# Show that this is a constant

• Apr 8th 2010, 06:04 AM
EinStone
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)

$\displaystyle log\Gamma(s)-log\Gamma(\frac{s}{2})-log\Gamma(\frac{s+1}{2})-s* log 2$ is a constant.
• Apr 8th 2010, 11:40 AM
chiph588@
Quote:

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)

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

I would raise take that formula and raise it to the power $\displaystyle e$, then use this definition of $\displaystyle \Gamma(s)$:

$\displaystyle \Gamma(s) = \lim_{n\to\infty} \frac{n^s(n-1)!}{s(s+1)\cdots(s+n-1)}$.
• Apr 8th 2010, 12:12 PM
chiph588@
Also, I would let $\displaystyle s \mapsto 2s$. It makes cancellation easier.