[[Special functions MOC]]
# Gamma function

The **gamma function** $\Gamma : \mathbb{C} \setminus -\mathbb{N}_{0} \to \mathbb{C}$ is defined for $z \in \mathbb{C}$ with $\Re(z)>0$ as #m/def/fun 
$$
\begin{align*}
\Gamma(a) = \int_{0}^{\infty} x^{a-1} \mathrm{e}^{-x} \, dx 
\end{align*}
$$
and otherwise by the [[analytic continuation]].

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