HYPERG

NAME

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

DESCRIPTION

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

SYNOPSIS

Functions

FUNCTIONS

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)

AUTHOR

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.