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

PDL::GSLSF::GAMMA - 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

=head1 Functions

=cut
EOD

# PP interface to GSL

pp_addhdr('
#include <gsl/gsl_sf.h>

#include "../gslerr.h"

');

pp_def('gsl_sf_lngamma',
       GenericTypes => [D],
       Pars=>'double x(); double [o]y(); double [o]s(); double [o]e()',
       Code =>'
gsl_sf_result r;
double sgn;
GSLERR(gsl_sf_lngamma_sgn_e,($x(),&r,&sgn))
$y() = r.val;
$e() = r.err; 
$s() = sgn;
',
       Doc =>'Log[Gamma(x)], x not a negative integer Uses real Lanczos method. Determines the sign of Gamma[x] as well as Log[|Gamma[x]|] for x < 0. So Gamma[x] = sgn * Exp[result_lg].'
      );

pp_def('gsl_sf_gamma',
       GenericTypes => [D],
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_gamma_e,($x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'Gamma(x), x not a negative integer'
      );

pp_def('gsl_sf_gammastar',
       GenericTypes => [D],
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_gammastar_e,($x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'Regulated Gamma Function, x > 0 Gamma^*(x) = Gamma(x)/(Sqrt[2Pi] x^(x-1/2) exp(-x)) = (1 + 1/(12x) + ...),  x->Inf'
      );

pp_def('gsl_sf_gammainv',
       GenericTypes => [D],
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_gammainv_e,($x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'1/Gamma(x)'
      );

pp_def('gsl_sf_lngamma_complex',
       GenericTypes => [D],
       Pars=>'double zr(); double zi(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye()',
       Code =>'
gsl_sf_result r;
gsl_sf_result ri;
GSLERR(gsl_sf_lngamma_complex_e,($zr(),$zi(),&r,&ri))
$x() = r.val;
$xe() = r.err; 
$y() = ri.val;
$ye() = ri.err; 
',
       Doc =>'Log[Gamma(z)] for z complex, z not a negative integer. Calculates: lnr = log|Gamma(z)|, arg = arg(Gamma(z))  in (-Pi, Pi]'
      );

pp_def('gsl_sf_taylorcoeff',
       GenericTypes => [D],
       OtherPars => 'int n',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_taylorcoeff_e,($COMP(n),$x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'x^n / n!'
      );

pp_def('gsl_sf_fact',
       GenericTypes => [L],
       Pars=>'x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_fact_e,($x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'n!'
      );

pp_def('gsl_sf_doublefact',
       GenericTypes => [L],
       Pars=>'x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_doublefact_e,($x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'n!! = n(n-2)(n-4)'
      );

pp_def('gsl_sf_lnfact',
       GenericTypes => [L],
       Pars=>'x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_lnfact_e,($x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'ln n!'
      );

pp_def('gsl_sf_lndoublefact',
       GenericTypes => [L],
       Pars=>'x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_lndoublefact_e,($x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'ln n!!'
      );

pp_def('gsl_sf_lnchoose',
       GenericTypes => [L],
       Pars=>'n(); m(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_lnchoose_e,($n(), $m(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'log(n choose m)'
      );

pp_def('gsl_sf_choose',
       GenericTypes => [L],
       Pars=>'n(); m(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_choose_e,($n(), $m(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'n choose m'
      );

pp_def('gsl_sf_lnpoch',
       GenericTypes => [D],
       OtherPars => 'double a',
       Pars=>'double x(); double [o]y(); double [o]s(); double [o]e()',
       Code =>'
gsl_sf_result r;
double sgn;
GSLERR(gsl_sf_lnpoch_sgn_e,($COMP(a),$x(),&r,&sgn))
$y() = r.val;
$e() = r.err; 
$s() = sgn;
',
       Doc =>'Logarithm of Pochammer (Apell) symbol, with sign information. result = log( |(a)_x| ), sgn    = sgn( (a)_x ) where (a)_x := Gamma[a + x]/Gamma[a]'
      );

pp_def('gsl_sf_poch',
       GenericTypes => [D],
       OtherPars => 'double a',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_poch_e,($COMP(a),$x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'Pochammer (Apell) symbol (a)_x := Gamma[a + x]/Gamma[x]'
      );

pp_def('gsl_sf_pochrel',
       GenericTypes => [D],
       OtherPars => 'double a',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_pochrel_e,($COMP(a),$x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'Relative Pochammer (Apell) symbol ((a,x) - 1)/x where (a,x) = (a)_x := Gamma[a + x]/Gamma[a]'
      );

pp_def('gsl_sf_gamma_inc_Q',
       GenericTypes => [D],
       OtherPars => 'double a',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_gamma_inc_Q_e,($COMP(a),$x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'Normalized Incomplete Gamma Function Q(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,x,Infinity} ]'
      );

pp_def('gsl_sf_gamma_inc_P',
       GenericTypes => [D],
       OtherPars => 'double a',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_gamma_inc_P_e,($COMP(a),$x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'Complementary Normalized Incomplete Gamma Function P(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,0,x} ]'
      );

pp_def('gsl_sf_lnbeta',
       GenericTypes => [D],
       Pars=>'double a(); double b(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_lnbeta_e,($a(),$b(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'Logarithm of Beta Function Log[B(a,b)]'
      );

pp_def('gsl_sf_beta',
       GenericTypes => [D],
	OtherPars => '',
       Pars=>'double a(); double b();double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_beta_e,($a(),$b(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'Beta Function B(a,b)'
      );

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();