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- /* specfunc/expint3.c
- *
- * Copyright (C) 1996, 1997, 1998, 1999, 2000 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 "gsl__config.h"
- #include "gsl_math.h"
- #include "gsl_errno.h"
- #include "gsl_sf_expint.h"
- #include "gsl_specfunc__error.h"
- #include "gsl_specfunc__chebyshev.h"
- #include "gsl_specfunc__cheb_eval.c"
- static double expint3_data[24] = {
- 1.269198414221126014,
- -0.248846446384140982,
- 0.80526220717231041e-01,
- -0.25772733251968330e-01,
- 0.7599878873073774e-02,
- -0.2030695581940405e-02,
- 0.490834586699330e-03,
- -0.107682239142021e-03,
- 0.21551726264290e-04,
- -0.3956705137384e-05,
- 0.6699240933896e-06,
- -0.105132180807e-06,
- 0.15362580199e-07,
- -0.20990960364e-08,
- 0.2692109538e-09,
- -0.325195242e-10,
- 0.37114816e-11,
- -0.4013652e-12,
- 0.412334e-13,
- -0.40338e-14,
- 0.3766e-15,
- -0.336e-16,
- 0.29e-17,
- -0.2e-18
- };
- static cheb_series expint3_cs = {
- expint3_data,
- 23,
- -1.0, 1.0,
- 15
- };
- static double expint3a_data[23] = {
- 1.9270464955068273729,
- -0.349293565204813805e-01,
- 0.14503383718983009e-02,
- -0.8925336718327903e-04,
- 0.70542392191184e-05,
- -0.6671727454761e-06,
- 0.724267589982e-07,
- -0.87825825606e-08,
- 0.11672234428e-08,
- -0.1676631281e-09,
- 0.257550158e-10,
- -0.41957888e-11,
- 0.7201041e-12,
- -0.1294906e-12,
- 0.24287e-13,
- -0.47331e-14,
- 0.95531e-15,
- -0.1991e-15,
- 0.428e-16,
- -0.94e-17,
- 0.21e-17,
- -0.5e-18,
- 0.1e-18
- };
- static cheb_series expint3a_cs = {
- expint3a_data,
- 22,
- -1.0, 1.0,
- 10
- };
- /*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
- int gsl_sf_expint_3_e(const double x, gsl_sf_result * result)
- {
- const double val_infinity = 0.892979511569249211;
- /* CHECK_POINTER(result) */
- if(x < 0.0) {
- DOMAIN_ERROR(result);
- }
- else if(x < 1.6*GSL_ROOT3_DBL_EPSILON) {
- result->val = x;
- result->err = 0.0;
- return GSL_SUCCESS;
- }
- else if(x <= 2.0) {
- const double t = x*x*x/4.0 - 1.0;
- gsl_sf_result result_c;
- cheb_eval_e(&expint3_cs, t, &result_c);
- result->val = x * result_c.val;
- result->err = x * result_c.err;
- return GSL_SUCCESS;
- }
- else if(x < pow(-GSL_LOG_DBL_EPSILON, 1.0/3.0)) {
- const double t = 16.0/(x*x*x) - 1.0;
- const double s = exp(-x*x*x)/(3.0*x*x);
- gsl_sf_result result_c;
- cheb_eval_e(&expint3a_cs, t, &result_c);
- result->val = val_infinity - result_c.val * s;
- result->err = val_infinity * GSL_DBL_EPSILON + s * result_c.err;
- return GSL_SUCCESS;
- }
- else {
- result->val = val_infinity;
- result->err = val_infinity * GSL_DBL_EPSILON;
- return GSL_SUCCESS;
- }
- }
- /*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
- #include "gsl_specfunc__eval.h"
- double gsl_sf_expint_3(double x)
- {
- EVAL_RESULT(gsl_sf_expint_3_e(x, &result));
- }
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