| /* 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 2 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_OVRFLW |
| */ |
| 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_OVRFLW |
| */ |
| 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__ */ |