Gamma Function of One Half/Proof 1

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 from Beta Function of Half with Half:


 * $\Beta \left({\dfrac 1 2, \dfrac 1 2}\right) = \pi$

Hence the result.