Zeros of the digamma function and its Barnes G-function analogue

Abstract

ABSTRACTThe zeros of the digamma function are known to be simple and real, but up to now few identities involving them have appeared in the literature. By establishing a Weierstrass infinite product for a particular regularization of the digamma function, we are able to find interesting formulas for the sums of the nth powers of the reciprocals of its zeros, for . We make a parallel study of the zeros of the logarithmic derivative of the Barnes G-function. We also compare asymptotic estimates of the zeros of the digamma function and those of its Barnes G-function analogue.