Problem in Gama function;can you answer soon.

[quantum220]

Hello i am very happy to sent my firest question,so i am very happy from forum.
my problem is : prove that

using

I try by:
let

 

[chiro]

Hello i am very happy to sent my firest question,so i am very happy from forum.
my problem is :
prove that

The pi term comes from the fact that Gamma(1/2) = SQRT(pi). The rest you can deduce from using the relationship Gamma(x + 1) = x * Gamma(x). Basically because they are negative you are going to get switching signs since every step is multiplying by a negative number and the rest can be obtained from the definition. (I'm assuming m is an integer of course)

 

[HallsofIvy]

If m= 0, that says that \Gamma(1/2)= \sqrt{\pi} which is true.

Now, use \Gamma(x+ 1)= x\Gamma(x)to prove the rest by induction on m.