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pp_addpm({At=>Top},<<'EOD');
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PDL::GSLSF::ELLINT - PDL interface to GSL Special Functions
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This is an interface to the Special Function package present in the GNU Scientific Library.
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#include <gsl/gsl_sf.h>
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#include "../gslerr.h"
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pp_def('gsl_sf_ellint_Kcomp',
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Pars=>'double k(); double [o]y(); double [o]e()',
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GSLERR(gsl_sf_ellint_Kcomp_e,($k(),GSL_PREC_DOUBLE,&r))
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Doc =>'Legendre form of complete elliptic integrals K(k) = Integral[1/Sqrt[1 - k^2 Sin[t]^2], {t, 0, Pi/2}].'
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pp_def('gsl_sf_ellint_Ecomp',
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Pars=>'double k(); double [o]y(); double [o]e()',
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GSLERR(gsl_sf_ellint_Ecomp_e,($k(),GSL_PREC_DOUBLE,&r))
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Doc =>'Legendre form of complete elliptic integrals E(k) = Integral[ Sqrt[1 - k^2 Sin[t]^2], {t, 0, Pi/2}]'
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pp_def('gsl_sf_ellint_F',
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Pars=>'double phi(); double k(); double [o]y(); double [o]e()',
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GSLERR(gsl_sf_ellint_F_e,($phi(),$k(),GSL_PREC_DOUBLE,&r))
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Doc =>'Legendre form of incomplete elliptic integrals F(phi,k) = Integral[1/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]'
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pp_def('gsl_sf_ellint_E',
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Pars=>'double phi(); double k(); double [o]y(); double [o]e()',
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GSLERR(gsl_sf_ellint_E_e,($phi(),$k(),GSL_PREC_DOUBLE,&r))
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Doc =>'Legendre form of incomplete elliptic integrals E(phi,k) = Integral[ Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]'
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pp_def('gsl_sf_ellint_P',
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Pars=>'double phi(); double k(); double n();
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double [o]y(); double [o]e()',
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GSLERR(gsl_sf_ellint_P_e,($phi(),$k(),$n(),GSL_PREC_DOUBLE,&r))
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Doc =>'Legendre form of incomplete elliptic integrals P(phi,k,n) = Integral[(1 + n Sin[t]^2)^(-1)/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]'
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pp_def('gsl_sf_ellint_D',
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Pars=>'double phi(); double k(); double n();
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double [o]y(); double [o]e()',
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GSLERR(gsl_sf_ellint_D_e,($phi(),$k(),$n(),GSL_PREC_DOUBLE,&r))
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Doc =>'Legendre form of incomplete elliptic integrals D(phi,k,n)'
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pp_def('gsl_sf_ellint_RC',
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Pars=>'double x(); double yy(); double [o]y(); double [o]e()',
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GSLERR(gsl_sf_ellint_RC_e,($x(),$yy(),GSL_PREC_DOUBLE,&r))
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Doc =>'Carlsons symmetric basis of functions RC(x,y) = 1/2 Integral[(t+x)^(-1/2) (t+y)^(-1)], {t,0,Inf}'
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pp_def('gsl_sf_ellint_RD',
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Pars=>'double x(); double yy(); double z(); double [o]y(); double [o]e()',
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GSLERR(gsl_sf_ellint_RD_e,($x(),$yy(),$z(),GSL_PREC_DOUBLE,&r))
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Doc =>'Carlsons symmetric basis of functions RD(x,y,z) = 3/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-3/2), {t,0,Inf}]'
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pp_def('gsl_sf_ellint_RF',
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Pars=>'double x(); double yy(); double z(); double [o]y(); double [o]e()',
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GSLERR(gsl_sf_ellint_RF_e,($x(),$yy(),$z(),GSL_PREC_DOUBLE,&r))
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Doc =>'Carlsons symmetric basis of functions RF(x,y,z) = 1/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2), {t,0,Inf}]'
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pp_def('gsl_sf_ellint_RJ',
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Pars=>'double x(); double yy(); double z(); double p(); double [o]y(); double [o]e()',
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GSLERR(gsl_sf_ellint_RJ_e,($x(),$yy(),$z(),$p(),GSL_PREC_DOUBLE,&r))
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Doc =>'Carlsons symmetric basis of functions RJ(x,y,z,p) = 3/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2) (t+p)^(-1), {t,0,Inf}]'
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pp_addpm({At=>Bot},<<'EOD');
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This file copyright (C) 1999 Christian Pellegrin <chri@infis.univ.trieste.it>,
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2002 Christian Soeller.
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All rights reserved. There
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is no warranty. You are allowed to redistribute this software /
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documentation under certain conditions. For details, see the file
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COPYING in the PDL distribution. If this file is separated from the
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PDL distribution, the copyright notice should be included in the file.
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The GSL SF modules were written by G. Jungman.