Extension of the integer factorial definition to the real and complex numbers.

There are multiple possible extensions.

The one chosen is such that f(x + 1) = x f(x), f(1) = 1 and log(f) is convex. This yields the gamma function as the definition of the extension, where,

G(s) = ò_{(0,}¥_{)} x^{s-1}e^{-x}dxThere are interesting formulas involving the gamma function including Sterling’s formula.