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- /* specfunc/bessel_Inu.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_exp.h"
- #include "gsl_sf_gamma.h"
- #include "gsl_sf_bessel.h"
- #include "gsl_specfunc__error.h"
- #include "gsl_specfunc__bessel.h"
- #include "gsl_specfunc__bessel_temme.h"
- /*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
- int
- gsl_sf_bessel_Inu_scaled_e(double nu, double x, gsl_sf_result * result)
- {
- /* CHECK_POINTER(result) */
- if(x < 0.0 || nu < 0.0) {
- DOMAIN_ERROR(result);
- }
- else if(x*x < 10.0*(nu+1.0)) {
- gsl_sf_result b;
- double ex = exp(-x);
- int stat = gsl_sf_bessel_IJ_taylor_e(nu, x, 1, 100, GSL_DBL_EPSILON, &b);
- result->val = b.val * ex;
- result->err = b.err * ex;
- result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
- return stat;
- }
- else if(0.5/(nu*nu + x*x) < GSL_ROOT3_DBL_EPSILON) {
- return gsl_sf_bessel_Inu_scaled_asymp_unif_e(nu, x, result);
- }
- else {
- int N = (int)(nu + 0.5);
- double mu = nu - N; /* -1/2 <= mu <= 1/2 */
- double K_mu, K_mup1, Kp_mu;
- double K_nu, K_nup1, K_num1;
- double I_nu_ratio;
- int stat_Irat;
- int stat_Kmu;
- int n;
- /* obtain K_mu, K_mup1 */
- if(x < 2.0) {
- stat_Kmu = gsl_sf_bessel_K_scaled_temme(mu, x, &K_mu, &K_mup1, &Kp_mu);
- }
- else {
- stat_Kmu = gsl_sf_bessel_K_scaled_steed_temme_CF2(mu, x, &K_mu, &K_mup1, &Kp_mu);
- }
- /* recurse forward to obtain K_num1, K_nu */
- K_nu = K_mu;
- K_nup1 = K_mup1;
- for(n=0; n<N; n++) {
- K_num1 = K_nu;
- K_nu = K_nup1;
- K_nup1 = 2.0*(mu+n+1)/x * K_nu + K_num1;
- }
- /* calculate I_{nu+1}/I_nu */
- stat_Irat = gsl_sf_bessel_I_CF1_ser(nu, x, &I_nu_ratio);
- /* solve for I_nu */
- result->val = 1.0/(x * (K_nup1 + I_nu_ratio * K_nu));
- result->err = GSL_DBL_EPSILON * (0.5*N + 2.0) * fabs(result->val);
- return GSL_ERROR_SELECT_2(stat_Kmu, stat_Irat);
- }
- }
- int
- gsl_sf_bessel_Inu_e(double nu, double x, gsl_sf_result * result)
- {
- gsl_sf_result b;
- int stat_I = gsl_sf_bessel_Inu_scaled_e(nu, x, &b);
- int stat_e = gsl_sf_exp_mult_err_e(x, fabs(x*GSL_DBL_EPSILON),
- b.val, b.err,
- result);
- return GSL_ERROR_SELECT_2(stat_e, stat_I);
- }
- /*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
- #include "gsl_specfunc__eval.h"
- double gsl_sf_bessel_Inu_scaled(double nu, double x)
- {
- EVAL_RESULT(gsl_sf_bessel_Inu_scaled_e(nu, x, &result));
- }
- double gsl_sf_bessel_Inu(double nu, double x)
- {
- EVAL_RESULT(gsl_sf_bessel_Inu_e(nu, x, &result));
- }
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