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. Neither the name of the University nor the names of its contributors 13.\" may be used to endorse or promote products derived from this software 14.\" without specific prior written permission. 15.\" 16.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 17.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 18.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 19.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 20.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 21.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 22.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 23.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 24.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 25.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 26.\" SUCH DAMAGE. 27.\" 28.\" from: @(#)erf.3 6.4 (Berkeley) 4/20/91 29.\" $FreeBSD$ 30.\" 31.Dd July 13, 2014 32.Dt ERF 3 33.Os 34.Sh NAME 35.Nm erf , 36.Nm erff , 37.Nm erfl , 38.Nm erfc , 39.Nm erfcf , 40.Nm erfcl 41.Nd error function operators 42.Sh LIBRARY 43.Lb libm 44.Sh SYNOPSIS 45.In math.h 46.Ft double 47.Fn erf "double x" 48.Ft float 49.Fn erff "float x" 50.Ft "long double" 51.Fn erfl "long double x" 52.Ft double 53.Fn erfc "double x" 54.Ft float 55.Fn erfcf "float x" 56.Ft "long double" 57.Fn erfcl "long double x" 58.Sh DESCRIPTION 59These functions calculate the error function of 60.Fa x . 61.Pp 62The 63.Fn erf , 64.Fn erff , 65and 66.Fn erfl 67functions calculate the error function of x; where 68.Bd -ragged -offset indent 69.if n \{\ 70erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. 71\} 72.if t \{\ 73erf\|(x) := 74(2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. 75\} 76.Ed 77.Pp 78The 79.Fn erfc , 80.Fn erfcf , 81and 82.Fn erfcl 83functions calculate the complementary error function of 84.Fa x ; 85that is 86.Fn erfc 87subtracts the result of the error function 88.Fn erf x 89from 1.0. 90.Sh SEE ALSO 91.Xr math 3 92.Sh HISTORY 93The 94.Fn erf 95and 96.Fn erfc 97functions appeared in 98.Bx 4.3 . 99