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PDL::GSLSF::ELLINT.3pm

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

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_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_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_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_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_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_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_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_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_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}]

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.