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Diffstat (limited to 'thirdparty/includes/GSL/gsl/gsl_sf_hyperg.h')
-rw-r--r-- | thirdparty/includes/GSL/gsl/gsl_sf_hyperg.h | 154 |
1 files changed, 154 insertions, 0 deletions
diff --git a/thirdparty/includes/GSL/gsl/gsl_sf_hyperg.h b/thirdparty/includes/GSL/gsl/gsl_sf_hyperg.h new file mode 100644 index 0000000..8366b88 --- /dev/null +++ b/thirdparty/includes/GSL/gsl/gsl_sf_hyperg.h @@ -0,0 +1,154 @@ +/* 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__ */ |