'\" t
.\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de)
.\"
.\" SPDX-License-Identifier: GPL-1.0-or-later
.\"
.\" 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 2023-10-31 "Linux man-pages 6.06"
.SH NAME
tgamma, tgammaf, tgammal \- true gamma function
.SH LIBRARY
Math library
.RI ( libm ", " \-lm )
.SH SYNOPSIS
.nf
.B #include <math.h>
.P
.BI "double tgamma(double " x );
.BI "float tgammaf(float " x );
.BI "long double tgammal(long double " x );
.fi
.P
.RS -4
Feature Test Macro Requirements for glibc (see
.BR feature_test_macros (7)):
.RE
.P
.BR tgamma (),
.BR tgammaf (),
.BR tgammal ():
.nf
    _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
.fi
.SH DESCRIPTION
These functions calculate the Gamma function of
.IR x .
.P
The Gamma function is defined by
.P
.RS
Gamma(x) = integral from 0 to infinity of t\[ha](x\-1) e\[ha]\-t dt
.RE
.P
It is defined for every real number except for nonpositive integers.
For nonnegative integral
.I m
one has
.P
.RS
Gamma(m+1) = m!
.RE
.P
and, more generally, for all
.IR x :
.P
.RS
Gamma(x+1) = x * Gamma(x)
.RE
.P
Furthermore, the following is valid for all values of
.I x
outside the poles:
.P
.RS
Gamma(x) * Gamma(1 \- x) = PI / sin(PI * x)
.RE
.SH RETURN VALUE
On success, these functions return Gamma(x).
.P
If
.I x
is a NaN, a NaN is returned.
.P
If
.I x
is positive infinity, positive infinity is returned.
.P
If
.I x
is a negative integer, or is negative infinity,
a domain error occurs,
and a NaN is returned.
.P
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.
.P
If the result underflows,
a range error occurs,
and the functions return 0, with the correct mathematical sign.
.P
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.
.P
The following errors can occur:
.TP
Domain error: \fIx\fP is a negative integer, or negative infinity
.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.
.P
glibc also gives the following error which is not specified
in 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, and
.I errno
is set to
.BR ERANGE .
.\" glibc (as at 2.8) also supports an inexact
.\" exception for various cases.
.SH ATTRIBUTES
For an explanation of the terms used in this section, see
.BR attributes (7).
.TS
allbox;
lbx lb lb
l l l.
Interface	Attribute	Value
T{
.na
.nh
.BR tgamma (),
.BR tgammaf (),
.BR tgammal ()
T}	Thread safety	MT-Safe
.TE
.SH STANDARDS
C11, POSIX.1-2008.
.SH HISTORY
glibc 2.1.
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
Before glibc 2.18, the glibc implementation of these functions did not set
.\" https://www.sourceware.org/bugzilla/show_bug.cgi?id=6809
.I errno
to
.B EDOM
when
.I x
is negative infinity.
.P
Before glibc 2.19,
.\" https://www.sourceware.org/bugzilla/show_bug.cgi?id=6810
the glibc implementation of these functions did not set
.I errno
to
.B ERANGE
on an underflow range error.
.P
.\"
In glibc versions 2.3.3 and earlier,
an argument of +0 or \-0 incorrectly produced a domain error
.RI ( errno
set to
.B EDOM
and an
.B FE_INVALID
exception raised), rather than a pole error.
.SH SEE ALSO
.BR gamma (3),
.BR lgamma (3)