# GammaFn

## GammaFn(x)

The complete gamma function.

One way to think of the gamma function is as a generalization of the Factorial function. Whereas, the factorial function has a range over the whole numbers, the Gamma function has a range over positive real numbers. The relationship between the gamma function and factorial is:

n! = GammaFn(n + 1)

The gamma function grows very quickly, resulting in a numeric overflow when «x» >171. The LGamma function computes the natural logarithm of the gamma function, and therefore can be used over much wider ranges.

The gamma function is defined as:

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