inst/.cvsignore, trunk/octave-forge/main/specfun/src, trunk/octave-forge/main/specfun/src/.cvsignore, trunk/octave-forge/main/splines/inst, trunk/octave-forge/main/splines/inst/.cvsignore, trunk/octave-forge/main/strings/inst, trunk/octave-forge/main/strings/inst/.cvsignore, trunk/octave-forge/main/strings/src, trunk/octave-forge/main/strings/src/.cvsignore, trunk/octave-forge/main/struct/inst, trunk/octave-forge/main/struct/inst/.cvsignore, trunk/octave-forge/main/symbolic/inst, trunk/octave-forge/main/symbolic/inst/.cvsignore, trunk/octave-forge/main/symbolic/src, trunk/octave-forge/main/symbolic/src/.cvsignore: Added a lot of .cvsignore's in main 2006-08-20 12:46 hauberg * COPYING, DESCRIPTION, Makeconf.add, Makefile, buildgsl_sf.sh, configure.add, coupling_3j.cc, coupling_6j.cc, coupling_9j.cc, double_double_to_double.cc.template, double_mode_to_double.cc.template, double_to_double.cc.template, int_double_to_double.cc.template, int_int_double_to_double.cc.template, int_to_double.cc.template, legendre_sphPlm_array.cc, precode.cc.template, replace_template.sh, src, src/Makeconf.add, src/Makeconf.base, src/Makeconf.in, src/Makefile, src/admin, src/admin/CONTENTS, src/admin/OctRe.pm, src/admin/change_va_arg.pm, src/admin/find_changes, src/admin/fntests.m, src/admin/get_authors, src/admin/get_contents, src/admin/make_index, src/admin/mkdoc, src/admin/mkpkgadd, src/admin/mktests.sh, src/admin/mktexi, src/admin/no_vr_val.pm, src/admin/octlink.sh, src/admin/run_forge, src/admin/template.ndev, src/admin/template.readme, src/autogen.sh, src/buildgsl_sf.sh, src/configure.add, src/configure.base, src/coupling_3j.cc, src/coupling_6j.cc, src/coupling_9j.cc, src/double_double_to_double.cc.template, src/double_mode_to_double.cc.template, src/double_to_double.cc.template, src/install-sh, src/int_double_to_double.cc.template, src/int_int_double_to_double.cc.template, src/int_to_double.cc.template, src/legendre_sphPlm_array.cc, src/octinst.sh.in, src/precode.cc.template, src/replace_template.sh: Changed the directory structure to match the package system 2006-05-19 06:58 jwe * trunk/octave-forge/extra/Windows/grab.cc, trunk/octave-forge/extra/Windows/win32api.cc, trunk/octave-forge/extra/graceplot/__grcmd__.cc, trunk/octave-forge/extra/linear-algebra/chol.cc, trunk/octave-forge/extra/symband/SymBand.cc, trunk/octave-forge/extra/tk_octave/tk_interp.cc, trunk/octave-forge/main/comm/gf.cc, trunk/octave-forge/main/fixed/examples/ffft.cc, trunk/octave-forge/main/fixed/examples/fixed_inc.cc, trunk/octave-forge/main/fixed/fixed-var.cc, trunk/octave-forge/main/fixed/fixed.cc, trunk/octave-forge/main/general/deref.cc, trunk/octave-forge/main/geometry/__voronoi__.cc, trunk/octave-forge/main/geometry/convhulln.cc, trunk/octave-forge/main/geometry/delaunayn.cc, trunk/octave-forge/main/geometry/tsearch.cc, coupling_3j.cc, coupling_6j.cc, coupling_9j.cc, legendre_sphPlm_array.cc, trunk/octave-forge/main/image/__imagemagick__.cc, trunk/octave-forge/main/image/bwfill.cc, trunk/octave-forge/main/image/conv2.cc, trunk/octave-forge/main/image/cordflt2.cc, trunk/octave-forge/main/image/graycomatrix.cc, trunk/octave-forge/main/image/houghtf.cc, trunk/octave-forge/main/image/jpgread.cc, trunk/octave-forge/main/image/jpgwrite.cc, trunk/octave-forge/main/image/pngread.cc, trunk/octave-forge/main/image/pngwrite.cc, trunk/octave-forge/main/image/rotate_scale.cc, trunk/octave-forge/main/io/dlmread.cc, trunk/octave-forge/main/io/textread.cc, trunk/octave-forge/main/linear-algebra/GramSchmidt.cc, trunk/octave-forge/main/linear-algebra/gsvd.cc, trunk/octave-forge/main/miscellaneous/cell2csv.cc, trunk/octave-forge/main/miscellaneous/csvconcat.cc, trunk/octave-forge/main/miscellaneous/csvexplode.cc, trunk/octave-forge/main/miscellaneous/listen.cc, trunk/octave-forge/main/miscellaneous/waitbar.cc, trunk/octave-forge/main/miscellaneous/xmlread.cc, trunk/octave-forge/main/octcdf/ov-netcdf.cc, trunk/octave-forge/main/optim/leval.cc, trunk/octave-forge/main/parallel/connect.cc, trunk/octave-forge/main/parallel/recv.cc, trunk/octave-forge/main/parallel/reval.cc, trunk/octave-forge/main/parallel/sclose.cc, trunk/octave-forge/main/parallel/send.cc, trunk/octave-forge/main/plot/grab.cc, trunk/octave-forge/main/plot/gtext.cc, trunk/octave-forge/main/signal/medfilt1.cc, trunk/octave-forge/main/signal/remez.cc, trunk/octave-forge/main/specfun/ellipj.cc, trunk/octave-forge/main/splines/trisolve.cc, trunk/octave-forge/main/strings/pcregexp.cc, trunk/octave-forge/main/symbolic/differentiate.cc, trunk/octave-forge/main/symbolic/numden.cc, trunk/octave-forge/main/symbolic/probably_prime.cc, trunk/octave-forge/main/symbolic/sym-create.cc, trunk/octave-forge/main/symbolic/symbols.cc, trunk/octave-forge/nonfree/gpc/gpc_clip.cc, trunk/octave-forge/nonfree/gpc/gpc_create.cc, trunk/octave-forge/nonfree/gpc/gpc_get.cc, trunk/octave-forge/nonfree/gpc/gpc_is_polygon.cc, trunk/octave-forge/nonfree/gpc/gpc_read.cc, trunk/octave-forge/nonfree/gpc/gpc_tristrip.cc, trunk/octave-forge/nonfree/gpc/gpc_write.cc: *** empty log message *** 2006-01-07 05:12 adb014 * trunk/octave-forge/FIXES, trunk/octave-forge/FIXES/.cvsignore, trunk/octave-forge/FIXES/Makefile, trunk/octave-forge/Makeconf.base, trunk/octave-forge/Makefile, trunk/octave-forge/admin/mkpkgadd, trunk/octave-forge/admin/mktests.sh, trunk/octave-forge/configure.base, trunk/octave-forge/extra/Windows/Makefile, trunk/octave-forge/extra/graceplot, trunk/octave-forge/extra/graceplot/.cvsignore, trunk/octave-forge/extra/graceplot/Makefile, trunk/octave-forge/extra/linear-algebra, trunk/octave-forge/extra/linear-algebra/.cvsignore, trunk/octave-forge/extra/symband, trunk/octave-forge/extra/symband/.cvsignore, trunk/octave-forge/extra/symband/Makefile, trunk/octave-forge/extra/testfun, trunk/octave-forge/extra/testfun/.cvsignore, trunk/octave-forge/extra/tk_octave/Makefile, trunk/octave-forge/main/cell, trunk/octave-forge/main/cell/.cvsignore, trunk/octave-forge/main/comm, trunk/octave-forge/main/comm/.cvsignore, trunk/octave-forge/main/comm/Makefile, trunk/octave-forge/main/fixed, trunk/octave-forge/main/fixed/.cvsignore, trunk/octave-forge/main/fixed/Makefile, trunk/octave-forge/main/fixed/examples, trunk/octave-forge/main/fixed/examples/.cvsignore, trunk/octave-forge/main/general, trunk/octave-forge/main/general/.cvsignore, trunk/octave-forge/main/general/Makefile, trunk/octave-forge/main/geometry, trunk/octave-forge/main/geometry/.cvsignore, ., .cvsignore, Makefile, trunk/octave-forge/main/image, trunk/octave-forge/main/image/.cvsignore, trunk/octave-forge/main/image/Makefile, trunk/octave-forge/main/io, trunk/octave-forge/main/io/.cvsignore, trunk/octave-forge/main/miscellaneous, trunk/octave-forge/main/miscellaneous/.cvsignore, trunk/octave-forge/main/miscellaneous/Makefile, trunk/octave-forge/main/octcdf/Makefile, trunk/octave-forge/main/optim, trunk/octave-forge/main/optim/.cvsignore, trunk/octave-forge/main/plot, trunk/octave-forge/main/plot/.cvsignore, trunk/octave-forge/main/signal, trunk/octave-forge/main/signal/.cvsignore, trunk/octave-forge/main/sparse, trunk/octave-forge/main/sparse/.cvsignore, trunk/octave-forge/main/sparse/Makefile, trunk/octave-forge/main/specfun, trunk/octave-forge/main/specfun/.cvsignore, trunk/octave-forge/main/splines, trunk/octave-forge/main/splines/.cvsignore, trunk/octave-forge/main/strings, trunk/octave-forge/main/strings/.cvsignore, trunk/octave-forge/main/struct, trunk/octave-forge/main/struct/.cvsignore, trunk/octave-forge/main/symbolic, trunk/octave-forge/main/symbolic/.cvsignore, trunk/octave-forge/nonfree/gpc, trunk/octave-forge/nonfree/gpc/.cvsignore: patch to allow 2.9.x autoload functionality to replace symbolic links 2005-05-28 19:22 pkienzle * trunk/octave-forge/Makeconf.base, Makefile: [for Dan McMahill] don't assume /bin/sh 2005-05-28 15:39 pkienzle * replace_template.sh: Eliminate csplit dependency 2005-03-01 16:33 pkienzle * trunk/octave-forge/configure.base, trunk/octave-forge/main/geometry/configure.add, configure.add, trunk/octave-forge/main/image/configure.add, trunk/octave-forge/main/miscellaneous/configure.add, trunk/octave-forge/main/strings/configure.add: Don't append to LIBS when checking for a function in a library 2005-02-28 21:34 pkienzle * Makeconf.add, Makefile, README, buildgsl_sf.sh, configure.add: Protect against older versions of GSL. 2005-02-28 21:25 pkienzle * double_double_to_double.cc.template, double_mode_to_double.cc.template, double_to_double.cc.template, int_double_to_double.cc.template, int_int_double_to_double.cc.template, int_to_double.cc.template, precode.cc.template: Add docs for error return; improve retval construction for err; mark files as C++ for emacs 2004-07-20 10:25 adb014 * double_double_to_double.cc.template, double_mode_to_double.cc.template, double_to_double.cc.template, int_double_to_double.cc.template, int_int_double_to_double.cc.template, int_to_double.cc.template: Possible ambiguous use of octave_value_list with latest octave CVS. Use octave_value instead. 2004-07-20 10:10 adb014 * coupling_3j.cc, coupling_6j.cc, coupling_9j.cc: Possible ambiguous use of octave_value_list with latest octave CVS. Use octave_value instead 2004-07-19 16:13 tpikonen * INDEX: Index-file for GSL functions. 2004-07-14 19:59 pkienzle * Makefile: Make sure -lgsl is used on all gsl oct-files. Symlinks shouldn't depend on base file. 2004-07-14 19:57 pkienzle * configure.add: Make sure -lgsl comes before -lgslcblas since some linkers care 2004-07-07 09:38 adb014 * trunk/octave-forge/FIXES/Makefile, trunk/octave-forge/Makefile, trunk/octave-forge/extra/Makefile, trunk/octave-forge/extra/graceplot/Makefile, trunk/octave-forge/extra/linear-algebra/Makefile, trunk/octave-forge/extra/symband/Makefile, trunk/octave-forge/extra/testfun/Makefile, trunk/octave-forge/main/Makefile, trunk/octave-forge/main/audio/Makefile, trunk/octave-forge/main/comm/Makefile, trunk/octave-forge/main/comm/doc/Makefile, trunk/octave-forge/main/comm/doc/comms.info, trunk/octave-forge/main/comm/doc/comms.ps, trunk/octave-forge/main/fixed/Makefile, trunk/octave-forge/main/fixed/doc/Makefile, trunk/octave-forge/main/fixed/doc/fixed.info, trunk/octave-forge/main/fixed/doc/fixed.ps, trunk/octave-forge/main/general/Makefile, Makefile, trunk/octave-forge/main/image/Makefile, trunk/octave-forge/main/io/Makefile, trunk/octave-forge/main/linear-algebra/Makefile, trunk/octave-forge/main/miscellaneous/Makefile, trunk/octave-forge/main/optim/Makefile, trunk/octave-forge/main/parallel/Makefile, trunk/octave-forge/main/signal/Makefile, trunk/octave-forge/main/specfun/Makefile, trunk/octave-forge/main/splines/Makefile, trunk/octave-forge/main/strings/Makefile, trunk/octave-forge/main/struct/Makefile, trunk/octave-forge/nonfree/Makefile, trunk/octave-forge/nonfree/splines/Makefile: Allow dist, distclean and clean targets to run without Makeconf. Replace include with sinclude in Makefiles. Build fixed and comm docs as part of dist target 2004-07-02 10:16 pkienzle * trunk/octave-forge/admin/RPM, trunk/octave-forge/admin/RPM/.cvsignore, ., .cvsignore, trunk/octave-forge/main/io, trunk/octave-forge/main/io/.cvsignore: Ignore build outputs 2004-06-15 08:51 tpikonen * Makefile, coupling_3j.cc, coupling_6j.cc, coupling_9j.cc: Add functions for Wigner 3j, 6j and 9j coupling coefficients. 2004-05-26 14:12 adb014 * Makeconf.add, Makefile, configure.add: Fixed test for libgsl, so that gsl toolbox doesn't try to build if missing 2004-05-13 14:01 tpikonen * Makefile, legendre_sphPlm_array.cc: Add function legendre_sphPlm_array.oct 2004-05-06 08:42 tpikonen * buildgsl_sf.sh: Add function sinc_gsl 2004-05-04 15:49 tpikonen * ., Makefile, buildgsl_sf.sh, configure.add, double_double_to_double.cc.template, double_mode_to_double.cc.template, double_to_double.cc.template, int_double_to_double.cc.template, int_int_double_to_double.cc.template, int_to_double.cc.template, precode.cc.template, replace_template.sh: Special functions from GNU Scientific Library