# Thread: Show that this is a constant

1. ## Show that this is a constant

I want to prove Legendre's doublign formula, and I want to show the following in order to do that. (Note that I don't want a proof of the doubling formula)

$log\Gamma(s)-log\Gamma(\frac{s}{2})-log\Gamma(\frac{s+1}{2})-s* log 2$ is a constant.

2. Originally Posted by EinStone
I want to prove Legendre's doublign formula, and I want to show the following in order to do that. (Note that I don't want a proof of the doubling formula)

$log\Gamma(s)-log\Gamma(\frac{s}{2})-log\Gamma(\frac{s+1}{2})-s* log 2$ is a constant.
I would raise take that formula and raise it to the power $e$, then use this definition of $\Gamma(s)$:

$\Gamma(s) = \lim_{n\to\infty} \frac{n^s(n-1)!}{s(s+1)\cdots(s+n-1)}$.

3. Also, I would let $s \mapsto 2s$. It makes cancellation easier.