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.\" $Id: j0.3,v 1.3 1995/10/22 18:16:39 bde Exp $ 34.\" 35.Dd April 19, 1991 36.Dt J0 3 37.Os BSD 4 38.Sh NAME 39.Nm j0 , 40.Nm j0f , 41.Nm j1 , 42.Nm j1f , 43.Nm jn , 44.Nm jnf , 45.Nm y0 , 46.Nm y0f , 47.Nm y1 , 48.Nm y1f , 49.Nm yn , 50.Nm ynf 51.Nd Bessel functions of first and second kind 52.Sh SYNOPSIS 53.Fd #include <math.h> 54.Ft double 55.Fn j0 "double x" 56.Ft float 57.Fn j0f "float x" 58.Ft double 59.Fn j1 "double x" 60.Ft float 61.Fn j1f "float x" 62.Ft double 63.Fn jn "int n" "double x" 64.Ft float 65.Fn jnf "int n" "float x" 66.Ft double 67.Fn y0 "double x" 68.Ft float 69.Fn y0f "float x" 70.Ft double 71.Fn y1 "double x" 72.Ft float 73.Fn y1f "float x" 74.Ft double 75.Fn yn "int n" "double x" 76.Ft float 77.Fn ynf "int n" "float x" 78.Sh DESCRIPTION 79The functions 80.Fn j0 , 81.Fn j0f , 82.Fn j1 83and 84.Fn j1f 85compute the 86.Em Bessel function of the first kind of the order 870 and the 88.Em order 891, respectively, 90for the 91real value 92.Fa x ; 93the functions 94.Fn jn 95and 96.Fn jnf 97compute the 98.Em Bessel function of the first kind of the integer 99.Em order 100.Fa n 101for the real value 102.Fa x . 103.Pp 104The functions 105.Fn y0 , 106.Fn y0f , 107.Fn y1 , 108and 109.Fn y1f 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 real 118value 119.Fa x ; 120the functions 121.Fn yn 122and 123.Fn ynf 124compute the 125.Em Bessel function of the second kind for the integer 126.Em order 127.Fa n 128for the positive 129.Em real 130value 131.Fa x . 132.Sh RETURN VALUES 133If these functions are successful, 134the computed value is returned. On the 135.Tn VAX 136and 137.Tn Tahoe 138architectures, 139for the Bessel functions of the second kind, 140a negative 141or zero 142.Fa x 143value 144results in an error; the global 145variable 146.Va errno 147is set to 148.Er EDOM 149and a reserve operand fault is generated. 150.Sh SEE ALSO 151.Xr math 3 152.Sh HISTORY 153This set of functions 154appeared in 155.At v7 . 156