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