.\" 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

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.

.PP

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 VERSIONS

These functions first appeared in glibc in version 2.1.

.SH ATTRIBUTES

For an explanation of the terms used in this section, see

.BR attributes (7).

.TS

allbox;

lbw30 lb lb

l l l.

Interface	Attribute	Value

T{

.BR tgamma (),

.BR tgammaf (),

.BR tgammal ()

T}	Thread safety	MT-Safe

.TE

.SH CONFORMING TO

C99, POSIX.1-2001, POSIX.1-2008.

.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 version 2.18, the glibc implementation of these functions did not set

.\" http://sources.redhat.com/bugzilla/show_bug.cgi?id=6809

.I errno

to

.B EDOM

when

.I x

is negative infinity.

.PP

Before glibc 2.19,

.\" http://sources.redhat.com/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.

.I x

.PP

.\"

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)

.SH COLOPHON

This page is part of release 4.15 of the Linux

.I man-pages

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/.