NAME

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

DESCRIPTION

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

SYNOPSIS

FUNCTIONS

   gsl_sf_ellint_Kcomp
         Signature: (double k(); double [o]y(); double [o]e())

       Legendre form of complete elliptic integrals K(k) = Integral[1/Sqrt[1 - k^2 Sin[t]^2], {t,
       0, Pi/2}].

       gsl_sf_ellint_Kcomp 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.

   gsl_sf_ellint_Ecomp
         Signature: (double k(); double [o]y(); double [o]e())

       Legendre form of complete elliptic integrals E(k) = Integral[  Sqrt[1 - k^2 Sin[t]^2], {t,
       0, Pi/2}]

       gsl_sf_ellint_Ecomp 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.

   gsl_sf_ellint_F
         Signature: (double phi(); double k(); double [o]y(); double [o]e())

       Legendre form of incomplete elliptic integrals F(phi,k)   = Integral[1/Sqrt[1 - k^2
       Sin[t]^2], {t, 0, phi}]

       gsl_sf_ellint_F 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.

   gsl_sf_ellint_E
         Signature: (double phi(); double k(); double [o]y(); double [o]e())

       Legendre form of incomplete elliptic integrals E(phi,k)   = Integral[  Sqrt[1 - k^2
       Sin[t]^2], {t, 0, phi}]

       gsl_sf_ellint_E 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.

   gsl_sf_ellint_P
         Signature: (double phi(); double k(); double n();
                     double [o]y(); double [o]e())

       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}]

       gsl_sf_ellint_P 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.

   gsl_sf_ellint_D
         Signature: (double phi(); double k(); double n();
                     double [o]y(); double [o]e())

       Legendre form of incomplete elliptic integrals D(phi,k,n)

       gsl_sf_ellint_D 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.

   gsl_sf_ellint_RC
         Signature: (double x(); double yy(); double [o]y(); double [o]e())

       Carlsons symmetric basis of functions RC(x,y)   = 1/2 Integral[(t+x)^(-1/2) (t+y)^(-1)],
       {t,0,Inf}

       gsl_sf_ellint_RC 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.

   gsl_sf_ellint_RD
         Signature: (double x(); double yy(); double z(); double [o]y(); double [o]e())

       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}]

       gsl_sf_ellint_RD 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.

   gsl_sf_ellint_RF
         Signature: (double x(); double yy(); double z(); double [o]y(); double [o]e())

       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}]

       gsl_sf_ellint_RF 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.

   gsl_sf_ellint_RJ
         Signature: (double x(); double yy(); double z(); double p(); double [o]y(); double [o]e())

       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}]

       gsl_sf_ellint_RJ 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.

AUTHOR

       This file copyright (C) 1999 Christian Pellegrin <chri@infis.univ.trieste.it>, 2002
       Christian Soeller.  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.