Gamma Function of One Half/Proof 2

Proof
From Euler's Reflection Formula:


 * $\forall z \notin \Z: \Gamma \left({z}\right) \Gamma \left({1 - z}\right) = \dfrac \pi {\sin \left({\pi z}\right)}$

Setting $z = \dfrac 1 2$:

By definition of the $\Gamma$ function:
 * $\forall z \in \R_{\ge 0}: \Gamma \left({z}\right) > 0$

and so the negative square root can be discarded.

Hence:
 * $\Gamma \left({\dfrac 1 2}\right) = \sqrt \pi$

as required.