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arXiv · 2102.04115

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

Xiaowei Wang
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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.

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Xiaowei Wang. 2021-02-08. The summation of infinite partial fraction decomposition I: some formulae related to the Hurwitz zeta function. https://arxiv.org/abs/2102.04115

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