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/* specfunc/gsl_sf_expint.h
*
* Copyright (C) 2007 Brian Gough
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002 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_EXPINT_H__
#define __GSL_SF_EXPINT_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
/* E_1(x) := Re[ Integrate[ Exp[-xt]/t, {t,1,Infinity}] ]
*
* x != 0.0
* exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
*/
int gsl_sf_expint_E1_e(const double x, gsl_sf_result * result);
double gsl_sf_expint_E1(const double x);
/* E_2(x) := Re[ Integrate[ Exp[-xt]/t^2, {t,1,Infinity}] ]
*
* x != 0.0
* exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
*/
int gsl_sf_expint_E2_e(const double x, gsl_sf_result * result);
double gsl_sf_expint_E2(const double x);
/* E_n(x) := Re[ Integrate[ Exp[-xt]/t^n, {t,1,Infinity}] ]
*
* x != 0.0
* exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
*/
int gsl_sf_expint_En_e(const int n, const double x, gsl_sf_result * result);
double gsl_sf_expint_En(const int n, const double x);
/* E_1_scaled(x) := exp(x) E_1(x)
*
* x != 0.0
* exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
*/
int gsl_sf_expint_E1_scaled_e(const double x, gsl_sf_result * result);
double gsl_sf_expint_E1_scaled(const double x);
/* E_2_scaled(x) := exp(x) E_2(x)
*
* x != 0.0
* exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
*/
int gsl_sf_expint_E2_scaled_e(const double x, gsl_sf_result * result);
double gsl_sf_expint_E2_scaled(const double x);
/* E_n_scaled(x) := exp(x) E_n(x)
*
* x != 0.0
* exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
*/
int gsl_sf_expint_En_scaled_e(const int n, const double x, gsl_sf_result * result);
double gsl_sf_expint_En_scaled(const int n, const double x);
/* Ei(x) := - PV Integrate[ Exp[-t]/t, {t,-x,Infinity}]
* := PV Integrate[ Exp[t]/t, {t,-Infinity,x}]
*
* x != 0.0
* exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
*/
int gsl_sf_expint_Ei_e(const double x, gsl_sf_result * result);
double gsl_sf_expint_Ei(const double x);
/* Ei_scaled(x) := exp(-x) Ei(x)
*
* x != 0.0
* exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
*/
int gsl_sf_expint_Ei_scaled_e(const double x, gsl_sf_result * result);
double gsl_sf_expint_Ei_scaled(const double x);
/* Shi(x) := Integrate[ Sinh[t]/t, {t,0,x}]
*
* exceptions: GSL_EOVRFLW, GSL_EUNDRFLW
*/
int gsl_sf_Shi_e(const double x, gsl_sf_result * result);
double gsl_sf_Shi(const double x);
/* Chi(x) := Re[ M_EULER + log(x) + Integrate[(Cosh[t]-1)/t, {t,0,x}] ]
*
* x != 0.0
* exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
*/
int gsl_sf_Chi_e(const double x, gsl_sf_result * result);
double gsl_sf_Chi(const double x);
/* Ei_3(x) := Integral[ Exp[-t^3], {t,0,x}]
*
* x >= 0.0
* exceptions: GSL_EDOM
*/
int gsl_sf_expint_3_e(const double x, gsl_sf_result * result);
double gsl_sf_expint_3(double x);
/* Si(x) := Integrate[ Sin[t]/t, {t,0,x}]
*
* exceptions: none
*/
int gsl_sf_Si_e(const double x, gsl_sf_result * result);
double gsl_sf_Si(const double x);
/* Ci(x) := -Integrate[ Cos[t]/t, {t,x,Infinity}]
*
* x > 0.0
* exceptions: GSL_EDOM
*/
int gsl_sf_Ci_e(const double x, gsl_sf_result * result);
double gsl_sf_Ci(const double x);
/* AtanInt(x) := Integral[ Arctan[t]/t, {t,0,x}]
*
*
* exceptions:
*/
int gsl_sf_atanint_e(const double x, gsl_sf_result * result);
double gsl_sf_atanint(const double x);
__END_DECLS
#endif /* __GSL_SF_EXPINT_H__ */
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