English

A note on the zeros and local extrema of Digamma related functions

Complex Variables 2016-02-10 v2

Abstract

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 GG function. At the end of the paper we provide rather accurate approximations of the hyperfactorial where, rather interestingly, the Lambert function appears.

Keywords

Cite

@article{arxiv.1409.2971,
  title  = {A note on the zeros and local extrema of Digamma related functions},
  author = {István Mező},
  journal= {arXiv preprint arXiv:1409.2971},
  year   = {2016}
}