I have seen the demonstration of beta distribution in youtube (https://www.youtube.com/watch?v=3vBBh0SDpqM) at the last B(m,n) is calculated as: (n-1)!(m-1)!/(m+n-1)!.

The question that I ask is:

This last result is obtained for m and n as integers ? if these last ones are réel, what will us obtained for the beta distribution.

I suppose that it will gamma distribution but i'm not sur.