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.\"     from: @(#)erf.3	6.4 (Berkeley) 4/20/91
.\"
.Dd July 13, 2014
.Dt ERF 3
.Os
.Sh NAME
.Nm erf ,
.Nm erff ,
.Nm erfl ,
.Nm erfc ,
.Nm erfcf ,
.Nm erfcl
.Nd error function operators
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In math.h
.Ft double
.Fn erf "double x"
.Ft float
.Fn erff "float x"
.Ft "long double"
.Fn erfl "long double x"
.Ft double
.Fn erfc "double x"
.Ft float
.Fn erfcf "float x"
.Ft "long double"
.Fn erfcl "long double x"
.Sh DESCRIPTION
These functions calculate the error function of
.Fa x .
.Pp
The
.Fn erf ,
.Fn erff ,
and
.Fn erfl
functions calculate the error function of x; where
.Bd -ragged -offset indent
.if n \{\
erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt.
\}
.if t \{\
erf\|(x) :=
(2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt.
\}
.Ed
.Pp
The
.Fn erfc ,
.Fn erfcf ,
and
.Fn erfcl
functions calculate the complementary error function of
.Fa x ;
that is
.Fn erfc
subtracts the result of the error function
.Fn erf x
from 1.0.
.Sh SEE ALSO
.Xr math 3
.Sh HISTORY
The
.Fn erf
and
.Fn erfc
functions appeared in
.Bx 4.3 .