SYNOPSIS

DESCRIPTION

RETURN VALUE

ERRORS

VERSIONS

ATTRIBUTES

CONFORMING TO

NOTES

BUGS

SEE ALSO

COLOPHON

tgamma, tgammaf, tgammal − true gamma function

**#include
<math.h>**

**double
tgamma(double** *x***);
float tgammaf(float**

long double tgammal(long double

Link with
*−lm*.

Feature Test
Macro Requirements for glibc (see
**feature_test_macros**(7)):

**tgamma**(),
**tgammaf**(), **tgammal**():

_XOPEN_SOURCE >= 600
|| _ISOC99_SOURCE ||
_POSIX_C_SOURCE >= 200112L;

or *cc -std=c99*

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)

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.

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 floating-point exception
(**FE_INVALID**) is raised (but see BUGS).

Pole error: *x* is +0 or
−0

*errno* is set to
**ERANGE**. A divide-by-zero floating-point exception
(**FE_DIVBYZERO**) is raised.

Range error: result overflow

*errno* is set to
**ERANGE**. An overflow floating-point exception
(**FE_OVERFLOW**) is raised.

glibc also
gives the following error which is not specified in C99 or
POSIX.1-2001.

Range error: result underflow

An underflow floating-point
exception (**FE_UNDERFLOW**) is raised.

*errno* is
not set for this case.

These functions first appeared in glibc in version 2.1.

For an
explanation of the terms used in this section, see
**attributes**(7).

C99, POSIX.1-2001.

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).

If *x* is
negative infinity, *errno* is not set (it should be set
to **EDOM**).

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.

**gamma**(3),
**lgamma**(3)

This page is
part of release 3.53 of the Linux *man-pages* project.
A description of the project, and information about
reporting bugs, can be found at
http://www.kernel.org/doc/man−pages/.