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

PDL::GSLSF::LEGENDRE - 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_legendre_Pl',
       GenericTypes => [D],
       OtherPars =>'int l',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_legendre_Pl_e,($COMP(l),$x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'P_l(x)'
      );

pp_def('gsl_sf_legendre_Pl_array',
       GenericTypes => [D],
       OtherPars =>'int l=>num',
       Pars=>'double x(); double [o]y(num)',
       Code =>'
GSLERR(gsl_sf_legendre_Pl_array,($COMP(l)-1,$x(),$P(y)))
',
       Doc =>'P_l(x) from 0 to n-1.'
      );

pp_def('gsl_sf_legendre_Ql',
       GenericTypes => [D],
       OtherPars =>'int l',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_legendre_Ql_e,($COMP(l),$x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'Q_l(x)'
      );

pp_def('gsl_sf_legendre_Plm',
       GenericTypes => [D],
       OtherPars =>'int l; int m',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_legendre_Plm_e,($COMP(l),$COMP(m),$x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'P_lm(x)'
      );

pp_def('gsl_sf_legendre_Plm_array',
       GenericTypes => [D],
       OtherPars =>'int l=>num; int m',
       Pars=>'double x(); double [o]y(num)',
       Code =>'
GSLERR(gsl_sf_legendre_Plm_array,($COMP(l)-2+$COMP(m),$COMP(m),$x(),$P(y)))
',
       Doc =>'P_lm(x) for l from 0 to n-2+m.'
      );

pp_def('gsl_sf_legendre_sphPlm',
       GenericTypes => [D],
       OtherPars =>'int l; int m',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_legendre_sphPlm_e,($COMP(l),$COMP(m),$x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'P_lm(x), normalized properly for use in spherical harmonics'
      );

pp_def('gsl_sf_legendre_sphPlm_array',
       GenericTypes => [D],
       OtherPars =>'int n=>num; int m',
       Pars=>'double x(); double [o]y(num)',
       Code =>'
GSLERR(gsl_sf_legendre_sphPlm_array,($COMP(n)-2+$COMP(m),$COMP(m),$x(),$P(y)))
',
       Doc =>'P_lm(x), normalized properly for use in spherical harmonics for l from 0 to n-2+m.'
      );

pp_def('gsl_sf_conicalP_half',
       GenericTypes => [D],
       OtherPars =>'double lambda',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_conicalP_half_e,($COMP(lambda),$x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'Irregular Spherical Conical Function P^{1/2}_{-1/2 + I lambda}(x)'
      );

pp_def('gsl_sf_conicalP_mhalf',
       GenericTypes => [D],
       OtherPars =>'double lambda',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_conicalP_mhalf_e,($COMP(lambda),$x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'Regular Spherical Conical Function P^{-1/2}_{-1/2 + I lambda}(x)'
      );

pp_def('gsl_sf_conicalP_0',
       GenericTypes => [D],
       OtherPars =>'double lambda',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_conicalP_0_e,($COMP(lambda),$x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'Conical Function P^{0}_{-1/2 + I lambda}(x)'
      );

pp_def('gsl_sf_conicalP_1',
       GenericTypes => [D],
       OtherPars =>'double lambda',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_conicalP_1_e,($COMP(lambda),$x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'Conical Function P^{1}_{-1/2 + I lambda}(x)'
      );

pp_def('gsl_sf_conicalP_sph_reg',
       GenericTypes => [D],
       OtherPars =>'int l; double lambda',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_conicalP_sph_reg_e,($COMP(l),$COMP(lambda),$x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'Regular Spherical Conical Function P^{-1/2-l}_{-1/2 + I lambda}(x)'
      );

pp_def('gsl_sf_conicalP_cyl_reg_e',
       GenericTypes => [D],
       OtherPars =>'int m; double lambda',
       Pars=>'double x(); double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_conicalP_cyl_reg_e,($COMP(m),$COMP(lambda),$x(),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'Regular Cylindrical Conical Function P^{-m}_{-1/2 + I lambda}(x)'
      );

pp_def('gsl_sf_legendre_H3d',
       GenericTypes => [D],
       OtherPars =>'int l; double lambda; double eta',
       Pars=>'double [o]y(); double [o]e()',
       Code =>'
gsl_sf_result r;
GSLERR(gsl_sf_legendre_H3d_e,($COMP(l),$COMP(lambda),$COMP(eta),&r))
$y() = r.val;
$e() = r.err; 
',
       Doc =>'lth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space.'
      );

pp_def('gsl_sf_legendre_H3d_array',
       GenericTypes => [D],
       OtherPars =>'int l=>num; double lambda; double eta',
       Pars=>'double [o]y(num)',
       Code =>'
GSLERR(gsl_sf_legendre_H3d_array,($COMP(l)-1,$COMP(lambda),$COMP(eta),$P(y)))
',
       Doc =>'Array of H3d(ell), for l from 0 to n-1.'
      );

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();