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: @(#)erf.3 6.4 (Berkeley) 4/20/91 33.\" $Id: erf.3,v 1.1.1.1 1994/08/19 09:39:42 jkh Exp $ 34.\" 35.Dd April 20, 1991 36.Dt ERF 3 37.Os BSD 4.3 38.Sh NAME 39.Nm erf , 40.Nm erff , 41.Nm erfc , 42.Nm erfcf 43.Nd error function operators 44.Sh SYNOPSIS 45.Fd #include <math.h> 46.Ft double 47.Fn erf "double x" 48.Ft float 49.Fn erff "float x" 50.Ft double 51.Fn erfc "double x" 52.Ft float 53.Fn erfcf "float x" 54.Sh DESCRIPTION 55These functions calculate the error function of 56.Fa x . 57.Pp 58The 59.Fn erf 60and the 61.Fn erff 62functions calculate the error function of x; where 63.Bd -filled -offset indent 64.if n \{\ 65erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. \} 66.if t \{\ 67erf\|(x) := 68(2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. \} 69.Ed 70.Pp 71The 72.Fn erfc 73and the 74.Fn erfcf 75functions calculate the complementary error function of 76.Fa x ; 77that is 78.Fn erfc 79subtracts the result of the error function 80.Fn erf x 81from 1.0. 82This is useful, since for large 83.Fa x 84places disappear. 85.Sh SEE ALSO 86.Xr math 3 87.Sh HISTORY 88The 89.Fn erf 90and 91.Fn erfc 92functions appeared in 93.Bx 4.3 . 94