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authorSandeep Gupta2017-07-05 12:41:25 +0530
committerSandeep Gupta2017-07-05 12:41:25 +0530
commitdd50e95a8193fb0faa846ccaa971a115ba69e71c (patch)
tree8d66abedd68dc5255ad323b95a16c9b592657f35 /2.3-1/thirdparty/includes/GSL/gsl/gsl_sf_hyperg.h
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LinearAlgebra and MatrixOperation Update
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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__ */