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.\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92 33.\" $Id: lgamma.3,v 1.6 1994/01/11 00:46:56 jtc Exp $ 34.\" 35.Dd December 3, 1992 36.Dt LGAMMA 3 37.Os BSD 4.3 38.Sh NAME 39.Nm lgamma , 40.Nm gamma 41.Nd log gamma function, gamma function 42.Sh SYNOPSIS 43.Fd #include <math.h> 44.Ft extern int 45.Fa signgam ; 46.sp 47.Ft double 48.Fn lgamma "double x" 49.Ft double 50.Fn gamma "double x" 51.Sh DESCRIPTION 52.Fn Lgamma x 53.if t \{\ 54returns ln\||\(*G(x)| where 55.Bd -unfilled -offset indent 56\(*G(x) = \(is\d\s8\z0\s10\u\u\s8\(if\s10\d t\u\s8x\-1\s10\d e\u\s8\-t\s10\d dt for x > 0 and 57.br 58\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1. 59.Ed 60.\} 61.if n \ 62returns ln\||\(*G(x)|. 63.Pp 64The external integer 65.Fa signgam 66returns the sign of \(*G(x). 67.Pp 68.Fn Gamma x 69returns \(*G(x), with no effect on 70.Fa signgam . 71.Sh IDIOSYNCRASIES 72Do not use the expression 73.Dq Li signgam\(**exp(lgamma(x)) 74to compute g := \(*G(x). 75Instead use a program like this (in C): 76.Bd -literal -offset indent 77lg = lgamma(x); g = signgam\(**exp(lg); 78.Ed 79.Pp 80Only after 81.Fn lgamma 82has returned can signgam be correct. 83.Pp 84For arguments in its range, 85.Fn gamma 86is preferred, as for positive arguments 87it is accurate to within one unit in the last place. 88Exponentiation of 89.Fn lgamma 90will lose up to 10 significant bits. 91.Sh RETURN VALUES 92.Fn Gamma 93and 94.Fn lgamma 95return appropriate values unless an argument is out of range. 96Overflow will occur for sufficiently large positive values, and 97non-positive integers. 98On the 99.Tn VAX, 100the reserved operator is returned, 101and 102.Va errno 103is set to 104.Er ERANGE 105For large non-integer negative values, 106.Fn gamma 107will underflow. 108.Sh SEE ALSO 109.Xr math 3 , 110.Xr infnan 3 111.Sh HISTORY 112The 113.Nm lgamma 114function appeared in 115.Bx 4.3 . 116The 117.Nm gamma 118function appeared in 119.Bx 4.4 . 120The name 121.Fn gamma 122was originally dedicated to the 123.Fn lgamma 124function, so some old code may no longer be compatible. 125