Gamma Function of One Half/Proof 1

Theorem

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

where $\Gamma$ denotes the Gamma function.

Proof
From the definition of the Beta function:


 * $\Beta \left({x, y}\right) := \dfrac {\Gamma \left({x}\right) \Gamma \left({y}\right)} {\Gamma \left({x + y}\right)}$

Setting $x = y = \dfrac 1 2$:

Then:

Hence the result.