# Tag Archives: Duplication

## Gamma duplication formula proof

$$\Gamma \left(\frac{1}{2}+n\right) = {(2n)! \over 4^n n!} \sqrt{\pi}$$ $$\textit{proof}$$ For the proof we use induction by assuming $n\geq 0$. If $n=0$ we have our basic identity $$\Gamma\left(\frac{1}{2}\right) = \sqrt{\pi}$$ Now we need … Continue reading