xref: /freebsd/lib/msun/man/j0.3 (revision ba8d15d3a8b10be9f3a0cb86a60246f225a36736)
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.\" 4. Neither the name of the University nor the names of its contributors
13.\"    may be used to endorse or promote products derived from this software
14.\"    without specific prior written permission.
15.\"
16.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
17.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
18.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
19.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
20.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
21.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
22.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
23.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
24.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
25.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
26.\" SUCH DAMAGE.
27.\"
28.\"     from: @(#)j0.3	6.7 (Berkeley) 4/19/91
29.\" $FreeBSD$
30.\"
31.Dd March 10, 2015
32.Dt J0 3
33.Os
34.Sh NAME
35.Nm j0 ,
36.Nm j0f ,
37.Nm j1 ,
38.Nm j1f ,
39.Nm jn ,
40.Nm jnf ,
41.Nm y0 ,
42.Nm y0f ,
43.Nm y1 ,
44.Nm y1f ,
45.Nm yn ,
46.Nm ynf
47.Nd Bessel functions of first and second kind
48.Sh LIBRARY
49.Lb libm
50.Sh SYNOPSIS
51.In math.h
52.Ft double
53.Fn j0 "double x"
54.Ft float
55.Fn j0f "float x"
56.Ft double
57.Fn j1 "double x"
58.Ft float
59.Fn j1f "float x"
60.Ft double
61.Fn jn "int n" "double x"
62.Ft float
63.Fn jnf "int n" "float x"
64.Ft double
65.Fn y0 "double x"
66.Ft float
67.Fn y0f "float x"
68.Ft double
69.Fn y1 "double x"
70.Ft float
71.Fn y1f "float x"
72.Ft double
73.Fn yn "int n" "double x"
74.Ft float
75.Fn ynf "int n" "float x"
76.Sh DESCRIPTION
77The functions
78.Fn j0 ,
79.Fn j0f ,
80.Fn j1 ,
81and
82.Fn j1f
83compute the Bessel function of the first kind of orders
840 and 1 for the real value
85.Fa x ;
86the functions
87.Fn jn
88and
89.Fn jnf
90compute the Bessel function of the first kind of the integer order
91.Fa n
92for the real value
93.Fa x .
94.Pp
95The functions
96.Fn y0 ,
97.Fn y0f ,
98.Fn y1 ,
99and
100.Fn y1f
101compute the linearly independent Bessel function of the second kind
102of orders 0 and 1 for the positive
103.Em real
104value
105.Fa x ;
106the functions
107.Fn yn
108and
109.Fn ynf
110compute the Bessel function of the second kind for the integer order
111.Fa n
112for the positive
113.Em real
114value
115.Fa x .
116.Sh RETURN VALUES
117These routines return values of their respective Bessel functions.
118For large positive inputs, they may underflow and return \*(Pm0.
119.Pp
120The following applies to
121.Fn y0 ,
122.Fn y0f ,
123.Fn y1 ,
124.Fn y1f ,
125.Fn yn ,
126and
127.Fn ynf .
128If
129.Fa x
130is negative, including -\*(If, these routines will generate an invalid
131exception and return \*(Na.
132If
133.Fa x
134is \*(Pm0, these routines
135will generate a divide-by-zero exception and return -\*(If.
136If
137.Fa x
138is a sufficiently small positive number, then
139.Fn y1 ,
140.Fn y1f ,
141.Fn yn ,
142and
143.Fn ynf
144will generate an overflow exception and return -\*(If.
145.Sh SEE ALSO
146.Xr math 3
147.Sh STANDARDS
148The
149.Fn j0 ,
150.Fn j1 ,
151.Fn jn ,
152.Fn y0 ,
153.Fn y1 ,
154and
155.Fn yn
156functions conform to
157.St -p1003.1-2001 .
158The
159.Ft float
160versions are extensions.
161.Sh HISTORY
162This set of functions
163appeared in
164.At v7 .
165