pp_addpm({At=>Top},<<'EOD');
=head1 NAME

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

=head1 DESCRIPTION

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

=head1 SYNOPSIS

=cut


EOD

# PP interface to GSL

pp_addhdr('
#include <gsl/gsl_sf.h>
#include "../gslerr.h"
');

pp_def('gsl_sf_hyperg_0F1',
       GenericTypes => [D],
       OtherPars =>'double c',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_hyperg_0F1_e,($COMP(c), $x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'/* 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])'
      );

pp_def('gsl_sf_hyperg_1F1',
       GenericTypes => [D],
       OtherPars =>'double a; double b',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_hyperg_1F1_e,($COMP(a),$COMP(b), $x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'Confluent hypergeometric function  for integer parameters. 1F1[a,b,x] = M(a,b,x)'
      );

pp_def('gsl_sf_hyperg_U',
       GenericTypes => [D],
       OtherPars =>'double a; double b',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_hyperg_U_e,($COMP(a),$COMP(b), $x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'Confluent hypergeometric function  for integer parameters. U(a,b,x)'
      );

pp_def('gsl_sf_hyperg_2F1',
       GenericTypes => [D],
       OtherPars =>'double a; double b; double c',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_hyperg_2F1_e,($COMP(a),$COMP(b), $COMP(c),$x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'Confluent hypergeometric function  for integer parameters. 2F1[a,b,c,x]'
      );

pp_def('gsl_sf_hyperg_2F1_conj',
       GenericTypes => [D],
       OtherPars =>'double a; double b; double c',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_hyperg_2F1_conj_e,($COMP(a),$COMP(b), $COMP(c),$x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x]'
      );

pp_def('gsl_sf_hyperg_2F1_renorm',
       GenericTypes => [D],
       OtherPars =>'double a; double b; double c',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_hyperg_2F1_renorm_e,($COMP(a),$COMP(b), $COMP(c),$x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'Renormalized Gauss hypergeometric function 2F1[a,b,c,x] / Gamma[c]'
      );

pp_def('gsl_sf_hyperg_2F1_conj_renorm',
       GenericTypes => [D],
       OtherPars =>'double a; double b; double c',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_hyperg_2F1_conj_renorm_e,($COMP(a),$COMP(b), $COMP(c),$x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'Renormalized Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x] / Gamma[c]'
      );

pp_def('gsl_sf_hyperg_2F0',
       GenericTypes => [D],
       OtherPars =>'double a; double b',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_hyperg_2F0_e,($COMP(a),$COMP(b), $x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'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)'
      );


pp_addpm({At=>Bot},<<'EOD');

=head1 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.

=cut


EOD

pp_done();