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

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

  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_0F1 does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  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_1F1 does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  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_U does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  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 does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  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_conj does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  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_renorm does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  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_2F1_conj_renorm does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  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)

gsl_sf_hyperg_2F0 does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

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.