Symbols:Greek/Gamma/Gamma Function

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Gamma Function

$\map \Gamma z$

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

$\displaystyle \map \Gamma z = \map {\MM \set {e^{-t} } } z = \int_0^{\to \infty} t^{z - 1} e^{-t} \rd t$

where $\MM$ is the Mellin transform.

For all other values of $z$ except the non-positive integers, $\map \Gamma z$ is defined as:

$\map \Gamma {z + 1} = z \, \map \Gamma z$

The $\LaTeX$ code for \(\map \Gamma z\) is \map \Gamma z .