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