The summation of infinite partial fraction decomposition I: some formulae related to the Hurwitz zeta function

Abstract

In this paper we establish a new summation method by expanding ${\prod }_k(1-\frac{z}{a_k}{)}^{-1}$ with two approaches: the Taylor expansion and the infinite partial fraction decomposition. Here we focus on the case when $a_k$ is arithmetic sequence. By this summation we obtain many equalities involve Hurwitz zeta function and Gammma function.

arXiv comment14 pages