/usr/include/gsl/gsl_sf_legendre.h is in libgsl0-dev 1.16+dfsg-1ubuntu1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 | /* specfunc/gsl_sf_legendre.h
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2004 Gerard Jungman
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
/* Author: G. Jungman */
#ifndef __GSL_SF_LEGENDRE_H__
#define __GSL_SF_LEGENDRE_H__
#include <gsl/gsl_sf_result.h>
#undef __BEGIN_DECLS
#undef __END_DECLS
#ifdef __cplusplus
# define __BEGIN_DECLS extern "C" {
# define __END_DECLS }
#else
# define __BEGIN_DECLS /* empty */
# define __END_DECLS /* empty */
#endif
__BEGIN_DECLS
/* P_l(x) l >= 0; |x| <= 1
*
* exceptions: GSL_EDOM
*/
int gsl_sf_legendre_Pl_e(const int l, const double x, gsl_sf_result * result);
double gsl_sf_legendre_Pl(const int l, const double x);
/* P_l(x) for l=0,...,lmax; |x| <= 1
*
* exceptions: GSL_EDOM
*/
int gsl_sf_legendre_Pl_array(
const int lmax, const double x,
double * result_array
);
/* P_l(x) and P_l'(x) for l=0,...,lmax; |x| <= 1
*
* exceptions: GSL_EDOM
*/
int gsl_sf_legendre_Pl_deriv_array(
const int lmax, const double x,
double * result_array,
double * result_deriv_array
);
/* P_l(x), l=1,2,3
*
* exceptions: none
*/
int gsl_sf_legendre_P1_e(double x, gsl_sf_result * result);
int gsl_sf_legendre_P2_e(double x, gsl_sf_result * result);
int gsl_sf_legendre_P3_e(double x, gsl_sf_result * result);
double gsl_sf_legendre_P1(const double x);
double gsl_sf_legendre_P2(const double x);
double gsl_sf_legendre_P3(const double x);
/* Q_0(x), x > -1, x != 1
*
* exceptions: GSL_EDOM
*/
int gsl_sf_legendre_Q0_e(const double x, gsl_sf_result * result);
double gsl_sf_legendre_Q0(const double x);
/* Q_1(x), x > -1, x != 1
*
* exceptions: GSL_EDOM
*/
int gsl_sf_legendre_Q1_e(const double x, gsl_sf_result * result);
double gsl_sf_legendre_Q1(const double x);
/* Q_l(x), x > -1, x != 1, l >= 0
*
* exceptions: GSL_EDOM
*/
int gsl_sf_legendre_Ql_e(const int l, const double x, gsl_sf_result * result);
double gsl_sf_legendre_Ql(const int l, const double x);
/* P_l^m(x) m >= 0; l >= m; |x| <= 1.0
*
* Note that this function grows combinatorially with l.
* Therefore we can easily generate an overflow for l larger
* than about 150.
*
* There is no trouble for small m, but when m and l are both large,
* then there will be trouble. Rather than allow overflows, these
* functions refuse to calculate when they can sense that l and m are
* too big.
*
* If you really want to calculate a spherical harmonic, then DO NOT
* use this. Instead use legendre_sphPlm() below, which uses a similar
* recursion, but with the normalized functions.
*
* exceptions: GSL_EDOM, GSL_EOVRFLW
*/
int gsl_sf_legendre_Plm_e(const int l, const int m, const double x, gsl_sf_result * result);
double gsl_sf_legendre_Plm(const int l, const int m, const double x);
/* P_l^m(x) m >= 0; l >= m; |x| <= 1.0
* l=|m|,...,lmax
*
* exceptions: GSL_EDOM, GSL_EOVRFLW
*/
int gsl_sf_legendre_Plm_array(
const int lmax, const int m, const double x,
double * result_array
);
/* P_l^m(x) and d(P_l^m(x))/dx; m >= 0; lmax >= m; |x| <= 1.0
* l=|m|,...,lmax
*
* exceptions: GSL_EDOM, GSL_EOVRFLW
*/
int gsl_sf_legendre_Plm_deriv_array(
const int lmax, const int m, const double x,
double * result_array,
double * result_deriv_array
);
/* P_l^m(x), normalized properly for use in spherical harmonics
* m >= 0; l >= m; |x| <= 1.0
*
* There is no overflow problem, as there is for the
* standard normalization of P_l^m(x).
*
* Specifically, it returns:
*
* sqrt((2l+1)/(4pi)) sqrt((l-m)!/(l+m)!) P_l^m(x)
*
* exceptions: GSL_EDOM
*/
int gsl_sf_legendre_sphPlm_e(const int l, int m, const double x, gsl_sf_result * result);
double gsl_sf_legendre_sphPlm(const int l, const int m, const double x);
/* sphPlm(l,m,x) values
* m >= 0; l >= m; |x| <= 1.0
* l=|m|,...,lmax
*
* exceptions: GSL_EDOM
*/
int gsl_sf_legendre_sphPlm_array(
const int lmax, int m, const double x,
double * result_array
);
/* sphPlm(l,m,x) and d(sphPlm(l,m,x))/dx values
* m >= 0; l >= m; |x| <= 1.0
* l=|m|,...,lmax
*
* exceptions: GSL_EDOM
*/
int gsl_sf_legendre_sphPlm_deriv_array(
const int lmax, const int m, const double x,
double * result_array,
double * result_deriv_array
);
/* size of result_array[] needed for the array versions of Plm
* (lmax - m + 1)
*/
int gsl_sf_legendre_array_size(const int lmax, const int m);
/* Irregular Spherical Conical Function
* P^{1/2}_{-1/2 + I lambda}(x)
*
* x > -1.0
* exceptions: GSL_EDOM
*/
int gsl_sf_conicalP_half_e(const double lambda, const double x, gsl_sf_result * result);
double gsl_sf_conicalP_half(const double lambda, const double x);
/* Regular Spherical Conical Function
* P^{-1/2}_{-1/2 + I lambda}(x)
*
* x > -1.0
* exceptions: GSL_EDOM
*/
int gsl_sf_conicalP_mhalf_e(const double lambda, const double x, gsl_sf_result * result);
double gsl_sf_conicalP_mhalf(const double lambda, const double x);
/* Conical Function
* P^{0}_{-1/2 + I lambda}(x)
*
* x > -1.0
* exceptions: GSL_EDOM
*/
int gsl_sf_conicalP_0_e(const double lambda, const double x, gsl_sf_result * result);
double gsl_sf_conicalP_0(const double lambda, const double x);
/* Conical Function
* P^{1}_{-1/2 + I lambda}(x)
*
* x > -1.0
* exceptions: GSL_EDOM
*/
int gsl_sf_conicalP_1_e(const double lambda, const double x, gsl_sf_result * result);
double gsl_sf_conicalP_1(const double lambda, const double x);
/* Regular Spherical Conical Function
* P^{-1/2-l}_{-1/2 + I lambda}(x)
*
* x > -1.0, l >= -1
* exceptions: GSL_EDOM
*/
int gsl_sf_conicalP_sph_reg_e(const int l, const double lambda, const double x, gsl_sf_result * result);
double gsl_sf_conicalP_sph_reg(const int l, const double lambda, const double x);
/* Regular Cylindrical Conical Function
* P^{-m}_{-1/2 + I lambda}(x)
*
* x > -1.0, m >= -1
* exceptions: GSL_EDOM
*/
int gsl_sf_conicalP_cyl_reg_e(const int m, const double lambda, const double x, gsl_sf_result * result);
double gsl_sf_conicalP_cyl_reg(const int m, const double lambda, const double x);
/* The following spherical functions are specializations
* of Legendre functions which give the regular eigenfunctions
* of the Laplacian on a 3-dimensional hyperbolic space.
* Of particular interest is the flat limit, which is
* Flat-Lim := {lambda->Inf, eta->0, lambda*eta fixed}.
*/
/* Zeroth radial eigenfunction of the Laplacian on the
* 3-dimensional hyperbolic space.
*
* legendre_H3d_0(lambda,eta) := sin(lambda*eta)/(lambda*sinh(eta))
*
* Normalization:
* Flat-Lim legendre_H3d_0(lambda,eta) = j_0(lambda*eta)
*
* eta >= 0.0
* exceptions: GSL_EDOM
*/
int gsl_sf_legendre_H3d_0_e(const double lambda, const double eta, gsl_sf_result * result);
double gsl_sf_legendre_H3d_0(const double lambda, const double eta);
/* First radial eigenfunction of the Laplacian on the
* 3-dimensional hyperbolic space.
*
* legendre_H3d_1(lambda,eta) :=
* 1/sqrt(lambda^2 + 1) sin(lam eta)/(lam sinh(eta))
* (coth(eta) - lambda cot(lambda*eta))
*
* Normalization:
* Flat-Lim legendre_H3d_1(lambda,eta) = j_1(lambda*eta)
*
* eta >= 0.0
* exceptions: GSL_EDOM
*/
int gsl_sf_legendre_H3d_1_e(const double lambda, const double eta, gsl_sf_result * result);
double gsl_sf_legendre_H3d_1(const double lambda, const double eta);
/* l'th radial eigenfunction of the Laplacian on the
* 3-dimensional hyperbolic space.
*
* Normalization:
* Flat-Lim legendre_H3d_l(l,lambda,eta) = j_l(lambda*eta)
*
* eta >= 0.0, l >= 0
* exceptions: GSL_EDOM
*/
int gsl_sf_legendre_H3d_e(const int l, const double lambda, const double eta, gsl_sf_result * result);
double gsl_sf_legendre_H3d(const int l, const double lambda, const double eta);
/* Array of H3d(ell), 0 <= ell <= lmax
*/
int gsl_sf_legendre_H3d_array(const int lmax, const double lambda, const double eta, double * result_array);
__END_DECLS
#endif /* __GSL_SF_LEGENDRE_H__ */
|