Legendre's Duplication Formula

Theorem
Let $\Gamma$ denote the gamma function.

Then:
 * $\forall z \notin \set {-\dfrac n 2: n \in \N}: \map \Gamma z \map \Gamma {z + \dfrac 1 2} = 2^{1 - 2 z} \sqrt \pi \, \map \Gamma {2 z}$

where $\N$ denotes the natural numbers.

Also denoted as
Some sources report this as:
 * $\forall z \notin \set{-\dfrac n 2: n \in \N}: 2^{2 z - 1} \map \Gamma z \, \map \Gamma {z + \dfrac 1 2} = \sqrt \pi \, \map \Gamma {2 z}$