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.\" 3. 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.\" 30.Dd March 10, 2015 31.Dt J0 3 32.Os 33.Sh NAME 34.Nm j0 , 35.Nm j0f , 36.Nm j1 , 37.Nm j1f , 38.Nm jn , 39.Nm jnf , 40.Nm y0 , 41.Nm y0f , 42.Nm y1 , 43.Nm y1f , 44.Nm yn , 45.Nm ynf 46.Nd Bessel functions of first and second kind 47.Sh LIBRARY 48.Lb libm 49.Sh SYNOPSIS 50.In math.h 51.Ft double 52.Fn j0 "double x" 53.Ft float 54.Fn j0f "float x" 55.Ft double 56.Fn j1 "double x" 57.Ft float 58.Fn j1f "float x" 59.Ft double 60.Fn jn "int n" "double x" 61.Ft float 62.Fn jnf "int n" "float x" 63.Ft double 64.Fn y0 "double x" 65.Ft float 66.Fn y0f "float x" 67.Ft double 68.Fn y1 "double x" 69.Ft float 70.Fn y1f "float x" 71.Ft double 72.Fn yn "int n" "double x" 73.Ft float 74.Fn ynf "int n" "float x" 75.Sh DESCRIPTION 76The functions 77.Fn j0 , 78.Fn j0f , 79.Fn j1 , 80and 81.Fn j1f 82compute the Bessel function of the first kind of orders 830 and 1 for the real value 84.Fa x ; 85the functions 86.Fn jn 87and 88.Fn jnf 89compute the Bessel function of the first kind of the integer order 90.Fa n 91for the real value 92.Fa x . 93.Pp 94The functions 95.Fn y0 , 96.Fn y0f , 97.Fn y1 , 98and 99.Fn y1f 100compute the linearly independent Bessel function of the second kind 101of orders 0 and 1 for the positive 102.Em real 103value 104.Fa x ; 105the functions 106.Fn yn 107and 108.Fn ynf 109compute the Bessel function of the second kind for the integer order 110.Fa n 111for the positive 112.Em real 113value 114.Fa x . 115.Sh RETURN VALUES 116These routines return values of their respective Bessel functions. 117For large positive inputs, they may underflow and return \*(Pm0. 118.Pp 119The following applies to 120.Fn y0 , 121.Fn y0f , 122.Fn y1 , 123.Fn y1f , 124.Fn yn , 125and 126.Fn ynf . 127If 128.Fa x 129is negative, including -\*(If, these routines will generate an invalid 130exception and return \*(Na. 131If 132.Fa x 133is \*(Pm0, these routines 134will generate a divide-by-zero exception and return -\*(If. 135If 136.Fa x 137is a sufficiently small positive number, then 138.Fn y1 , 139.Fn y1f , 140.Fn yn , 141and 142.Fn ynf 143will generate an overflow exception and return -\*(If. 144.Sh SEE ALSO 145.Xr math 3 146.Sh STANDARDS 147The 148.Fn j0 , 149.Fn j1 , 150.Fn jn , 151.Fn y0 , 152.Fn y1 , 153and 154.Fn yn 155functions conform to 156.St -p1003.1-2001 . 157The 158.Ft float 159versions are extensions. 160.Sh HISTORY 161This set of functions 162appeared in 163.At v7 . 164