.\" Copyright (c) 1985, 1991 Regents of the University of California.
.\" All rights reserved.
.\"
.\" Redistribution and use in source and binary forms, with or without
.\" modification, are permitted provided that the following conditions
.\" are met:
.\" 1. Redistributions of source code must retain the above copyright
.\"    notice, this list of conditions and the following disclaimer.
.\" 2. Redistributions in binary form must reproduce the above copyright
.\"    notice, this list of conditions and the following disclaimer in the
.\"    documentation and/or other materials provided with the distribution.
.\" 3. Neither the name of the University nor the names of its contributors
.\"    may be used to endorse or promote products derived from this software
.\"    without specific prior written permission.
.\"
.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
.\" SUCH DAMAGE.
.\"
.\"     from: @(#)j0.3	6.7 (Berkeley) 4/19/91
.\"
.Dd March 10, 2015
.Dt J0 3
.Os
.Sh NAME
.Nm j0 ,
.Nm j0f ,
.Nm j1 ,
.Nm j1f ,
.Nm jn ,
.Nm jnf ,
.Nm y0 ,
.Nm y0f ,
.Nm y1 ,
.Nm y1f ,
.Nm yn ,
.Nm ynf
.Nd Bessel functions of first and second kind
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In math.h
.Ft double
.Fn j0 "double x"
.Ft float
.Fn j0f "float x"
.Ft double
.Fn j1 "double x"
.Ft float
.Fn j1f "float x"
.Ft double
.Fn jn "int n" "double x"
.Ft float
.Fn jnf "int n" "float x"
.Ft double
.Fn y0 "double x"
.Ft float
.Fn y0f "float x"
.Ft double
.Fn y1 "double x"
.Ft float
.Fn y1f "float x"
.Ft double
.Fn yn "int n" "double x"
.Ft float
.Fn ynf "int n" "float x"
.Sh DESCRIPTION
The functions
.Fn j0 ,
.Fn j0f ,
.Fn j1 ,
and
.Fn j1f
compute the Bessel function of the first kind of orders
0 and 1 for the real value
.Fa x ;
the functions
.Fn jn
and
.Fn jnf
compute the Bessel function of the first kind of the integer order
.Fa n
for the real value
.Fa x .
.Pp
The functions
.Fn y0 ,
.Fn y0f ,
.Fn y1 ,
and
.Fn y1f
compute the linearly independent Bessel function of the second kind
of orders 0 and 1 for the positive
.Em real
value
.Fa x ;
the functions
.Fn yn
and
.Fn ynf
compute the Bessel function of the second kind for the integer order
.Fa n
for the positive
.Em real
value
.Fa x .
.Sh RETURN VALUES
These routines return values of their respective Bessel functions.
For large positive inputs, they may underflow and return \*(Pm0.
.Pp
The following applies to
.Fn y0 ,
.Fn y0f ,
.Fn y1 ,
.Fn y1f ,
.Fn yn ,
and
.Fn ynf .
If
.Fa x
is negative, including -\*(If, these routines will generate an invalid
exception and return \*(Na.
If
.Fa x
is \*(Pm0, these routines
will generate a divide-by-zero exception and return -\*(If.
If
.Fa x
is a sufficiently small positive number, then
.Fn y1 ,
.Fn y1f ,
.Fn yn ,
and
.Fn ynf
will generate an overflow exception and return -\*(If.
.Sh SEE ALSO
.Xr math 3
.Sh STANDARDS
The
.Fn j0 ,
.Fn j1 ,
.Fn jn ,
.Fn y0 ,
.Fn y1 ,
and
.Fn yn
functions conform to
.St -p1003.1-2001 .
The
.Ft float
versions are extensions.
.Sh HISTORY
This set of functions
appeared in
.At v7 .