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