Why does F(α+1)=αF(α) still contain the gamma function on the right side?

[Ry122]

http://img202.imageshack.us/img202/3224/620u.jpg

In A for this question

F(alpha+1)=alpha*F(alpha)

and I'm curious as to how the RHS of this still has the gamma function in it?

 

[SteamKing]

You need to study the properties of the Gamma function:

http://en.wikipedia.org/wiki/Gamma_function