Series expansions for the Riemann zeta function

Alexey Kuznetsov

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arXiv · 2312.03261

Series expansions for the Riemann zeta function

Alexey Kuznetsov

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Abstract

We prove a general result on representing the Riemann zeta function as a convergent infinite series in a complex vertical strip containing the critical line. We use this result to re-derive known expansions as well as to discover new series representations of the Riemann zeta function in terms of the incomplete gamma functions, generalized hypergeometric functions and Meijer $G$-functions.

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Alexey Kuznetsov. 2023-12-06. Series expansions for the Riemann zeta function. https://arxiv.org/abs/2312.03261

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