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.\" $FreeBSD$ 34.\" 35.Dd April 19, 1991 36.Dt J0 3 37.Os 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 LIBRARY 53.Lb libm 54.Sh SYNOPSIS 55.In math.h 56.Ft double 57.Fn j0 "double x" 58.Ft float 59.Fn j0f "float x" 60.Ft double 61.Fn j1 "double x" 62.Ft float 63.Fn j1f "float x" 64.Ft double 65.Fn jn "int n" "double x" 66.Ft float 67.Fn jnf "int n" "float x" 68.Ft double 69.Fn y0 "double x" 70.Ft float 71.Fn y0f "float x" 72.Ft double 73.Fn y1 "double x" 74.Ft float 75.Fn y1f "float x" 76.Ft double 77.Fn yn "int n" "double x" 78.Ft float 79.Fn ynf "int n" "float x" 80.Sh DESCRIPTION 81The functions 82.Fn j0 , 83.Fn j0f , 84.Fn j1 85and 86.Fn j1f 87compute the 88.Em Bessel function of the first kind of the order 890 and the 90.Em order 911, respectively, 92for the 93real value 94.Fa x ; 95the functions 96.Fn jn 97and 98.Fn jnf 99compute the 100.Em Bessel function of the first kind of the integer 101.Em order 102.Fa n 103for the real value 104.Fa x . 105.Pp 106The functions 107.Fn y0 , 108.Fn y0f , 109.Fn y1 , 110and 111.Fn y1f 112compute the linearly independent 113.Em Bessel function of the second kind of the order 1140 and the 115.Em order 1161, respectively, 117for the 118positive 119.Em real 120value 121.Fa x ; 122the functions 123.Fn yn 124and 125.Fn ynf 126compute the 127.Em Bessel function of the second kind for the integer 128.Em order 129.Fa n 130for the positive 131.Em real 132value 133.Fa x . 134.Sh RETURN VALUES 135If these functions are successful, 136the computed value is returned. 137On the 138.Tn VAX 139and 140.Tn Tahoe 141architectures, 142for the Bessel functions of the second kind, 143a negative 144or zero 145.Fa x 146value 147results in an error; the global 148variable 149.Va errno 150is set to 151.Er EDOM 152and a reserve operand fault is generated. 153.Sh SEE ALSO 154.Xr math 3 155.Sh HISTORY 156This set of functions 157appeared in 158.At v7 . 159