1/* specfunc/gsl_sf_fermi_dirac.h
2 *
3 * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
4 *
5 * This program is free software; you can redistribute it and/or modify
6 * it under the terms of the GNU General Public License as published by
7 * the Free Software Foundation; either version 3 of the License, or (at
8 * your option) any later version.
9 *
10 * This program is distributed in the hope that it will be useful, but
11 * WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 * General Public License for more details.
14 *
15 * You should have received a copy of the GNU General Public License
16 * along with this program; if not, write to the Free Software
17 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
18 */
19
20/* Author: G. Jungman */
21
22#ifndef __GSL_SF_FERMI_DIRAC_H__
23#define __GSL_SF_FERMI_DIRAC_H__
24
25#include <gsl/gsl_sf_result.h>
26
27#undef __BEGIN_DECLS
28#undef __END_DECLS
29#ifdef __cplusplus
30# define __BEGIN_DECLS extern "C" {
31# define __END_DECLS }
32#else
33# define __BEGIN_DECLS /* empty */
34# define __END_DECLS /* empty */
35#endif
36
37__BEGIN_DECLS
38
39
40/* Complete Fermi-Dirac Integrals:
41 *
42 * F_j(x) := 1/Gamma[j+1] Integral[ t^j /(Exp[t-x] + 1), {t,0,Infinity}]
43 *
44 *
45 * Incomplete Fermi-Dirac Integrals:
46 *
47 * F_j(x,b) := 1/Gamma[j+1] Integral[ t^j /(Exp[t-x] + 1), {t,b,Infinity}]
48 */
49
50
51/* Complete integral F_{-1}(x) = e^x / (1 + e^x)
52 *
53 * exceptions: GSL_EUNDRFLW
54 */
55int gsl_sf_fermi_dirac_m1_e(const double x, gsl_sf_result * result);
56double gsl_sf_fermi_dirac_m1(const double x);
57
58
59/* Complete integral F_0(x) = ln(1 + e^x)
60 *
61 * exceptions: GSL_EUNDRFLW
62 */
63int gsl_sf_fermi_dirac_0_e(const double x, gsl_sf_result * result);
64double gsl_sf_fermi_dirac_0(const double x);
65
66
67/* Complete integral F_1(x)
68 *
69 * exceptions: GSL_EUNDRFLW, GSL_EOVRFLW
70 */
71int gsl_sf_fermi_dirac_1_e(const double x, gsl_sf_result * result);
72double gsl_sf_fermi_dirac_1(const double x);
73
74
75/* Complete integral F_2(x)
76 *
77 * exceptions: GSL_EUNDRFLW, GSL_EOVRFLW
78 */
79int gsl_sf_fermi_dirac_2_e(const double x, gsl_sf_result * result);
80double gsl_sf_fermi_dirac_2(const double x);
81
82
83/* Complete integral F_j(x)
84 * for integer j
85 *
86 * exceptions: GSL_EUNDRFLW, GSL_EOVRFLW
87 */
88int gsl_sf_fermi_dirac_int_e(const int j, const double x, gsl_sf_result * result);
89double gsl_sf_fermi_dirac_int(const int j, const double x);
90
91
92/* Complete integral F_{-1/2}(x)
93 *
94 * exceptions: GSL_EUNDRFLW, GSL_EOVRFLW
95 */
96int gsl_sf_fermi_dirac_mhalf_e(const double x, gsl_sf_result * result);
97double gsl_sf_fermi_dirac_mhalf(const double x);
98
99
100/* Complete integral F_{1/2}(x)
101 *
102 * exceptions: GSL_EUNDRFLW, GSL_EOVRFLW
103 */
104int gsl_sf_fermi_dirac_half_e(const double x, gsl_sf_result * result);
105double gsl_sf_fermi_dirac_half(const double x);
106
107
108/* Complete integral F_{3/2}(x)
109 *
110 * exceptions: GSL_EUNDRFLW, GSL_EOVRFLW
111 */
112int gsl_sf_fermi_dirac_3half_e(const double x, gsl_sf_result * result);
113double gsl_sf_fermi_dirac_3half(const double x);
114
115
116/* Incomplete integral F_0(x,b) = ln(1 + e^(b-x)) - (b-x)
117 *
118 * exceptions: GSL_EUNDRFLW, GSL_EDOM
119 */
120int gsl_sf_fermi_dirac_inc_0_e(const double x, const double b, gsl_sf_result * result);
121double gsl_sf_fermi_dirac_inc_0(const double x, const double b);
122
123
124__END_DECLS
125
126#endif /* __GSL_SF_FERMI_DIRAC_H__ */
127