Prove that $\Gamma\left(\frac{1}{2}\right)= \sqrt\pi$
Using $$\Gamma(p)\Gamma(1-p) = \frac{\pi}{\sin(\pi p)}$$
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2Hint: what is $\sin(\pi/2)$? – gammatester Aug 05 '13 at 12:35
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@Sid: Welcome to MSE! It really helps readability to format questions using MathJax (see FAQ). Regards – Amzoti Aug 05 '13 at 12:50
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Let $p=\frac12$, we have $$\Gamma\left(\frac12\right)\Gamma\left(\frac12\right)=\frac{\pi}{\sin\frac{\pi}{2}}=\pi$$ therefore $$\Gamma\left(\frac12\right)=\sqrt \pi$$
zytsang
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3(Because $\Gamma>0$. This is trivial, but forgetting that the square is not injective is often cause of problems) – Clement C. Aug 05 '13 at 13:50