Series expansions for the Riemann zeta function

2023/12/06 by Alexey N. Kuznetsov∥, Kuznetsov, Alexey
Mathematics · #Advanced Mathematical Identities #Mathematical functions and polynomials #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2312.03261

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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