## FANDOM

2 Pages

The gamma function $\Gamma(x)$is the extension of the factorial function, with its argument shifted by one, to the complex plane.

For any complex number with a positive real part, the gamma function is defined by the integral $\Gamma(z) = \int_{0}^{\infty} x^{z-1} e^{-x} dx$. Values of the gamma function elsewhere in the complex plane are found through analytic continuation, or by using the identity $z \Gamma (z) = \Gamma (z+1)$.

## Alternate FormsEdit

The gamma function can be written in terms of the factorial function for nonzero integer values as $\Gamma(x) = \left( x-1\right)!$.