Sunday, July 31, 2016

analysis - Why is $Gammaleft(frac{1}{2}right)=sqrt{pi}$ ?

It seems as if no one has asked this here before, unless I don't know how to search.



The Gamma function is
$$
\Gamma(\alpha)=\int_0^\infty x^{\alpha-1} e^{-x}\,dx.
$$
Why is
$$
\Gamma\left(\frac{1}{2}\right)=\sqrt{\pi}\ ?

$$
(I'll post my own answer, but I know there are many ways to show this, so post your own!)

No comments:

Post a Comment

analysis - Injection, making bijection

I have injection $f \colon A \rightarrow B$ and I want to get bijection. Can I just resting codomain to $f(A)$? I know that every function i...