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.\" 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. .\" 4. 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 .\" $FreeBSD: release/9.1.0/lib/msun/man/j0.3 176390 2008-02-18 19:02:49Z das $ .\" .Dd February 18, 2008 .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 .Em Bessel function of the first kind of the order 0 and the .Em order 1, respectively, for the real value .Fa x ; the functions .Fn jn and .Fn jnf compute the .Em Bessel function of the first kind of the integer .Em 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 .Em Bessel function of the second kind of the order 0 and the .Em order 1, respectively, for the positive .Em real value .Fa x ; the functions .Fn yn and .Fn ynf compute the .Em Bessel function of the second kind for the integer .Em 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, these routines will generate an invalid exception and return \*(Na. If .Fa x is 0 or a sufficiently small positive number, these routines 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 .