PDL::GSLSF::ELLINT (3)

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NAME

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

DESCRIPTION

This is an interface to the Special Function package present in the 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 [o]y(); double [o]e())

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

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

(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

(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

(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

(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 in the distribution. If this file is separated from the distribution, the copyright notice should be included in the file.

The

modules were written by G. Jungman.