Gamma Function of One Half/Proof 2

Proof
From Euler's Reflection Formula:


 * $\forall z \notin \Z: \map \Gamma z \map \Gamma {1 - z} = \dfrac \pi {\map \sin {\pi z} }$

Setting $z = \dfrac 1 2$:

By definition of the gamma function:
 * $\forall z \in \R_{\ge 0}: \map \Gamma z > 0$

and so the negative square root can be discarded.

Hence:
 * $\map \Gamma {\dfrac 1 2} = \sqrt \pi$

as required.