this repo has no description
1.\" Copyright (c) 1985, 1991 Regents of the University of California.
2.\" All rights reserved.
3.\"
4.\" Redistribution and use in source and binary forms, with or without
5.\" modification, are permitted provided that the following conditions
6.\" are met:
7.\" 1. Redistributions of source code must retain the above copyright
8.\" notice, this list of conditions and the following disclaimer.
9.\" 2. Redistributions in binary form must reproduce the above copyright
10.\" notice, this list of conditions and the following disclaimer in the
11.\" documentation and/or other materials provided with the distribution.
12.\" 3. All advertising materials mentioning features or use of this software
13.\" must display the following acknowledgement:
14.\" This product includes software developed by the University of
15.\" California, Berkeley and its contributors.
16.\" 4. Neither the name of the University nor the names of its contributors
17.\" may be used to endorse or promote products derived from this software
18.\" without specific prior written permission.
19.\"
20.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
21.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
22.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
23.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
24.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
25.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
26.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
27.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
28.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
29.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
30.\" SUCH DAMAGE.
31.\"
32.\" from: @(#)j0.3 6.7 (Berkeley) 4/19/91
33.\" $Id: j0.3,v 1.3 2003/08/17 20:36:47 scp Exp $
34.\"
35.Dd December 11, 2006
36.Dt J0 3
37.Os BSD 4
38.Sh NAME
39.Nm j0 ,
40.Nm j1 ,
41.Nm jn ,
42.Nm y0 ,
43.Nm y1 ,
44.Nm yn
45.Nd bessel functions of first and second kind
46.Sh SYNOPSIS
47.Fd #include <math.h>
48.Ft double
49.Fn j0 "double x"
50.\.Ft float
51.\.Fn j0f "float x"
52.Ft double
53.Fn j1 "double x"
54.\.Ft float
55.\.Fn j1f "float x"
56.Ft double
57.Fn jn "int n" "double x"
58.\.Ft float
59.\.Fn jnf "int n" "float x"
60.Ft double
61.Fn y0 "double x"
62.\.Ft float
63.\.Fn y0f "float x"
64.Ft double
65.Fn y1 "double x"
66.\.Ft float
67.\.Fn y1f "float x"
68.Ft double
69.Fn yn "int n" "double x"
70.\.Ft float
71.\.Fn ynf "int n" "float x"
72.Sh DESCRIPTION
73The functions
74.Fn j0 "x"
75and
76.Fn j1 "x"
77compute the Bessel function of the first kind of the order
780 and the order 1, respectively; the function
79.Fn jn "n" "x"
80computes the Bessel function of the first kind of the integer order n.
81.Pp
82The functions
83.Fn y0 "x"
84and
85.Fn y1 "x"
86compute the linearly independent Bessel function of the second kind of the order
870 and the order 1, respectively, for the positive integer value x (expressed as a double);
88the function
89.Fn yn "n" "x"
90computes the Bessel function of the second kind for the integer order n
91for the positive integer value x (expressed as a double).
92.Sh SPECIAL VALUES
93.Fn j0 "0"
94returns 1.
95.Pp
96.Fn j0 "�infinity"
97returns 0.
98.Pp
99.Fn j0 "NaN"
100returns a NaN.
101.Pp
102.Fn j1 "0"
103returns 0.
104.Pp
105.Fn j1 "+infinity"
106returns 0.
107.Pp
108.Fn j1 "NaN"
109returns a NaN.
110.Pp
111.Fn y0 "0"
112,
113.Fn y1 "0"
114, and
115.Fn yn "n" "0"
116all return -infinity and raise the "division-by-zero" floating-point flag.