PDL::GSLSF::LEGENDRE - PDL interface to GSL Special Functions

This is an interface to the Special Function package present in the GNU Scientific Library.

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

P_l(x)

gsl_sf_legendre_Pl does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

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

P_l(x) from 0 to n-1.

gsl_sf_legendre_Pl_array does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

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

Q_l(x)

gsl_sf_legendre_Ql does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

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

P_lm(x)

gsl_sf_legendre_Plm does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

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

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

gsl_sf_legendre_Plm_array does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  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 does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  Signature: (double x(); double [o]y(n); 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_legendre_sphPlm_array does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  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_half does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  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_mhalf does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

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

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

gsl_sf_conicalP_0 does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

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

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

gsl_sf_conicalP_1 does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  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_sph_reg does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  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_conicalP_cyl_reg_e does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  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 does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

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

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

gsl_sf_legendre_H3d_array does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

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.