PDL::GSLSF::HYPERG - PDL interface to GSL Special Functions This is an interface to the Special Function package present in the GNU Scientific Library.

gsl_sf_hyperg_0F1
Signature: (double x(); double [o]y(); double [o]e(); double c) /* 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])

gsl_sf_hyperg_1F1
Signature: (double x(); double [o]y(); double [o]e(); double a; double b) Confluent hypergeometric function for integer parameters. 1F1[a,b,x] = M(a,b,x)

gsl_sf_hyperg_U
Signature: (double x(); double [o]y(); double [o]e(); double a; double b) Confluent hypergeometric function for integer parameters. U(a,b,x)

gsl_sf_hyperg_2F1
Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c) Confluent hypergeometric function for integer parameters. 2F1[a,b,c,x]

gsl_sf_hyperg_2F1_conj
Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c) Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x]

gsl_sf_hyperg_2F1_renorm
Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c) Renormalized Gauss hypergeometric function 2F1[a,b,c,x] / Gamma[c]

gsl_sf_hyperg_2F1_conj_renorm
Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c) Renormalized Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x] / Gamma[c]

gsl_sf_hyperg_2F0
Signature: (double x(); double [o]y(); double [o]e(); double a; double b) 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) This file copyright (C) 1999 Christian Pellegrin <chri@infis.univ.trieste.it> All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation under certain conditions. For details, see the file COPYING in the PDL distribution. If this file is separated from the PDL distribution, the copyright notice should be included in the file. The GSL SF modules were written by G. Jungman.