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. All advertising materials mentioning features or use of this software 13.\" must display the following acknowledgement: 14.\" This product includes software developed by the University of 15.\" California, Berkeley and its contributors. 16.\" 4. Neither the name of the University nor the names of its contributors 17.\" may be used to endorse or promote products derived from this software 18.\" without specific prior written permission. 19.\" 20.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 21.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 22.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 23.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 24.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 25.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 26.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 27.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 28.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 29.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 30.\" SUCH DAMAGE. 31.\" 32.\" from: @(#)j0.3 6.7 (Berkeley) 4/19/91 33.\" $NetBSD: j0.3,v 1.10 1998/02/05 18:52:08 perry Exp $ 34.\" 35.Dd April 19, 1991 36.Dt J0 3 37.Os 38.Sh NAME 39.Nm j0 , 40.Nm j1 , 41.Nm jn , 42.Nm y0 , 43.Nm y1 , 44.Nm yn 45.Nd bessel functions of first and second kind 46.Sh LIBRARY 47.Lb libm 48.Sh SYNOPSIS 49.Fd #include <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 , 77.Fn j0f , 78.Fn j1 79and 80.Fn j1f 81compute the 82.Em Bessel function of the first kind of the order 830 and the 84.Em order 851, respectively, 86for the 87real value 88.Fa x ; 89the functions 90.Fn jn 91and 92.Fn jnf 93compute the 94.Em Bessel function of the first kind of the integer order 95.Fa n 96for the real value 97.Fa x . 98.Pp 99The functions 100.Fn y0 , 101.Fn y0f , 102.Fn y1 103and 104.Fn y1f 105compute the linearly independent 106.Em Bessel function of the second kind of the order 1070 and the 108.Em order 1091, respectively, 110for the 111positive 112.Em integer 113value 114.Fa x 115(expressed as a double); 116the functions 117.Fn yn 118and 119.Fn ynf 120compute the 121.Em Bessel function of the second kind for the integer order 122.Fa n 123for the positive 124.Em integer 125value 126.Fa x 127(expressed as a double). 128.Sh RETURN VALUES 129If these functions are successful, 130the computed value is returned, otherwise 131the global 132variable 133.Va errno 134is set to 135.Er EDOM 136and a reserve operand fault is generated. 137.\" On the 138.\" .Tn VAX 139.\" and 140.\" .Tn Tahoe 141.\" architectures, a negative 142.\" .Fa x 143.\" value 144.\" results in an error. 145.Sh SEE ALSO 146.Xr math 3 147.\" .Xr matherr 3 148.Sh HISTORY 149This set of functions 150appeared in 151.At v7 . 152