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/* specfunc/gsl_sf_hyperg.h
*
* 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 */
#ifndef __GSL_SF_HYPERG_H__
#define __GSL_SF_HYPERG_H__
#include <gsl/gsl_sf_result.h>
#undef __BEGIN_DECLS
#undef __END_DECLS
#ifdef __cplusplus
# define __BEGIN_DECLS extern "C" {
# define __END_DECLS }
#else
# define __BEGIN_DECLS /* empty */
# define __END_DECLS /* empty */
#endif
__BEGIN_DECLS
/* Hypergeometric function related to Bessel functions
* 0F1[c,x] =
* Gamma[c] x^(1/2(1-c)) I_{c-1}(2 Sqrt[x])
* Gamma[c] (-x)^(1/2(1-c)) J_{c-1}(2 Sqrt[-x])
*
* exceptions: GSL_EOVRFLW, GSL_EUNDRFLW
*/
int gsl_sf_hyperg_0F1_e(double c, double x, gsl_sf_result * result);
double gsl_sf_hyperg_0F1(const double c, const double x);
/* Confluent hypergeometric function for integer parameters.
* 1F1[m,n,x] = M(m,n,x)
*
* exceptions:
*/
int gsl_sf_hyperg_1F1_int_e(const int m, const int n, const double x, gsl_sf_result * result);
double gsl_sf_hyperg_1F1_int(const int m, const int n, double x);
/* Confluent hypergeometric function.
* 1F1[a,b,x] = M(a,b,x)
*
* exceptions:
*/
int gsl_sf_hyperg_1F1_e(const double a, const double b, const double x, gsl_sf_result * result);
double gsl_sf_hyperg_1F1(double a, double b, double x);
/* Confluent hypergeometric function for integer parameters.
* U(m,n,x)
*
* exceptions:
*/
int gsl_sf_hyperg_U_int_e(const int m, const int n, const double x, gsl_sf_result * result);
double gsl_sf_hyperg_U_int(const int m, const int n, const double x);
/* Confluent hypergeometric function for integer parameters.
* U(m,n,x)
*
* exceptions:
*/
int gsl_sf_hyperg_U_int_e10_e(const int m, const int n, const double x, gsl_sf_result_e10 * result);
/* Confluent hypergeometric function.
* U(a,b,x)
*
* exceptions:
*/
int gsl_sf_hyperg_U_e(const double a, const double b, const double x, gsl_sf_result * result);
double gsl_sf_hyperg_U(const double a, const double b, const double x);
/* Confluent hypergeometric function.
* U(a,b,x)
*
* exceptions:
*/
int gsl_sf_hyperg_U_e10_e(const double a, const double b, const double x, gsl_sf_result_e10 * result);
/* Gauss hypergeometric function 2F1[a,b,c,x]
* |x| < 1
*
* exceptions:
*/
int gsl_sf_hyperg_2F1_e(double a, double b, const double c, const double x, gsl_sf_result * result);
double gsl_sf_hyperg_2F1(double a, double b, double c, double x);
/* Gauss hypergeometric function
* 2F1[aR + I aI, aR - I aI, c, x]
* |x| < 1
*
* exceptions:
*/
int gsl_sf_hyperg_2F1_conj_e(const double aR, const double aI, const double c, const double x, gsl_sf_result * result);
double gsl_sf_hyperg_2F1_conj(double aR, double aI, double c, double x);
/* Renormalized Gauss hypergeometric function
* 2F1[a,b,c,x] / Gamma[c]
* |x| < 1
*
* exceptions:
*/
int gsl_sf_hyperg_2F1_renorm_e(const double a, const double b, const double c, const double x, gsl_sf_result * result);
double gsl_sf_hyperg_2F1_renorm(double a, double b, double c, double x);
/* Renormalized Gauss hypergeometric function
* 2F1[aR + I aI, aR - I aI, c, x] / Gamma[c]
* |x| < 1
*
* exceptions:
*/
int gsl_sf_hyperg_2F1_conj_renorm_e(const double aR, const double aI, const double c, const double x, gsl_sf_result * result);
double gsl_sf_hyperg_2F1_conj_renorm(double aR, double aI, double c, double x);
/* Mysterious hypergeometric function. The series representation
* is a divergent hypergeometric series. However, for x < 0 we
* have 2F0(a,b,x) = (-1/x)^a U(a,1+a-b,-1/x)
*
* exceptions: GSL_EDOM
*/
int gsl_sf_hyperg_2F0_e(const double a, const double b, const double x, gsl_sf_result * result);
double gsl_sf_hyperg_2F0(const double a, const double b, const double x);
__END_DECLS
#endif /* __GSL_SF_HYPERG_H__ */
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