  We consider the three conjectures stated in a 2003 paper of Wu, concerning
the asymptotics of particular sums of products of binomials, powers and
logarithms. These sums relate to the form of the regularised integrals used in
loop regularisation. We show all three are true, extend them to more general
powers and produce their full asymptotic series. We also extend a classical
result to produce an exact formula for the sum in the last.
