/* 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__ */