1.\" $OpenBSD: j0.3,v 1.15 2013/07/17 05:42:11 schwarze Exp $ 2.\" Copyright (c) 1985, 1991 Regents of the University of California. 3.\" All rights reserved. 4.\" 5.\" Redistribution and use in source and binary forms, with or without 6.\" modification, are permitted provided that the following conditions 7.\" are met: 8.\" 1. Redistributions of source code must retain the above copyright 9.\" notice, this list of conditions and the following disclaimer. 10.\" 2. Redistributions in binary form must reproduce the above copyright 11.\" notice, this list of conditions and the following disclaimer in the 12.\" documentation and/or other materials provided with the distribution. 13.\" 3. Neither the name of the University nor the names of its contributors 14.\" may be used to endorse or promote products derived from this software 15.\" without specific prior written permission. 16.\" 17.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 18.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 19.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 20.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 21.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 22.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 23.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 24.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 25.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 26.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 27.\" SUCH DAMAGE. 28.\" 29.\" from: @(#)j0.3 6.7 (Berkeley) 4/19/91 30.\" 31.Dd $Mdocdate: July 17 2013 $ 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 SYNOPSIS 49.In math.h 50.Ft double 51.Fn j0 "double x" 52.Ft float 53.Fn j0f "float x" 54.Ft double 55.Fn j1 "double x" 56.Ft float 57.Fn j1f "float x" 58.Ft double 59.Fn jn "int n" "double x" 60.Ft float 61.Fn jnf "int n" "float x" 62.Ft double 63.Fn y0 "double x" 64.Ft float 65.Fn y0f "float x" 66.Ft double 67.Fn y1 "double x" 68.Ft float 69.Fn y1f "float x" 70.Ft double 71.Fn yn "int n" "double x" 72.Ft float 73.Fn ynf "int n" "float x" 74.Sh DESCRIPTION 75The functions 76.Fn j0 77and 78.Fn j1 79compute the 80.Em Bessel function of the first kind of the order 810 and the 82.Em order 831, respectively, 84for the 85real value 86.Fa x ; 87the function 88.Fn jn 89computes the 90.Em Bessel function of the first kind of the integer order 91.Fa n 92for the real value 93.Fa x . 94The functions 95.Fn j0f , 96.Fn j1f , 97and 98.Fn jnf 99are single precision versions of 100.Fn j0 , 101.Fn j1 , 102and 103.Fn jn , 104respectively. 105.Pp 106The functions 107.Fn y0 108and 109.Fn y1 110compute the linearly independent 111.Em Bessel function of the second kind of the order 1120 and the 113.Em order 1141, respectively, 115for the 116positive 117.Em integer 118value 119.Fa x 120(expressed as a double); 121the function 122.Fn yn 123computes the 124.Em Bessel function of the second kind for the integer order 125.Fa n 126for the positive 127.Em integer 128value 129.Fa x 130(expressed as a double). 131The functions 132.Fn y0f , 133.Fn y1f , 134and 135.Fn ynf 136are single precision versions of 137.Fn y0 , 138.Fn y1 , 139and 140.Fn yn , 141respectively. 142.Sh RETURN VALUES 143If these functions are successful, 144the computed value is returned, otherwise the global variable 145.Va errno 146is set to EDOM or ERANGE. 147.Sh HISTORY 148The functions 149.Fn j0 , 150.Fn j1 , 151.Fn jn , 152.Fn y0 , 153.Fn y1 , 154and 155.Fn yn 156first appeared in 157.At v7 . 158