LEGENDRE

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.

Index

NAME
DESCRIPTION
SYNOPSIS
Functions
FUNCTIONS
gsl_sf_legendre_Pl
gsl_sf_legendre_Pl_array
gsl_sf_legendre_Ql
gsl_sf_legendre_Plm
gsl_sf_legendre_Plm_array
gsl_sf_legendre_sphPlm
gsl_sf_legendre_sphPlm_array
gsl_sf_conicalP_half
gsl_sf_conicalP_mhalf
gsl_sf_conicalP_0
gsl_sf_conicalP_1
gsl_sf_conicalP_sph_reg
gsl_sf_conicalP_cyl_reg_e
gsl_sf_legendre_H3d
gsl_sf_legendre_H3d_array
AUTHOR