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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.

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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 1.3 1993/08/14 13:42:38 mycroft Exp $
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 erfc
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
54calculates the error function of x; where
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
65function calculates the complementary error function of
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 .