1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
|
/* specfunc/bessel_amp_phase.c
*
* 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 */
#include <config.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_sf_bessel.h>
#include "bessel_amp_phase.h"
/* chebyshev expansions for amplitude and phase
functions used in bessel evaluations
These are the same for J0,Y0 and for J1,Y1, so
they sit outside those functions.
*/
static double bm0_data[21] = {
0.09284961637381644,
-0.00142987707403484,
0.00002830579271257,
-0.00000143300611424,
0.00000012028628046,
-0.00000001397113013,
0.00000000204076188,
-0.00000000035399669,
0.00000000007024759,
-0.00000000001554107,
0.00000000000376226,
-0.00000000000098282,
0.00000000000027408,
-0.00000000000008091,
0.00000000000002511,
-0.00000000000000814,
0.00000000000000275,
-0.00000000000000096,
0.00000000000000034,
-0.00000000000000012,
0.00000000000000004
};
const cheb_series _gsl_sf_bessel_amp_phase_bm0_cs = {
bm0_data,
20,
-1, 1,
10
};
static double bth0_data[24] = {
-0.24639163774300119,
0.001737098307508963,
-0.000062183633402968,
0.000004368050165742,
-0.000000456093019869,
0.000000062197400101,
-0.000000010300442889,
0.000000001979526776,
-0.000000000428198396,
0.000000000102035840,
-0.000000000026363898,
0.000000000007297935,
-0.000000000002144188,
0.000000000000663693,
-0.000000000000215126,
0.000000000000072659,
-0.000000000000025465,
0.000000000000009229,
-0.000000000000003448,
0.000000000000001325,
-0.000000000000000522,
0.000000000000000210,
-0.000000000000000087,
0.000000000000000036
};
const cheb_series _gsl_sf_bessel_amp_phase_bth0_cs = {
bth0_data,
23,
-1, 1,
12
};
static double bm1_data[21] = {
0.1047362510931285,
0.00442443893702345,
-0.00005661639504035,
0.00000231349417339,
-0.00000017377182007,
0.00000001893209930,
-0.00000000265416023,
0.00000000044740209,
-0.00000000008691795,
0.00000000001891492,
-0.00000000000451884,
0.00000000000116765,
-0.00000000000032265,
0.00000000000009450,
-0.00000000000002913,
0.00000000000000939,
-0.00000000000000315,
0.00000000000000109,
-0.00000000000000039,
0.00000000000000014,
-0.00000000000000005,
};
const cheb_series _gsl_sf_bessel_amp_phase_bm1_cs = {
bm1_data,
20,
-1, 1,
10
};
static double bth1_data[24] = {
0.74060141026313850,
-0.004571755659637690,
0.000119818510964326,
-0.000006964561891648,
0.000000655495621447,
-0.000000084066228945,
0.000000013376886564,
-0.000000002499565654,
0.000000000529495100,
-0.000000000124135944,
0.000000000031656485,
-0.000000000008668640,
0.000000000002523758,
-0.000000000000775085,
0.000000000000249527,
-0.000000000000083773,
0.000000000000029205,
-0.000000000000010534,
0.000000000000003919,
-0.000000000000001500,
0.000000000000000589,
-0.000000000000000237,
0.000000000000000097,
-0.000000000000000040,
};
const cheb_series _gsl_sf_bessel_amp_phase_bth1_cs = {
bth1_data,
23,
-1, 1,
12
};
int
gsl_sf_bessel_asymp_Mnu_e(const double nu, const double x, double * result)
{
const double r = 2.0*nu/x;
const double r2 = r*r;
const double x2 = x*x;
const double term1 = (r2-1.0/x2)/8.0;
const double term2 = (r2-1.0/x2)*(r2-9.0/x2)*3.0/128.0;
const double Mnu2_c = 2.0/(M_PI) * (1.0 + term1 + term2);
*result = sqrt(Mnu2_c)/sqrt(x); /* will never underflow this way */
return GSL_SUCCESS;
}
int
gsl_sf_bessel_asymp_thetanu_corr_e(const double nu, const double x, double * result)
{
const double r = 2.0*nu/x;
const double r2 = r*r;
const double x2 = x*x;
const double term1 = x*(r2 - 1.0/x2)/8.0;
const double term2 = x*(r2 - 1.0/x2)*(r2 - 25.0/x2)/384.0;
*result = (-0.25*M_PI + term1 + term2);
return GSL_SUCCESS;
}
|
