.\" Copyright (c) 1985, 1991 Regents of the University of California. | |

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.\" from: @(#)erf.3 6.4 (Berkeley) 4/20/91 | |

.\" $FreeBSD: src/lib/msun/man/erf.3,v 1.11 2004/07/02 23:52:20 ru Exp $ | |

.\" | |

.Dd April 20, 1991 | |

.Dt ERF 3 | |

.Os | |

.Sh NAME | |

.Nm erf , | |

.Nm erff , | |

.Nm erfc , | |

.Nm erfcf | |

.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 double | |

.Fn erfc "double x" | |

.Ft float | |

.Fn erfcf "float x" | |

.Sh DESCRIPTION | |

These functions calculate the error function of | |

.Fa x . | |

.Pp | |

The | |

.Fn erf | |

and the | |

.Fn erff | |

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 | |

and the | |

.Fn erfcf | |

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. | |

This is useful, since for large | |

.Fa x | |

places disappear. | |

.Sh SEE ALSO | |

.Xr math 3 | |

.Sh HISTORY | |

The | |

.Fn erf | |

and | |

.Fn erfc | |

functions appeared in | |

.Bx 4.3 . |