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
|
/* @(#)w_j0.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
FUNCTION
<<jN>>, <<jNf>>, <<yN>>, <<yNf>>---Bessel functions
INDEX
j0
INDEX
j0f
INDEX
j1
INDEX
j1f
INDEX
jn
INDEX
jnf
INDEX
y0
INDEX
y0f
INDEX
y1
INDEX
y1f
INDEX
yn
INDEX
ynf
SYNOPSIS
#include <math.h>
double j0(double <[x]>);
float j0f(float <[x]>);
double j1(double <[x]>);
float j1f(float <[x]>);
double jn(int <[n]>, double <[x]>);
float jnf(int <[n]>, float <[x]>);
double y0(double <[x]>);
float y0f(float <[x]>);
double y1(double <[x]>);
float y1f(float <[x]>);
double yn(int <[n]>, double <[x]>);
float ynf(int <[n]>, float <[x]>);
DESCRIPTION
The Bessel functions are a family of functions that solve the
differential equation
@ifnottex
. 2 2 2
. x y'' + xy' + (x - p )y = 0
@end ifnottex
@tex
$$x^2{d^2y\over dx^2} + x{dy\over dx} + (x^2-p^2)y = 0$$
@end tex
These functions have many applications in engineering and physics.
<<jn>> calculates the Bessel function of the first kind of order
<[n]>. <<j0>> and <<j1>> are special cases for order 0 and order
1 respectively.
Similarly, <<yn>> calculates the Bessel function of the second kind of
order <[n]>, and <<y0>> and <<y1>> are special cases for order 0 and
1.
<<jnf>>, <<j0f>>, <<j1f>>, <<ynf>>, <<y0f>>, and <<y1f>> perform the
same calculations, but on <<float>> rather than <<double>> values.
RETURNS
The value of each Bessel function at <[x]> is returned.
PORTABILITY
None of the Bessel functions are in ANSI C.
*/
/*
* wrapper j0(double x), y0(double x)
*/
#include "fdlibm.h"
#include <errno.h>
#ifndef _DOUBLE_IS_32BITS
#if !defined(_IEEE_LIBM) || !defined(HAVE_ALIAS_ATTRIBUTE)
#ifdef __STDC__
double j0(double x) /* wrapper j0 */
#else
double j0(x) /* wrapper j0 */
double x;
#endif
{
double z = __ieee754_j0(x);
if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
if(fabs(x)>X_TLOSS) {
/* j0(|x|>X_TLOSS) */
errno = ERANGE;
return 0.0;
} else
return z;
}
#endif
#if !defined(_IEEE_LIBM) || !defined(HAVE_ALIAS_ATTRIBUTE)
#ifdef __STDC__
double y0(double x) /* wrapper y0 */
#else
double y0(x) /* wrapper y0 */
double x;
#endif
{
double z;
z = __ieee754_y0(x);
if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z;
if(x < 0.0){
/* y0(x<0) = NaN */
errno = EDOM;
}
if(x == 0.0){
/* y0(0) = -inf */
errno = ERANGE;
}
if(x>X_TLOSS) {
/* y0(x>X_TLOSS) */
errno = ERANGE;
}
return z;
}
#endif
#endif /* defined(_DOUBLE_IS_32BITS) */
|
