1LEGENDRE(3) User Contributed Perl Documentation LEGENDRE(3)
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6 PDL::GSLSF::LEGENDRE - PDL interface to GSL Special Functions
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9 This is an interface to the Special Function package present in the GNU
10 Scientific Library.
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13 gsl_sf_legendre_Pl
14 Signature: (double x(); double [o]y(); double [o]e(); int l)
15 P_l(x)
17 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.
21 gsl_sf_legendre_Pl_array
23 Signature: (double x(); double [o]y(num); int l=>num)
24 P_l(x) from 0 to n-1.
26 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.
30 gsl_sf_legendre_Ql
32 Signature: (double x(); double [o]y(); double [o]e(); int l)
33 Q_l(x)
35 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.
39 gsl_sf_legendre_Plm
41 Signature: (double x(); double [o]y(); double [o]e(); int l; int m)
42 P_lm(x)
44 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.
48 gsl_sf_legendre_array
50 Signature: (double x(); double [o]y(n); double [t]work(wn); char norm; int lmax; int csphase)
51 Calculate all normalized associated Legendre polynomials.
53 $Plm = gsl_sf_legendre_array($x,'P',4,-1);
55 The calculation is done for degree 0 <= l <= lmax and order 0 <= m <= l
57 on the range abs(x)<=1.
58 The parameter norm should be:
60 'P' for unnormalized associated Legendre polynomials P_l^m(x),
62 'S' for Schmidt semi-normalized associated Legendre polynomials
63 S_l^m(x),
64 'Y' for spherical harmonic associated Legendre polynomials Y_l^m(x), or
65 'N' for fully normalized associated Legendre polynomials N_l^m(x).
66 lmax is the maximum degree l. csphase should be (-1) to INCLUDE the
68 Condon-Shortley phase factor (-1)^m, or (+1) to EXCLUDE it.
69 See "gsl_sf_legendre_array_index" to get the value of "l" and "m" in
71 the returned vector.
72 gsl_sf_legendre_array processes bad values. It will set the bad-value
74 flag of all output ndarrays if the flag is set for any of the input
75 ndarrays.
76 gsl_sf_legendre_array_index
78 Signature: (int [o]l(n); int [o]m(n); int lmax)
79 Calculate the relation between gsl_sf_legendre_arrays index and l and m
81 values.
82 Note that this function is called differently than the corresponding
84 GSL function, to make it more useful for PDL: here you just input the
85 maximum l (lmax) that was used in "gsl_sf_legendre_array" and it
86 calculates all l and m values.
87 gsl_sf_legendre_array_index does not process bad values. It will set
89 the bad-value flag of all output ndarrays if the flag is set for any of
90 the input ndarrays.
91 gsl_sf_legendre_sphPlm
93 Signature: (double x(); double [o]y(); double [o]e(); int l; int m)
94 P_lm(x), normalized properly for use in spherical harmonics
96 gsl_sf_legendre_sphPlm does not process bad values. It will set the
98 bad-value flag of all output ndarrays if the flag is set for any of the
99 input ndarrays.
100 gsl_sf_conicalP_half
102 Signature: (double x(); double [o]y(); double [o]e(); double lambda)
103 Irregular Spherical Conical Function P^{1/2}_{-1/2 + I lambda}(x)
105 gsl_sf_conicalP_half does not process bad values. It will set the bad-
107 value flag of all output ndarrays if the flag is set for any of the
108 input ndarrays.
109 gsl_sf_conicalP_mhalf
111 Signature: (double x(); double [o]y(); double [o]e(); double lambda)
112 Regular Spherical Conical Function P^{-1/2}_{-1/2 + I lambda}(x)
114 gsl_sf_conicalP_mhalf does not process bad values. It will set the
116 bad-value flag of all output ndarrays if the flag is set for any of the
117 input ndarrays.
118 gsl_sf_conicalP_0
120 Signature: (double x(); double [o]y(); double [o]e(); double lambda)
121 Conical Function P^{0}_{-1/2 + I lambda}(x)
123 gsl_sf_conicalP_0 does not process bad values. It will set the bad-
125 value flag of all output ndarrays if the flag is set for any of the
126 input ndarrays.
127 gsl_sf_conicalP_1
129 Signature: (double x(); double [o]y(); double [o]e(); double lambda)
130 Conical Function P^{1}_{-1/2 + I lambda}(x)
132 gsl_sf_conicalP_1 does not process bad values. It will set the bad-
134 value flag of all output ndarrays if the flag is set for any of the
135 input ndarrays.
136 gsl_sf_conicalP_sph_reg
138 Signature: (double x(); double [o]y(); double [o]e(); int l; double lambda)
139 Regular Spherical Conical Function P^{-1/2-l}_{-1/2 + I lambda}(x)
141 gsl_sf_conicalP_sph_reg does not process bad values. It will set the
143 bad-value flag of all output ndarrays if the flag is set for any of the
144 input ndarrays.
145 gsl_sf_conicalP_cyl_reg_e
147 Signature: (double x(); double [o]y(); double [o]e(); int m; double lambda)
148 Regular Cylindrical Conical Function P^{-m}_{-1/2 + I lambda}(x)
150 gsl_sf_conicalP_cyl_reg_e does not process bad values. It will set the
152 bad-value flag of all output ndarrays if the flag is set for any of the
153 input ndarrays.
154 gsl_sf_legendre_H3d
156 Signature: (double [o]y(); double [o]e(); int l; double lambda; double eta)
157 lth radial eigenfunction of the Laplacian on the 3-dimensional
159 hyperbolic space.
160 gsl_sf_legendre_H3d does not process bad values. It will set the bad-
162 value flag of all output ndarrays if the flag is set for any of the
163 input ndarrays.
164 gsl_sf_legendre_H3d_array
166 Signature: (double [o]y(num); int l=>num; double lambda; double eta)
167 Array of H3d(ell), for l from 0 to n-1.
169 gsl_sf_legendre_H3d_array does not process bad values. It will set the
171 bad-value flag of all output ndarrays if the flag is set for any of the
172 input ndarrays.
173
175 This file copyright (C) 1999 Christian Pellegrin
176 <chri@infis.univ.trieste.it> All rights reserved. There is no warranty.
177 You are allowed to redistribute this software / documentation under
178 certain conditions. For details, see the file COPYING in the PDL
179 distribution. If this file is separated from the PDL distribution, the
180 copyright notice should be included in the file.
181 The GSL SF modules were written by G. Jungman.
183perl v5.34.0 2022-02-28 LEGENDRE(3)