1.\" $OpenBSD: erf.3,v 1.8 2000/03/02 00:29:49 todd Exp $ 2.\" Copyright (c) 1985, 1991 Regents of the University of California. 3.\" All rights reserved. 4.\" 5.\" Redistribution and use in source and binary forms, with or without 6.\" modification, are permitted provided that the following conditions 7.\" are met: 8.\" 1. Redistributions of source code must retain the above copyright 9.\" notice, this list of conditions and the following disclaimer. 10.\" 2. Redistributions in binary form must reproduce the above copyright 11.\" notice, this list of conditions and the following disclaimer in the 12.\" documentation and/or other materials provided with the distribution. 13.\" 3. All advertising materials mentioning features or use of this software 14.\" must display the following acknowledgement: 15.\" This product includes software developed by the University of 16.\" California, Berkeley and its contributors. 17.\" 4. Neither the name of the University nor the names of its contributors 18.\" may be used to endorse or promote products derived from this software 19.\" without specific prior written permission. 20.\" 21.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 22.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 23.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 24.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 25.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 26.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 27.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 28.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 29.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 30.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 31.\" SUCH DAMAGE. 32.\" 33.\" from: @(#)erf.3 6.4 (Berkeley) 4/20/91 34.\" 35.Dd April 20, 1991 36.Dt ERFC 3 37.Os 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 60calculates the error function of x; where 61.Bd -filled -offset indent 62.if n \{\ 63erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. \} 64.if t \{\ 65erf\|(x) := 66(2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. \} 67.Ed 68.Pp 69The 70.Fn erfc 71function calculates the complementary error function of 72.Fa x ; 73that is 74.Fn erfc 75subtracts the result of the error function 76.Fn erf x 77from 1.0. 78This is useful, since for large 79.Fa x 80places disappear. 81.Sh SEE ALSO 82.Xr math 3 83.Sh HISTORY 84The 85.Fn erf 86and 87.Fn erfc 88functions appeared in 89.Bx 4.3 . 90