A note on some infinite sums of Hurwitz zeta functions

2021/04/02 by R. B. Paris, Paris, R B
Mathematics · #11M35 #33E20 #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Inequalities and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2104.00957

openalex publication_date 2021/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider some closed-form evaluations of certain infinite sums involving the Hurwitz zeta function ζ(s,α) of the form ∑_k=1^∞ (± 1)^k k^m ζ(s,k), where m is a non-negative integer. For the sums with m=0 and the argument k in ζ(s,k) replaced by ka+b, where a and b are positive parameters, we also obtain a transformation formula suitable for computation in the limit a→0.

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