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 February 18, 2008 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 84.Em Bessel function of the first kind of the order 850 and the 86.Em order 871, respectively, 88for the 89real value 90.Fa x ; 91the functions 92.Fn jn 93and 94.Fn jnf 95compute the 96.Em Bessel function of the first kind of the integer 97.Em order 98.Fa n 99for the real value 100.Fa x . 101.Pp 102The functions 103.Fn y0 , 104.Fn y0f , 105.Fn y1 , 106and 107.Fn y1f 108compute the linearly independent 109.Em Bessel function of the second kind of the order 1100 and the 111.Em order 1121, respectively, 113for the 114positive 115.Em real 116value 117.Fa x ; 118the functions 119.Fn yn 120and 121.Fn ynf 122compute the 123.Em Bessel function of the second kind for the integer 124.Em order 125.Fa n 126for the positive 127.Em real 128value 129.Fa x . 130.Sh RETURN VALUES 131These routines return values of their respective Bessel functions. 132For large positive inputs, they may underflow and return \*(Pm0. 133.Pp 134The following applies to 135.Fn y0 , 136.Fn y0f , 137.Fn y1 , 138.Fn y1f , 139.Fn yn , 140and 141.Fn ynf . 142If 143.Fa x 144is negative, these routines will generate an invalid exception and 145return \*(Na. 146If 147.Fa x 148is 0 or a sufficiently small positive number, these routines 149will generate an overflow exception and return -\*(If. 150.Sh SEE ALSO 151.Xr math 3 152.Sh STANDARDS 153The 154.Fn j0 , 155.Fn j1 , 156.Fn jn , 157.Fn y0 , 158.Fn y1 , 159and 160.Fn yn 161functions conform to 162.St -p1003.1-2001 . 163The 164.Ft float 165versions are extensions. 166.Sh HISTORY 167This set of functions 168appeared in 169.At v7 . 170