/* 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__ */