/* 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 <config.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_sf_exp.h>
#include <gsl/gsl_sf_gamma.h>
#include <gsl/gsl_sf_bessel.h>
#include "error.h"
#include "bessel.h"
#include "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 "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));
}