123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294 |
- /* 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_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__ */
|