1HYPERG(3)             User Contributed Perl Documentation            HYPERG(3)
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NAME

6       PDL::GSLSF::HYPERG - PDL interface to GSL Special Functions
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DESCRIPTION

9       This is an interface to the Special Function package present in the GNU
10       Scientific Library.
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SYNOPSIS

Functions

FUNCTIONS

15       gsl_sf_hyperg_0F1
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17         Signature: (double x(); double [o]y(); double [o]e(); double c)
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19       /* Hypergeometric function related to Bessel functions 0F1[c,x] =
20       Gamma[c]    x^(1/2(1-c)) I_{c-1}(2 Sqrt[x]) Gamma[c] (-x)^(1/2(1-c))
21       J_{c-1}(2 Sqrt[-x])
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23       gsl_sf_hyperg_1F1
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25         Signature: (double x(); double [o]y(); double [o]e(); double a; double b)
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27       Confluent hypergeometric function  for integer parameters. 1F1[a,b,x] =
28       M(a,b,x)
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30       gsl_sf_hyperg_U
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32         Signature: (double x(); double [o]y(); double [o]e(); double a; double b)
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34       Confluent hypergeometric function  for integer parameters. U(a,b,x)
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36       gsl_sf_hyperg_2F1
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38         Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)
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40       Confluent hypergeometric function  for integer parameters. 2F1[a,b,c,x]
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42       gsl_sf_hyperg_2F1_conj
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44         Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)
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46       Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x]
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48       gsl_sf_hyperg_2F1_renorm
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50         Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)
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52       Renormalized Gauss hypergeometric function 2F1[a,b,c,x] / Gamma[c]
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54       gsl_sf_hyperg_2F1_conj_renorm
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56         Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)
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58       Renormalized Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c,
59       x] / Gamma[c]
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61       gsl_sf_hyperg_2F0
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63         Signature: (double x(); double [o]y(); double [o]e(); double a; double b)
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65       Mysterious hypergeometric function. The series representation is a
66       divergent hypergeometric series. However, for x < 0 we have 2F0(a,b,x)
67       = (-1/x)^a U(a,1+a-b,-1/x)
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AUTHOR

70       This file copyright (C) 1999 Christian Pellegrin <chri@infis.univ.tri‐
71       este.it> All rights reserved. There is no warranty. You are allowed to
72       redistribute this software / documentation under certain conditions.
73       For details, see the file COPYING in the PDL distribution. If this file
74       is separated from the PDL distribution, the copyright notice should be
75       included in the file.
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77       The GSL SF modules were written by G. Jungman.
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81perl v5.8.8                       2006-12-02                         HYPERG(3)