/usr/include/gsl/gsl_sf_gamma.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 | /* specfunc/gsl_sf_gamma.h
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 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_GAMMA_H__
#define __GSL_SF_GAMMA_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
/* Log[Gamma(x)], x not a negative integer
* Uses real Lanczos method.
* Returns the real part of Log[Gamma[x]] when x < 0,
* i.e. Log[|Gamma[x]|].
*
* exceptions: GSL_EDOM, GSL_EROUND
*/
int gsl_sf_lngamma_e(double x, gsl_sf_result * result);
double gsl_sf_lngamma(const double x);
/* Log[Gamma(x)], x not a negative integer
* Uses real Lanczos method. Determines
* the sign of Gamma[x] as well as Log[|Gamma[x]|] for x < 0.
* So Gamma[x] = sgn * Exp[result_lg].
*
* exceptions: GSL_EDOM, GSL_EROUND
*/
int gsl_sf_lngamma_sgn_e(double x, gsl_sf_result * result_lg, double *sgn);
/* Gamma(x), x not a negative integer
* Uses real Lanczos method.
*
* exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EROUND
*/
int gsl_sf_gamma_e(const double x, gsl_sf_result * result);
double gsl_sf_gamma(const double x);
/* Regulated Gamma Function, x > 0
* Gamma^*(x) = Gamma(x)/(Sqrt[2Pi] x^(x-1/2) exp(-x))
* = (1 + 1/(12x) + ...), x->Inf
* A useful suggestion of Temme.
*
* exceptions: GSL_EDOM
*/
int gsl_sf_gammastar_e(const double x, gsl_sf_result * result);
double gsl_sf_gammastar(const double x);
/* 1/Gamma(x)
* Uses real Lanczos method.
*
* exceptions: GSL_EUNDRFLW, GSL_EROUND
*/
int gsl_sf_gammainv_e(const double x, gsl_sf_result * result);
double gsl_sf_gammainv(const double x);
/* Log[Gamma(z)] for z complex, z not a negative integer
* Uses complex Lanczos method. Note that the phase part (arg)
* is not well-determined when |z| is very large, due
* to inevitable roundoff in restricting to (-Pi,Pi].
* This will raise the GSL_ELOSS exception when it occurs.
* The absolute value part (lnr), however, never suffers.
*
* Calculates:
* lnr = log|Gamma(z)|
* arg = arg(Gamma(z)) in (-Pi, Pi]
*
* exceptions: GSL_EDOM, GSL_ELOSS
*/
int gsl_sf_lngamma_complex_e(double zr, double zi, gsl_sf_result * lnr, gsl_sf_result * arg);
/* x^n / n!
*
* x >= 0.0, n >= 0
* exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
*/
int gsl_sf_taylorcoeff_e(const int n, const double x, gsl_sf_result * result);
double gsl_sf_taylorcoeff(const int n, const double x);
/* n!
*
* exceptions: GSL_EDOM, GSL_EOVRFLW
*/
int gsl_sf_fact_e(const unsigned int n, gsl_sf_result * result);
double gsl_sf_fact(const unsigned int n);
/* n!! = n(n-2)(n-4) ...
*
* exceptions: GSL_EDOM, GSL_EOVRFLW
*/
int gsl_sf_doublefact_e(const unsigned int n, gsl_sf_result * result);
double gsl_sf_doublefact(const unsigned int n);
/* log(n!)
* Faster than ln(Gamma(n+1)) for n < 170; defers for larger n.
*
* exceptions: none
*/
int gsl_sf_lnfact_e(const unsigned int n, gsl_sf_result * result);
double gsl_sf_lnfact(const unsigned int n);
/* log(n!!)
*
* exceptions: none
*/
int gsl_sf_lndoublefact_e(const unsigned int n, gsl_sf_result * result);
double gsl_sf_lndoublefact(const unsigned int n);
/* log(n choose m)
*
* exceptions: GSL_EDOM
*/
int gsl_sf_lnchoose_e(unsigned int n, unsigned int m, gsl_sf_result * result);
double gsl_sf_lnchoose(unsigned int n, unsigned int m);
/* n choose m
*
* exceptions: GSL_EDOM, GSL_EOVRFLW
*/
int gsl_sf_choose_e(unsigned int n, unsigned int m, gsl_sf_result * result);
double gsl_sf_choose(unsigned int n, unsigned int m);
/* Logarithm of Pochhammer (Apell) symbol
* log( (a)_x )
* where (a)_x := Gamma[a + x]/Gamma[a]
*
* a > 0, a+x > 0
*
* exceptions: GSL_EDOM
*/
int gsl_sf_lnpoch_e(const double a, const double x, gsl_sf_result * result);
double gsl_sf_lnpoch(const double a, const double x);
/* Logarithm of Pochhammer (Apell) symbol, with sign information.
* result = log( |(a)_x| )
* sgn = sgn( (a)_x )
* where (a)_x := Gamma[a + x]/Gamma[a]
*
* a != neg integer, a+x != neg integer
*
* exceptions: GSL_EDOM
*/
int gsl_sf_lnpoch_sgn_e(const double a, const double x, gsl_sf_result * result, double * sgn);
/* Pochhammer (Apell) symbol
* (a)_x := Gamma[a + x]/Gamma[x]
*
* a != neg integer, a+x != neg integer
*
* exceptions: GSL_EDOM, GSL_EOVRFLW
*/
int gsl_sf_poch_e(const double a, const double x, gsl_sf_result * result);
double gsl_sf_poch(const double a, const double x);
/* Relative Pochhammer (Apell) symbol
* ((a,x) - 1)/x
* where (a,x) = (a)_x := Gamma[a + x]/Gamma[a]
*
* exceptions: GSL_EDOM
*/
int gsl_sf_pochrel_e(const double a, const double x, gsl_sf_result * result);
double gsl_sf_pochrel(const double a, const double x);
/* Normalized Incomplete Gamma Function
*
* Q(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,x,Infinity} ]
*
* a >= 0, x >= 0
* Q(a,0) := 1
* Q(0,x) := 0, x != 0
*
* exceptions: GSL_EDOM
*/
int gsl_sf_gamma_inc_Q_e(const double a, const double x, gsl_sf_result * result);
double gsl_sf_gamma_inc_Q(const double a, const double x);
/* Complementary Normalized Incomplete Gamma Function
*
* P(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,0,x} ]
*
* a > 0, x >= 0
*
* exceptions: GSL_EDOM
*/
int gsl_sf_gamma_inc_P_e(const double a, const double x, gsl_sf_result * result);
double gsl_sf_gamma_inc_P(const double a, const double x);
/* Non-normalized Incomplete Gamma Function
*
* Gamma(a,x) := Integral[ t^(a-1) e^(-t), {t,x,Infinity} ]
*
* x >= 0.0
* Gamma(a, 0) := Gamma(a)
*
* exceptions: GSL_EDOM
*/
int gsl_sf_gamma_inc_e(const double a, const double x, gsl_sf_result * result);
double gsl_sf_gamma_inc(const double a, const double x);
/* Logarithm of Beta Function
* Log[B(a,b)]
*
* a > 0, b > 0
* exceptions: GSL_EDOM
*/
int gsl_sf_lnbeta_e(const double a, const double b, gsl_sf_result * result);
double gsl_sf_lnbeta(const double a, const double b);
int gsl_sf_lnbeta_sgn_e(const double x, const double y, gsl_sf_result * result, double * sgn);
/* Beta Function
* B(a,b)
*
* a > 0, b > 0
* exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
*/
int gsl_sf_beta_e(const double a, const double b, gsl_sf_result * result);
double gsl_sf_beta(const double a, const double b);
/* Normalized Incomplete Beta Function
* B_x(a,b)/B(a,b)
*
* a > 0, b > 0, 0 <= x <= 1
* exceptions: GSL_EDOM, GSL_EUNDRFLW
*/
int gsl_sf_beta_inc_e(const double a, const double b, const double x, gsl_sf_result * result);
double gsl_sf_beta_inc(const double a, const double b, const double x);
/* The maximum x such that gamma(x) is not
* considered an overflow.
*/
#define GSL_SF_GAMMA_XMAX 171.0
/* The maximum n such that gsl_sf_fact(n) does not give an overflow. */
#define GSL_SF_FACT_NMAX 170
/* The maximum n such that gsl_sf_doublefact(n) does not give an overflow. */
#define GSL_SF_DOUBLEFACT_NMAX 297
__END_DECLS
#endif /* __GSL_SF_GAMMA_H__ */
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