include/gsl/gsl_sf_erf.h

0001 /* specfunc/gsl_sf_erf.h
0002  *
0003  * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
0004  *
0005  * This program is free software; you can redistribute it and/or modify
0006  * it under the terms of the GNU General Public License as published by
0007  * the Free Software Foundation; either version 3 of the License, or (at
0008  * your option) any later version.
0009  *
0010  * This program is distributed in the hope that it will be useful, but
0011  * WITHOUT ANY WARRANTY; without even the implied warranty of
0012  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
0013  * General Public License for more details.
0014  *
0015  * You should have received a copy of the GNU General Public License
0016  * along with this program; if not, write to the Free Software
0017  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
0018  */
0019
0020 /* Author:  G. Jungman */
0021
0022 #ifndef __GSL_SF_ERF_H__
0023 #define __GSL_SF_ERF_H__
0024
0025 #include <gsl/gsl_sf_result.h>
0026
0027 #undef __BEGIN_DECLS
0028 #undef __END_DECLS
0029 #ifdef __cplusplus
0030 # define __BEGIN_DECLS extern "C" {
0031 # define __END_DECLS }
0032 #else
0033 # define __BEGIN_DECLS /* empty */
0034 # define __END_DECLS /* empty */
0035 #endif
0036
0037 __BEGIN_DECLS
0038
0039
0040 /* Complementary Error Function
0041  * erfc(x) := 2/Sqrt[Pi] Integrate[Exp[-t^2], {t,x,Infinity}]
0042  *
0043  * exceptions: none
0044  */
0045 int gsl_sf_erfc_e(double x, gsl_sf_result * result);
0046 double gsl_sf_erfc(double x);
0047
0048
0049 /* Log Complementary Error Function
0050  *
0051  * exceptions: none
0052  */
0053 int gsl_sf_log_erfc_e(double x, gsl_sf_result * result);
0054 double gsl_sf_log_erfc(double x);
0055
0056
0057 /* Error Function
0058  * erf(x) := 2/Sqrt[Pi] Integrate[Exp[-t^2], {t,0,x}]
0059  *
0060  * exceptions: none
0061  */
0062 int gsl_sf_erf_e(double x, gsl_sf_result * result);
0063 double gsl_sf_erf(double x);
0064
0065
0066 /* Probability functions:
0067  * Z(x) :  Abramowitz+Stegun 26.2.1
0068  * Q(x) :  Abramowitz+Stegun 26.2.3
0069  *
0070  * exceptions: none
0071  */
0072 int gsl_sf_erf_Z_e(double x, gsl_sf_result * result);
0073 int gsl_sf_erf_Q_e(double x, gsl_sf_result * result);
0074 double gsl_sf_erf_Z(double x);
0075 double gsl_sf_erf_Q(double x);
0076
0077
0078 /* Hazard function, also known as the inverse Mill's ratio.
0079  *
0080  *   H(x) := Z(x)/Q(x)
0081  *         = Sqrt[2/Pi] Exp[-x^2 / 2] / Erfc[x/Sqrt[2]]
0082  *
0083  * exceptions: GSL_EUNDRFLW
0084  */
0085 int gsl_sf_hazard_e(double x, gsl_sf_result * result);
0086 double gsl_sf_hazard(double x);
0087
0088
0089 __END_DECLS
0090
0091 #endif /* __GSL_SF_ERF_H__ */