  Little is known about the zeros of the Digamma function. Establishing some
Weierstrassian infinite product representations for a given regularization of
the Digamma function we find interesting sums of its zeros. In addition, we
study the same questions for the zeros of the logarithmic derivative of the
Barnes $G$ function. At the end of the paper we provide rather accurate
approximations of the hyperfactorial where, rather interestingly, the Lambert
function appears.
