On some new formulae involving the Stieltjes constants

TL;DR

This paper introduces new infinite series representations for the generalized Stieltjes constants involving logarithmic terms and explores related relations with derivatives of the Hurwitz zeta function.

Contribution

It provides novel formulae for Stieltjes constants and investigates their connections with derivatives of the Hurwitz zeta function.

Findings

New series representations for Stieltjes constants involving logarithms

Relations between Stieltjes constants and derivatives of Hurwitz zeta function

Enhanced understanding of the properties of Stieltjes constants

Abstract

We show that the generalised Stieltjes constants may be represented by infinite series involving logarithmic terms. Some relations involving the derivatives of the Hurwitz zeta function are also investigated