# RedHat 9 (Linux i386) - man page for pdl::gslsf::ellint (redhat section 3)

```ELLINT(3)						User Contributed Perl Documentation						 ELLINT(3)

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
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.

perl v5.8.0							    2003-01-29								 ELLINT(3)```