Euler Gamma function of x.

The gamma function is defined for all x except for the negative integers. For positive x it can be computed via the integral

\[\Gamma(x) = \int_0^\infty t^{x-1}e^{-t}dt\]

For negative x it can be computed as

\[\Gamma(x) = \frac{\Gamma(x + k)}{x(x+1)\cdot...\cdot(x+k-1)}\]

where \(k\) is any integer such that \(x+k\) is positive.

If x is a positive integer, then \(\Gamma(x) = (x - 1)!\).

See also