Section (3) tgamma
Name
tgamma, tgammaf, tgammal — true gamma function
Synopsis
#include <math.h>
double
tgamma( 
double x) ; 
float
tgammaf( 
float x) ; 
long double
tgammal( 
long double x) ; 
Note  


Note  

Link with 
DESCRIPTION
These functions calculate the Gamma function of x
.
The Gamma function is defined by
Gamma(x) = integral from 0 to infinity of t^(x−1) e^−t dt
It is defined for every real number except for nonpositive
integers. For nonnegative integral m
one has
Gamma(m+1) = m!
and, more generally, for all x
:
Gamma(x+1) = x * Gamma(x)
Furthermore, the following is valid for all values of
x
outside the
poles:
Gamma(x) * Gamma(1 − x) = PI / sin(PI * x)
RETURN VALUE
On success, these functions return Gamma(x).
If x
is a NaN, a
NaN is returned.
If x
is positive
infinity, positive infinity is returned.
If x
is a negative
integer, or is negative infinity, a domain error occurs, and
a NaN is returned.
If the result overflows, a range error occurs, and the
functions return HUGE_VAL
,
HUGE_VALF
, or HUGE_VALL
, respectively, with the correct
mathematical sign.
If the result underflows, a range error occurs, and the functions return 0, with the correct mathematical sign.
If x
is −0
or +0, a pole error occurs, and the functions return
HUGE_VAL
, HUGE_VALF
, or HUGE_VALL
, respectively, with the same sign
as the 0.
ERRORS
See math_error(7) for information on how to determine whether an error has occurred when calling these functions.
The following errors can occur:
 Domain error:
x
is a negative integer, or negative infinity 
errno
is set to EDOM. An invalid floatingpoint exception (FE_INVALID
) is raised (but see BUGS).  Pole error:
x
is +0 or −0 
errno
is set to ERANGE. A dividebyzero floatingpoint exception (FE_DIVBYZERO
) is raised.  Range error: result overflow

errno
is set to ERANGE. An overflow floatingpoint exception (FE_OVERFLOW
) is raised.
glibc also gives the following error which is not specified in C99 or POSIX.12001.
 Range error: result underflow

An underflow floatingpoint exception (
FE_UNDERFLOW
) is raised, anderrno
is set to ERANGE.
ATTRIBUTES
For an explanation of the terms used in this section, see attributes(7).
Interface  Attribute  Value 
tgamma (), tgammaf (), tgammal () 
Thread safety  MTSafe 
NOTES
This function had to be called true gamma function since there is already a function gamma(3) that returns something else (see gamma(3) for details).
BUGS
Before version 2.18, the glibc implementation of these
functions did not set errno
to
EDOM when x
is negative infinity.
Before glibc 2.19, the glibc implementation of these
functions did not set errno
to
ERANGE on an underflow range
error. x
In glibc versions 2.3.3 and earlier, an argument of +0 or
−0 incorrectly produced a domain error (errno
set to EDOM and an FE_INVALID
exception raised), rather than a
pole error.
COLOPHON
This page is part of release 4.16 of the Linux manpages
project. A
description of the project, information about reporting bugs,
and the latest version of this page, can be found at
https://www.kernel.org/doc/man−pages/.
Copyright 2002 Walter Harms (walter.harmsinformatik.unioldenburg.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.manpagesgmail.com> Modified 20041115, fixed error noted by Fabian Kreutz <kreutzdbs.unihannover.de> 