1LEGENDRE(3)           User Contributed Perl Documentation          LEGENDRE(3)
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NAME

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

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

13   gsl_sf_legendre_Pl
14         Signature: (double x(); double [o]y(); double [o]e(); int l)
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16       P_l(x)
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18       gsl_sf_legendre_Pl does not process bad values.  It will set the bad-
19       value flag of all output ndarrays if the flag is set for any of the
20       input ndarrays.
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22   gsl_sf_legendre_Pl_array
23         Signature: (double x(); double [o]y(num); int l=>num)
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25       P_l(x) from 0 to n-1.
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27       gsl_sf_legendre_Pl_array does not process bad values.  It will set the
28       bad-value flag of all output ndarrays if the flag is set for any of the
29       input ndarrays.
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31   gsl_sf_legendre_Ql
32         Signature: (double x(); double [o]y(); double [o]e(); int l)
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34       Q_l(x)
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36       gsl_sf_legendre_Ql does not process bad values.  It will set the bad-
37       value flag of all output ndarrays if the flag is set for any of the
38       input ndarrays.
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40   gsl_sf_legendre_Plm
41         Signature: (double x(); double [o]y(); double [o]e(); int l; int m)
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43       P_lm(x)
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45       gsl_sf_legendre_Plm does not process bad values.  It will set the bad-
46       value flag of all output ndarrays if the flag is set for any of the
47       input ndarrays.
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49   gsl_sf_legendre_array
50         Signature: (double x(); double [o]y(n); double [t]work(wn); char norm;  int lmax; int csphase)
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52       Calculate all normalized associated Legendre polynomials.
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54       $Plm = gsl_sf_legendre_array($x,'P',4,-1);
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56       The calculation is done for degree 0 <= l <= lmax and order 0 <= m <= l
57       on the range abs(x)<=1.
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59       The parameter norm should be:
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61       'S' for Schmidt semi-normalized associated Legendre polynomials
62       S_l^m(x),
63       'Y' for spherical harmonic associated Legendre polynomials Y_l^m(x), or
64       'N' for fully normalized associated Legendre polynomials N_l^m(x).
65       'P' (or any other) for unnormalized associated Legendre polynomials
66       P_l^m(x),
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68       lmax is the maximum degree l.  csphase should be (-1) to INCLUDE the
69       Condon-Shortley phase factor (-1)^m, or (+1) to EXCLUDE it.
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71       See "gsl_sf_legendre_array_index" to get the value of "l" and "m" in
72       the returned vector.
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74       gsl_sf_legendre_array processes bad values.  It will set the bad-value
75       flag of all output ndarrays if the flag is set for any of the input
76       ndarrays.
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78   gsl_sf_legendre_array_index
79         Signature: (int [o]l(n); int [o]m(n); int lmax)
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81       Calculate the relation between gsl_sf_legendre_arrays index and l and m
82       values.
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84       Note that this function is called differently than the corresponding
85       GSL function, to make it more useful for PDL: here you just input the
86       maximum l (lmax) that was used in "gsl_sf_legendre_array" and it
87       calculates all l and m values.
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89       gsl_sf_legendre_array_index does not process bad values.  It will set
90       the bad-value flag of all output ndarrays if the flag is set for any of
91       the input ndarrays.
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93   gsl_sf_legendre_sphPlm
94         Signature: (double x(); double [o]y(); double [o]e(); int l; int m)
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96       P_lm(x), normalized properly for use in spherical harmonics
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98       gsl_sf_legendre_sphPlm does not process bad values.  It will set the
99       bad-value flag of all output ndarrays if the flag is set for any of the
100       input ndarrays.
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102   gsl_sf_conicalP_half
103         Signature: (double x(); double [o]y(); double [o]e(); double lambda)
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105       Irregular Spherical Conical Function P^{1/2}_{-1/2 + I lambda}(x)
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107       gsl_sf_conicalP_half does not process bad values.  It will set the bad-
108       value flag of all output ndarrays if the flag is set for any of the
109       input ndarrays.
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111   gsl_sf_conicalP_mhalf
112         Signature: (double x(); double [o]y(); double [o]e(); double lambda)
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114       Regular Spherical Conical Function P^{-1/2}_{-1/2 + I lambda}(x)
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116       gsl_sf_conicalP_mhalf does not process bad values.  It will set the
117       bad-value flag of all output ndarrays if the flag is set for any of the
118       input ndarrays.
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120   gsl_sf_conicalP_0
121         Signature: (double x(); double [o]y(); double [o]e(); double lambda)
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123       Conical Function P^{0}_{-1/2 + I lambda}(x)
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125       gsl_sf_conicalP_0 does not process bad values.  It will set the bad-
126       value flag of all output ndarrays if the flag is set for any of the
127       input ndarrays.
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129   gsl_sf_conicalP_1
130         Signature: (double x(); double [o]y(); double [o]e(); double lambda)
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132       Conical Function P^{1}_{-1/2 + I lambda}(x)
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134       gsl_sf_conicalP_1 does not process bad values.  It will set the bad-
135       value flag of all output ndarrays if the flag is set for any of the
136       input ndarrays.
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138   gsl_sf_conicalP_sph_reg
139         Signature: (double x(); double [o]y(); double [o]e(); int l; double lambda)
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141       Regular Spherical Conical Function P^{-1/2-l}_{-1/2 + I lambda}(x)
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143       gsl_sf_conicalP_sph_reg does not process bad values.  It will set the
144       bad-value flag of all output ndarrays if the flag is set for any of the
145       input ndarrays.
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147   gsl_sf_conicalP_cyl_reg_e
148         Signature: (double x(); double [o]y(); double [o]e(); int m; double lambda)
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150       Regular Cylindrical Conical Function P^{-m}_{-1/2 + I lambda}(x)
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152       gsl_sf_conicalP_cyl_reg_e does not process bad values.  It will set the
153       bad-value flag of all output ndarrays if the flag is set for any of the
154       input ndarrays.
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156   gsl_sf_legendre_H3d
157         Signature: (double [o]y(); double [o]e(); int l; double lambda; double eta)
158
159       lth radial eigenfunction of the Laplacian on the 3-dimensional
160       hyperbolic space.
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162       gsl_sf_legendre_H3d does not process bad values.  It will set the bad-
163       value flag of all output ndarrays if the flag is set for any of the
164       input ndarrays.
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166   gsl_sf_legendre_H3d_array
167         Signature: (double [o]y(num); int l=>num; double lambda; double eta)
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169       Array of H3d(ell), for l from 0 to n-1.
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171       gsl_sf_legendre_H3d_array does not process bad values.  It will set the
172       bad-value flag of all output ndarrays if the flag is set for any of the
173       input ndarrays.
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AUTHOR

176       This file copyright (C) 1999 Christian Pellegrin
177       <chri@infis.univ.trieste.it> All rights reserved. There is no warranty.
178       You are allowed to redistribute this software / documentation under
179       certain conditions. For details, see the file COPYING in the PDL
180       distribution. If this file is separated from the PDL distribution, the
181       copyright notice should be included in the file.
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183       The GSL SF modules were written by G. Jungman.
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187perl v5.36.0                      2023-01-20                       LEGENDRE(3)
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