Prove $\Gamma(\frac{1}{2}) = \sqrt{\pi}$ and $\Gamma(\frac{3}{2})$

[gtfitzpatrick]

Homework Statement

Prove \Gamma(1/2) = \sqrt{\pi}

hence proove \Gamma(3/2) = (\sqrt{\pi})/2

solution

i have proved the first part by using sustitution and changing to polar co ords.
To prove the the second part i guess i don't have to work it all out again. i know that \Gamma(x+1) = x \Gamma(x) but i can't this to help me...

 

[gtfitzpatrick]

oh my god I am an idiot, staring me in the face hahaha