```TGAMMA(3)                  Linux Programmer's Manual                 TGAMMA(3)

NAME
tgamma, tgammaf, tgammal - true gamma function

SYNOPSIS
#include <math.h>

double tgamma(double x);
float tgammaf(float x);
long double tgammal(long double x);

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

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 math-
ematical 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  excep-
tion (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 incor-
rectly produced a domain error (errno set to  EDOM  and  an  FE_INVALID
exception raised), rather than a pole error.