I'm trying to find a gamma rep for $ 15 \cdot 13 \cdot 11 \cdot 9 \cdot 7 \cdot ... $
Steps so far:
It's a simple sequence of $ n \cdot (n-2) \cdot (n-4) \cdot (n-6) \cdot (n-8)... $ and so on.
Allegedly I am supposed to find an equivalent expression using factorials and powers of 2
$$= n\cdot(n-2(1)) \cdot (n-2(2)) \cdot (n-2(3)) \cdot (n-2(4)) \cdot ... $$ I know that $$\Gamma(n) = (n-1)!$$ and $$ n\Gamma(n) = n \cdot (n-1)! $$
I've fiddled and monkeyed with this for a while now. How in the world the above sequence translates into a gamma/factorial equivalent I have no idea.
Update: I'm not even sure how powers of two are involved.
It seems like a simpler expression can be constructed, but I believe the point of the exercise is to transform it into gamma functions, which is where I start drawing a blank.