The Beta function is defined by-
$\textstyle\displaystyle{B(x,y)=\int_{0}^{1}t^{x-1}(1-t)^{y-1}dt}$
From this we can derive-
$\textstyle\displaystyle{B(x,y)=\frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}}$
Which also gives us the generalization-
$\textstyle\displaystyle{B(x_1,\dots,x_n)=\frac{\Gamma(x_1)\cdots\Gamma(x_n)}{\Gamma(x_1+\cdots+x_n)}}$
Now I was wondering if there was an integral representation of the multivariate beta function just like there is for the beta function.
I thought there would be one in the Wikipedia page but there isn't so I came here.
