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.\" $NetBSD: j0.3,v 1.16 2003/08/07 16:44:48 agc Exp $ 30.\" 31.Dd April 19, 1991 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 order 97.Fa n 98for the real value 99.Fa x . 100.Pp 101The functions 102.Fn y0 , 103.Fn y0f , 104.Fn y1 105and 106.Fn y1f 107compute the linearly independent 108.Em Bessel function of the second kind of the order 1090 and the 110.Em order 1111, respectively, 112for the 113positive 114.Em integer 115value 116.Fa x 117(expressed as a double); 118the functions 119.Fn yn 120and 121.Fn ynf 122compute the 123.Em Bessel function of the second kind for the integer order 124.Fa n 125for the positive 126.Em integer 127value 128.Fa x 129(expressed as a double). 130.Sh RETURN VALUES 131If these functions are successful, 132the computed value is returned, otherwise 133the global 134variable 135.Va errno 136is set to 137.Er EDOM 138and a reserve operand fault is generated. 139.\" On the 140.\" .Tn VAX 141.\" and 142.\" .Tn Tahoe 143.\" architectures, a negative 144.\" .Fa x 145.\" value 146.\" results in an error. 147.Sh SEE ALSO 148.Xr math 3 149.\" .Xr matherr 3 150.Sh HISTORY 151This set of functions 152appeared in 153.At v7 . 154