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Diffstat (limited to 'gsl-1.9/specfunc/gsl_sf_gamma.h')
| -rw-r--r-- | gsl-1.9/specfunc/gsl_sf_gamma.h | 293 |
1 files changed, 293 insertions, 0 deletions
diff --git a/gsl-1.9/specfunc/gsl_sf_gamma.h b/gsl-1.9/specfunc/gsl_sf_gamma.h new file mode 100644 index 0000000..b8fa713 --- /dev/null +++ b/gsl-1.9/specfunc/gsl_sf_gamma.h @@ -0,0 +1,293 @@ +/* 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 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__ */ |