pdl::gslsf::ellint(3) [redhat man page]

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

       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.

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

LEGENDRE(3)						User Contributed Perl Documentation					       LEGENDRE(3)

NAME

       PDL::GSLSF::LEGENDRE - 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_legendre_Pl

	 Signature: (double x(); double [o]y(); double [o]e(); int l)

       P_l(x)

       gsl_sf_legendre_Pl_array

	 Signature: (double x(); double [o]y(num); int l=>num)

       P_l(x) from 0 to n-1.

       gsl_sf_legendre_Ql

	 Signature: (double x(); double [o]y(); double [o]e(); int l)

       Q_l(x)

       gsl_sf_legendre_Plm

	 Signature: (double x(); double [o]y(); double [o]e(); int l; int m)

       P_lm(x)

       gsl_sf_legendre_Plm_array

	 Signature: (double x(); double [o]y(num); int l=>num; int m)

       P_lm(x) for l from 0 to n-2+m.

       gsl_sf_legendre_sphPlm

	 Signature: (double x(); double [o]y(); double [o]e(); int l; int m)

       P_lm(x), normalized properly for use in spherical harmonics

       gsl_sf_legendre_sphPlm_array

	 Signature: (double x(); double [o]y(num); int n=>num; int m)

       P_lm(x), normalized properly for use in spherical harmonics for l from 0 to n-2+m.

       gsl_sf_conicalP_half

	 Signature: (double x(); double [o]y(); double [o]e(); double lambda)

       Irregular Spherical Conical Function P^{1/2}_{-1/2 + I lambda}(x)

       gsl_sf_conicalP_mhalf

	 Signature: (double x(); double [o]y(); double [o]e(); double lambda)

       Regular Spherical Conical Function P^{-1/2}_{-1/2 + I lambda}(x)

       gsl_sf_conicalP_0

	 Signature: (double x(); double [o]y(); double [o]e(); double lambda)

       Conical Function P^{0}_{-1/2 + I lambda}(x)

       gsl_sf_conicalP_1

	 Signature: (double x(); double [o]y(); double [o]e(); double lambda)

       Conical Function P^{1}_{-1/2 + I lambda}(x)

       gsl_sf_conicalP_sph_reg

	 Signature: (double x(); double [o]y(); double [o]e(); int l; double lambda)

       Regular Spherical Conical Function P^{-1/2-l}_{-1/2 + I lambda}(x)

       gsl_sf_conicalP_cyl_reg_e

	 Signature: (double x(); double [o]y(); double [o]e(); int m; double lambda)

       Regular Cylindrical Conical Function P^{-m}_{-1/2 + I lambda}(x)

       gsl_sf_legendre_H3d

	 Signature: (double [o]y(); double [o]e(); int l; double lambda; double eta)

       lth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space.

       gsl_sf_legendre_H3d_array

	 Signature: (double [o]y(num); int l=>num; double lambda; double eta)

       Array of H3d(ell), for l from 0 to n-1.

AUTHOR

       This file copyright (C) 1999 Christian Pellegrin <chri@infis.univ.trieste.it> 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.

perl v5.8.0							    2003-01-29							       LEGENDRE(3)