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

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.

References in corpus (2)

• Two series expansions for the logarithm of the gamma function involving Stirling numbers and containing only rational coefficients for certain arguments related to ${\pi }^{-1}$
• Subconvexity for the Riemann zeta-function and the divisor problem