Legendre's Duplication Formula

Theorem
Let $\Gamma$ denote the gamma function.

Then:
 * $\displaystyle \forall z \notin \left\{ -\frac n 2 : n \in \N_0 \right\}, \Gamma \left({z}\right) \Gamma \left (z + \frac 1 2 \right) = 2^{1-2z} \sqrt \pi \Gamma \left({2 z}\right)$

where $N_0 = \N \cup \left\{{0}\right\}$.