#include <math.h>

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 non-positive integers. For non-negative 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)

This function returns the value of the Gamma function for the argument x. It had to be called "true gamma function" since there is already a function gamma(3) that returns something else.

ERRORS

In order to check for errors, set errno to zero and call feclearexcept(FE_ALL_EXCEPT) before calling these functions. On return, if errno is non-zero or fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.

A range error occurs if x is too large. A pole error occurs if x is zero. A domain error (or a pole error) occurs if x is a negative integer.

CONFORMING TO

C99.

SEE ALSO

gamma(3), lgamma(3)