PDL::GSLSF::ELLINT - PDL interface to GSL Special Functions
This is an interface to the Special Function package present in the GNU Scientific Library.
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}].
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}]
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}]
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}]
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}]
Signature: (double phi(); double k(); double n(); double [o]y(); double [o]e())
Legendre form of incomplete elliptic integrals D(phi,k,n)
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}
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}]
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}]
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.