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 1.7 1996/03/30 01:34:04 jtc Exp $ 34.\" 35.Dd April 19, 1991 36.Dt J0 3 37.Os BSD 4 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 SYNOPSIS 47.Fd #include <math.h> 48.Ft double 49.Fn j0 "double x" 50.Ft float 51.Fn j0f "float x" 52.Ft double 53.Fn j1 "double x" 54.Ft float 55.Fn j1f "float x" 56.Ft double 57.Fn jn "int n" "double x" 58.Ft float 59.Fn jnf "int n" "float x" 60.Ft double 61.Fn y0 "double x" 62.Ft float 63.Fn y0f "float x" 64.Ft double 65.Fn y1 "double x" 66.Ft float 67.Fn y1f "float x" 68.Ft double 69.Fn yn "int n" "double x" 70.Ft float 71.Fn ynf "int n" "float x" 72.Sh DESCRIPTION 73The functions 74.Fn j0 , 75.Fn j0f , 76.Fn j1 77and 78.Fn j1f 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 functions 88.Fn jn 89and 90.Fn jnf 91compute the 92.Em Bessel function of the first kind of the integer order 93.Fa n 94for the real value 95.Fa x . 96.Pp 97The functions 98.Fn y0 , 99.Fn y0f , 100.Fn y1 101and 102.Fn y1f 103compute the linearly independent 104.Em Bessel function of the second kind of the order 1050 and the 106.Em order 1071, respectively, 108for the 109positive 110.Em integer 111value 112.Fa x 113(expressed as a double); 114the functions 115.Fn yn 116and 117.Fn ynf 118compute the 119.Em Bessel function of the second kind for the integer order 120.Fa n 121for the positive 122.Em integer 123value 124.Fa x 125(expressed as a double). 126.Sh RETURN VALUES 127If these functions are successful, 128the computed value is returned. On the 129.Tn VAX 130and 131.Tn Tahoe 132architectures, 133a negative 134.Fa x 135value 136results in an error; the global 137variable 138.Va errno 139is set to 140.Er EDOM 141and a reserve operand fault is generated. 142.Sh SEE ALSO 143.Xr math 3 , 144.Xr matherr 3 145.Sh HISTORY 146This set of functions 147appeared in 148.At v7 . 149