my problem is to find out for what values of m and n the beta function

( defined by: [integral from 0 to 1] t^(m-1) * (1-t)^(n-1)dt)

is convergent... I have worked on it for several hours and am stuck

obviously the problems are at the endpoints, so i broke it up into two integrals, an integral from 0 to 1/2 and an integral from 1/2 to 1.

Now my only inclination is to use the comparison theorem for different combinations of possible values for m and n...I have shown divergence or convergence in several cases but can't narrow it down to only being convergent for m,n > 0, can anyone help?