.\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de)
.\" Distributed under GPL
.\" 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 2008-08-05 "GNU" "Linux Programmer's Manual"
.SH NAME
tgamma, tgammaf, tgammal \- true gamma function
.SH SYNOPSIS
.B #include <math.h>
.sp
.BI "double tgamma(double " x );
.br
.BI "float tgammaf(float " x );
.br
.BI "long double tgammal(long double " x );
.sp
Link with \fI\-lm\fP.
.sp
.in -4n
Feature Test Macro Requirements for glibc (see
.BR feature_test_macros (7)):
.in
.sp
.ad l
.BR tgamma (),
.BR tgammaf (),
.BR tgammal ():
_XOPEN_SOURCE\ >=\ 600 || _ISOC99_SOURCE; or
.I cc\ -std=c99
.ad b
.SH DESCRIPTION
The Gamma function is defined by
.sp
    Gamma(x) = integral from 0 to infinity of t^(x\-1) e^\-t dt
.sp
It is defined for every real number except for non-positive integers.
For non-negative integral \fIm\fP one has
.sp
    Gamma(m+1) = m!
.sp
and, more generally, for all \fIx\fP:
.sp
    Gamma(x+1) = x * Gamma(x)
.sp
Furthermore, the following is valid for all values of \fIx\fP
outside the poles:
.sp
    Gamma(x) * Gamma(1 \- x) = PI / sin(PI * x)
.PP
.SH RETURN VALUE
On success, these functions return Gamma(x).

If
.I x
is a NaN, a NaN is returned.

If
.I x
is positive infinity, positive infinity is returned.

If
.I 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
.BR HUGE_VAL ,
.BR HUGE_VALF ,
or
.BR 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
.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
Domain error: \fIx\fP a negative integer, or negative infinity
.\" FIXME . errno is not set to EDOM for x == -inf
.\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6809
.I errno
is set to
.BR EDOM .
An invalid floating-point exception
.RB ( FE_INVALID )
is raised (but see BUGS).
.TP
Pole error: \fIx\fP is +0 or \-0
.I errno
is set to
.BR ERANGE .
A divide-by-zero floating-point exception
.RB ( FE_DIVBYZERO )
is raised.
.TP
Range error: result overflow
.I errno
is set to
.BR ERANGE .
An overflow floating-point exception
.RB ( FE_OVERFLOW )
is raised.
.PP
glibc also gives the following error which is not specified
C99 or POSIX.1-2001.
.TP
Range error: result underflow
.\" e.g., tgamma(-172.5) on glibc 2.8/x86-32
.\" .I errno
.\" is set to
.\" .BR ERANGE .
An underflow floating-point exception
.RB ( FE_UNDERFLOW )
is raised.
.IP
.I errno
is not set for this case.
.\" FIXME . Is it intentional that errno is not set:
.\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6810
.\"
.\" glibc (as at 2.8) also supports and an inexact
.\" exception for various cases.
.SH "CONFORMING TO"
C99, POSIX.1-2001.
.SH NOTES
This function had to be called "true gamma function"
since there is already a function
.BR gamma (3)
that returns something else (see
.BR gamma (3)
for details).
.SH BUGS
If
.I x
is negative infinity,
.I errno
is not set (it should be set to
.BE EDOM ).
.\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6809
.SH "SEE ALSO"
.BR gamma (3),
.BR lgamma (3)