170 lines
3.6 KiB
Groff
170 lines
3.6 KiB
Groff
.\" Copyright (c) 1985, 1991 Regents of the University of California.
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.\" All rights reserved.
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.\"
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.\" Redistribution and use in source and binary forms, with or without
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.\" modification, are permitted provided that the following conditions
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.\" are met:
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.\" 1. Redistributions of source code must retain the above copyright
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.\" notice, this list of conditions and the following disclaimer.
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.\" 2. Redistributions in binary form must reproduce the above copyright
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.\" notice, this list of conditions and the following disclaimer in the
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.\" documentation and/or other materials provided with the distribution.
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.\" 4. Neither the name of the University nor the names of its contributors
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.\" may be used to endorse or promote products derived from this software
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.\" without specific prior written permission.
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.\"
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.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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.\" SUCH DAMAGE.
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.\"
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.\" from: @(#)j0.3 6.7 (Berkeley) 4/19/91
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.\" $FreeBSD$
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.\"
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.Dd February 18, 2008
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.Dt J0 3
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.Os
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.Sh NAME
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.Nm j0 ,
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.Nm j0f ,
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.Nm j1 ,
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.Nm j1f ,
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.Nm jn ,
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.Nm jnf ,
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.Nm y0 ,
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.Nm y0f ,
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.Nm y1 ,
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.Nm y1f ,
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.Nm yn ,
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.Nm ynf
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.Nd Bessel functions of first and second kind
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.Sh LIBRARY
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.Lb libm
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.Sh SYNOPSIS
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.In math.h
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.Ft double
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.Fn j0 "double x"
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.Ft float
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.Fn j0f "float x"
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.Ft double
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.Fn j1 "double x"
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.Ft float
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.Fn j1f "float x"
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.Ft double
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.Fn jn "int n" "double x"
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.Ft float
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.Fn jnf "int n" "float x"
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.Ft double
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.Fn y0 "double x"
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.Ft float
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.Fn y0f "float x"
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.Ft double
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.Fn y1 "double x"
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.Ft float
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.Fn y1f "float x"
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.Ft double
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.Fn yn "int n" "double x"
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.Ft float
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.Fn ynf "int n" "float x"
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.Sh DESCRIPTION
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The functions
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.Fn j0 ,
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.Fn j0f ,
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.Fn j1
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and
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.Fn j1f
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compute the
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.Em Bessel function of the first kind of the order
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0 and the
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.Em order
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1, respectively,
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for the
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real value
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.Fa x ;
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the functions
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.Fn jn
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and
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.Fn jnf
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compute the
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.Em Bessel function of the first kind of the integer
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.Em order
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.Fa n
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for the real value
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.Fa x .
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.Pp
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The functions
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.Fn y0 ,
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.Fn y0f ,
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.Fn y1 ,
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and
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.Fn y1f
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compute the linearly independent
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.Em Bessel function of the second kind of the order
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0 and the
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.Em order
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1, respectively,
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for the
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positive
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.Em real
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value
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.Fa x ;
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the functions
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.Fn yn
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and
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.Fn ynf
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compute the
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.Em Bessel function of the second kind for the integer
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.Em order
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.Fa n
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for the positive
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.Em real
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value
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.Fa x .
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.Sh RETURN VALUES
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These routines return values of their respective Bessel functions.
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For large positive inputs, they may underflow and return \*(Pm0.
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.Pp
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The following applies to
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.Fn y0 ,
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.Fn y0f ,
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.Fn y1 ,
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.Fn y1f ,
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.Fn yn ,
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and
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.Fn ynf .
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If
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.Fa x
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is negative, these routines will generate an invalid exception and
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return \*(Na.
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If
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.Fa x
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is 0 or a sufficiently small positive number, these routines
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will generate an overflow exception and return -\*(If.
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.Sh SEE ALSO
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.Xr math 3
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.Sh STANDARDS
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The
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.Fn j0 ,
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.Fn j1 ,
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.Fn jn ,
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.Fn y0 ,
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.Fn y1 ,
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and
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.Fn yn
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functions conform to
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.St -p1003.1-2001 .
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The
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.Ft float
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versions are extensions.
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.Sh HISTORY
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This set of functions
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appeared in
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.At v7 .
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