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 '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),
67 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.
70 See "gsl_sf_legendre_array_index" to get the value of "l" and "m" in
72 the returned vector.
73 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.
77 gsl_sf_legendre_array_index
79 Signature: (int [o]l(n); int [o]m(n); int lmax)
80 Calculate the relation between gsl_sf_legendre_arrays index and l and m
82 values.
83 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.
88 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.
92 gsl_sf_legendre_sphPlm
94 Signature: (double x(); double [o]y(); double [o]e(); int l; int m)
95 P_lm(x), normalized properly for use in spherical harmonics
97 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.
101 gsl_sf_conicalP_half
103 Signature: (double x(); double [o]y(); double [o]e(); double lambda)
104 Irregular Spherical Conical Function P^{1/2}_{-1/2 + I lambda}(x)
106 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.
110 gsl_sf_conicalP_mhalf
112 Signature: (double x(); double [o]y(); double [o]e(); double lambda)
113 Regular Spherical Conical Function P^{-1/2}_{-1/2 + I lambda}(x)
115 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.
119 gsl_sf_conicalP_0
121 Signature: (double x(); double [o]y(); double [o]e(); double lambda)
122 Conical Function P^{0}_{-1/2 + I lambda}(x)
124 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.
128 gsl_sf_conicalP_1
130 Signature: (double x(); double [o]y(); double [o]e(); double lambda)
131 Conical Function P^{1}_{-1/2 + I lambda}(x)
133 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.
137 gsl_sf_conicalP_sph_reg
139 Signature: (double x(); double [o]y(); double [o]e(); int l; double lambda)
140 Regular Spherical Conical Function P^{-1/2-l}_{-1/2 + I lambda}(x)
142 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.
146 gsl_sf_conicalP_cyl_reg_e
148 Signature: (double x(); double [o]y(); double [o]e(); int m; double lambda)
149 Regular Cylindrical Conical Function P^{-m}_{-1/2 + I lambda}(x)
151 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.
155 gsl_sf_legendre_H3d
157 Signature: (double [o]y(); double [o]e(); int l; double lambda; double eta)
158 lth radial eigenfunction of the Laplacian on the 3-dimensional
160 hyperbolic space.
161 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.
165 gsl_sf_legendre_H3d_array
167 Signature: (double [o]y(num); int l=>num; double lambda; double eta)
168 Array of H3d(ell), for l from 0 to n-1.
170 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.
174
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.
182 The GSL SF modules were written by G. Jungman.
184perl v5.38.0 2023-07-21 LEGENDRE(3)