Category:Gamma Function

This category contains results about the Gamma function.
Definitions specific to this category can be found in Definitions/Gamma Function.

The Gamma function $\Gamma: \C \to \C \ $ is defined, for the open right half-plane, as:

$\displaystyle \Gamma \left({z}\right) = \mathcal M \left\{ {e^{-t} }\right\} \left({z}\right) = \int_0^{\to \infty} t^{z-1} e^{-t} \rd t$

where $\mathcal M$ is the Mellin transform.

For all other values of $z$ except the non-positive integers, $\Gamma \left({z}\right)$ is defined as:

$\Gamma \left({z + 1}\right) = z \Gamma \left({z}\right)$