Hey All:

I was looking at a Beta function identity in a math physics book I have and

it said to show $\displaystyle {\beta}(n,1/2)=2^{2n-1}{\beta}(n,n)$.

I done that OK. But....how does one prove

$\displaystyle {\beta}(n,1/2)=\frac{2^{2n}(n!)^{2}}{n(2n)!}$?.

I know the various gamma and beta identities, but got a little stuck on

where this comes from.

I know $\displaystyle {\Gamma}(n+1)=n!, \;\ {\Gamma}(2n+1)=(2n)!$ and so forth.

I tried various ways, but failed to get it to come together.

Where is the world do those factorials come from in that beta identity. I am missing something. Probably obvious. Always is.