A complement to a recent paper on some infinite sums with the zeta values
Iaroslav V. Blagouchine

TL;DR
This paper explores the series involving zeta values, revealing new connections to the critical line values of the zeta function and the Euler constant, extending recent findings on infinite sums.
Contribution
It introduces novel links between the series with alternating zeta terms and fundamental constants, expanding understanding of zeta function evaluations.
Findings
Connection to zeta function on the critical line
Relation to Euler constant
Extension of recent series evaluation results
Abstract
Recently, several new results related to the evaluation of the series sum (-1)^n zeta(n)/(n+k) were published. In this short note we show that this series also possesses an interesting connection to the values of the zeta-function on the critical line and to the Euler constant.
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Taxonomy
TopicsAnalytic Number Theory Research · Advanced Mathematical Identities · Advanced Mathematical Theories
