Things to remark: $\Gamma(x) = \int_0^{\infty} t^{x-1}e^{-t}dt.$
$\int_0^1 t^{x-1}(1-t)^{y-1}dt $ = $\frac {\Gamma(x)\Gamma(y)}{\Gamma(x+y)}$ = $B(x,y)$.
I don't understand from where do $(102)$ follow?
There is the $8.19$ theorem:
Any help would be appreciated.