Gamma Function of One Half/Proof 1

Proof
From the definition of the Beta function:


 * $\map \Beta {x, y} := \dfrac {\map \Gamma x \map \Gamma y} {\map \Gamma {x + y} }$

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

Then from Beta Function of Half with Half:


 * $\map \Beta {\dfrac 1 2, \dfrac 1 2} = \pi$

Hence the result.