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.

FUNCTIONS

  gsl_sf_legendre_Pl
  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 ndarrays if the flag is set for any of the input ndarrays.

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

  gsl_sf_legendre_Ql
  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 ndarrays if the flag is set for any of the input ndarrays.

  gsl_sf_legendre_Plm
  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 ndarrays if the flag is set for any of the input ndarrays.

  gsl_sf_legendre_array
  Signature: (double x(); double [o]y(n=CALC($COMP(lmax)*($COMP(lmax)+1)/2+$COMP(lmax)+1)); double [t]work(wn=CALC(gsl_sf_legendre_array_n($COMP(lmax)))); char norm;  int lmax; int csphase)

Calculate all normalized associated Legendre polynomials.

$Plm = gsl_sf_legendre_array($x,'P',4,-1);

The calculation is done for degree 0 <= l <= lmax and order 0 <= m <= l on the range abs(x)<=1.

The parameter norm should be:

'S' for Schmidt semi-normalized associated Legendre polynomials S_l^m(x),
'Y' for spherical harmonic associated Legendre polynomials Y_l^m(x), or
'N' for fully normalized associated Legendre polynomials N_l^m(x).
'P' (or any other) for unnormalized associated Legendre polynomials P_l^m(x),

lmax is the maximum degree l. csphase should be (-1) to INCLUDE the Condon-Shortley phase factor (-1)^m, or (+1) to EXCLUDE it.

See "gsl_sf_legendre_array_index" to get the value of "l" and "m" in the returned vector.

gsl_sf_legendre_array processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  gsl_sf_legendre_array_index
  Signature: (int [o]l(n=CALC($COMP(lmax)*($COMP(lmax)+1)/2+$COMP(lmax)+1)); int [o]m(n); int lmax)

Calculate the relation between gsl_sf_legendre_arrays index and l and m values.

Note that this function is called differently than the corresponding GSL function, to make it more useful for PDL: here you just input the maximum l (lmax) that was used in "gsl_sf_legendre_array" and it calculates all l and m values.

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

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

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

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

  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_0 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  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_1 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

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

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

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

  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.

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

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.