system.3: ffix

[thirdparty/man-pages.git] / man3 / tgamma.3

.\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de)
.\"
.\" %%%LICENSE_START(GPL_NOVERSION_ONELINE)
.\" Distributed under GPL
.\" %%%LICENSE_END
.\"
.\" Based on glibc infopages
.\" and Copyright 2008, Linux Foundation, written by Michael Kerrisk
.\"     <mtk.manpages@gmail.com>
.\" Modified 2004-11-15, fixed error noted by Fabian Kreutz
.\"	 <kreutz@dbs.uni-hannover.de>
.\"
.TH TGAMMA 3 2017-09-15 "GNU" "Linux Programmer's Manual"
.SH NAME
tgamma, tgammaf, tgammal \- true gamma function
.SH SYNOPSIS
.B #include <math.h>
.PP
.BI "double tgamma(double " x );
.br
.BI "float tgammaf(float " x );
.br
.BI "long double tgammal(long double " x );
.PP
Link with \fI\-lm\fP.
.PP
.in -4n
Feature Test Macro Requirements for glibc (see
.BR feature_test_macros (7)):
.in
.PP
.ad l
.BR tgamma (),
.BR tgammaf (),
.BR tgammal ():
.RS 4
_ISOC99_SOURCE ||
_POSIX_C_SOURCE\ >=\ 200112L
.RE
.ad
.SH DESCRIPTION
These functions calculate the Gamma function of
.IR x .
.PP
The Gamma function is defined by
.PP
.RS
Gamma(x) = integral from 0 to infinity of t^(x\-1) e^\-t dt
.RE
.PP
It is defined for every real number except for nonpositive integers.
For nonnegative integral
.I m
one has
.PP
.RS
Gamma(m+1) = m!
.RE
.PP
and, more generally, for all
.IR x :
.PP
.RS
Gamma(x+1) = x * Gamma(x)
.RE
.PP
Furthermore, the following is valid for all values of
.I x
outside the poles:
.PP
.RS
Gamma(x) * Gamma(1 \- x) = PI / sin(PI * x)
.RE
.SH RETURN VALUE
On success, these functions return Gamma(x).
.PP
If
.I x
is a NaN, a NaN is returned.
.PP
If
.I x
is positive infinity, positive infinity is returned.
.PP
If
.I x
is a negative integer, or is negative infinity,
a domain error occurs,
and a NaN is returned.
.PP
If the result overflows,
a range error occurs,
and the functions return
.BR HUGE_VAL ,
.BR HUGE_VALF ,
or
.BR HUGE_VALL ,
respectively, with the correct mathematical sign.
.PP
If the result underflows,
a range error occurs,
and the functions return 0, with the correct mathematical sign.
.PP
If
.I x
is \-0 or +0,
a pole error occurs,
and the functions return
.BR HUGE_VAL ,
.BR HUGE_VALF ,
or
.BR HUGE_VALL ,
respectively, with the same sign as the 0.
.SH ERRORS
See
.BR math_error (7)
for information on how to determine whether an error has occurred
when calling these functions.
.PP
The following errors can occur:
.TP