PDL::GSLSF::ELLINT - PDL interface to GSL Special Functions This is an interface to the Special Function package present in the GNU Scientific Library.

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}] 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.