_XOPEN_SOURCE >= 600 || _ISOC99_SOURCE ||
_POSIX_C_SOURCE >= 200112L;
or
cc -std=c99

DESCRIPTION

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 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.

VERSIONS

These functions first appeared in glibc in version 2.1.

CONFORMING TO

C99, POSIX.1-2001.

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

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.

This page is part of release 3.27 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/.