A complement to a recent paper on some infinite sums with the zeta values

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.