1. ## simplify factorials/gamma's

Hi guys

I recently ran into a problem after doing an integral, I'm left with $\frac{\beta^{\alpha}}{\Gamma(\alpha)}\frac{\Gamma( \alpha - k)}{\beta^{\alpha-k}}$

I know that I would be left with $\beta^{k}$ on the numerator. But in the denominator. I'm not sure how the factorials would cancel.

Any help is appreciated

2. ## Re: simplify factorials/gamma's

$\dfrac{n!}{(n-k)!} = \underbrace{n(n-1)\cdots (n-k+1)}_{k\text{ terms}}$

Can you use the Pochhammer rising factorial?

3. ## Re: simplify factorials/gamma's

Are you given that $\alpha$ and k are integers? That is the only way a gamma function can be written as a factorial.

4. ## Re: simplify factorials/gamma's

Hi guys

yep I'm told for positive integer values $k$ such that $k<\alpha$