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/* specfunc/hyperg_0F1.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 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, 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 <gsl/gsl_sf_hyperg.h>
#include "error.h"
#define locEPS (1000.0*GSL_DBL_EPSILON)
/* Evaluate bessel_I(nu, x), allowing nu < 0.
* This is fine here because we do not not allow
* nu to be a negative integer.
* x > 0.
*/
static
int
hyperg_0F1_bessel_I(const double nu, const double x, gsl_sf_result * result)
{
if(x > GSL_LOG_DBL_MAX) {
OVERFLOW_ERROR(result);
}
if(nu < 0.0) {
const double anu = -nu;
const double s = 2.0/M_PI * sin(anu*M_PI);
const double ex = exp(x);
gsl_sf_result I;
gsl_sf_result K;
int stat_I = gsl_sf_bessel_Inu_scaled_e(anu, x, &I);
int stat_K = gsl_sf_bessel_Knu_scaled_e(anu, x, &K);
result->val = ex * I.val + s * (K.val / ex);
result->err = ex * I.err + fabs(s * K.err/ex);
result->err += fabs(s * (K.val/ex)) * GSL_DBL_EPSILON * anu * M_PI;
return GSL_ERROR_SELECT_2(stat_K, stat_I);
}
else {
const double ex = exp(x);
gsl_sf_result I;
int stat_I = gsl_sf_bessel_Inu_scaled_e(nu, x, &I);
result->val = ex * I.val;
result->err = ex * I.err + GSL_DBL_EPSILON * fabs(result->val);
return stat_I;
}
}
/* Evaluate bessel_J(nu, x), allowing nu < 0.
* This is fine here because we do not not allow
* nu to be a negative integer.
* x > 0.
*/
static
int
hyperg_0F1_bessel_J(const double nu, const double x, gsl_sf_result * result)
{
if(nu < 0.0) {
const double anu = -nu;
const double s = sin(anu*M_PI);
const double c = cos(anu*M_PI);
gsl_sf_result J;
gsl_sf_result Y;
int stat_J = gsl_sf_bessel_Jnu_e(anu, x, &J);
int stat_Y = gsl_sf_bessel_Ynu_e(anu, x, &Y);
result->val = c * J.val - s * Y.val;
result->err = fabs(c * J.err) + fabs(s * Y.err);
result->err += fabs(anu * M_PI) * GSL_DBL_EPSILON * fabs(J.val + Y.val);
return GSL_ERROR_SELECT_2(stat_Y, stat_J);
}
else {
return gsl_sf_bessel_Jnu_e(nu, x, result);
}
}
/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
int
gsl_sf_hyperg_0F1_e(double c, double x, gsl_sf_result * result)
{
const double rintc = floor(c + 0.5);
const int c_neg_integer = (c < 0.0 && fabs(c - rintc) < locEPS);
/* CHECK_POINTER(result) */
if(c == 0.0 || c_neg_integer) {
DOMAIN_ERROR(result);
}
else if(x < 0.0) {
gsl_sf_result Jcm1;
gsl_sf_result lg_c;
double sgn;
int stat_g = gsl_sf_lngamma_sgn_e(c, &lg_c, &sgn);
int stat_J = hyperg_0F1_bessel_J(c-1.0, 2.0*sqrt(-x), &Jcm1);
if(stat_g != GSL_SUCCESS) {
result->val = 0.0;
result->err = 0.0;
return stat_g;
}
else if(Jcm1.val == 0.0) {
result->val = 0.0;
result->err = 0.0;
return stat_J;
}
else {
const double tl = log(-x)*0.5*(1.0-c);
double ln_pre_val = lg_c.val + tl;
double ln_pre_err = lg_c.err + 2.0 * GSL_DBL_EPSILON * fabs(tl);
return gsl_sf_exp_mult_err_e(ln_pre_val, ln_pre_err,
sgn*Jcm1.val, Jcm1.err,
result);
}
}
else if(x == 0.0) {
result->val = 1.0;
result->err = 1.0;
return GSL_SUCCESS;
}
else {
gsl_sf_result Icm1;
gsl_sf_result lg_c;
double sgn;
int stat_g = gsl_sf_lngamma_sgn_e(c, &lg_c, &sgn);
int stat_I = hyperg_0F1_bessel_I(c-1.0, 2.0*sqrt(x), &Icm1);
if(stat_g != GSL_SUCCESS) {
result->val = 0.0;
result->err = 0.0;
return stat_g;
}
else if(Icm1.val == 0.0) {
result->val = 0.0;
result->err = 0.0;
return stat_I;
}
else {
const double tl = log(x)*0.5*(1.0-c);
const double ln_pre_val = lg_c.val + tl;
const double ln_pre_err = lg_c.err + 2.0 * GSL_DBL_EPSILON * fabs(tl);
return gsl_sf_exp_mult_err_e(ln_pre_val, ln_pre_err,
sgn*Icm1.val, Icm1.err,
result);
}
}
}
/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
#include "eval.h"
double gsl_sf_hyperg_0F1(const double c, const double x)
{
EVAL_RESULT(gsl_sf_hyperg_0F1_e(c, x, &result));
}
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