On the Stieltjes constants with respect to harmonic zeta functions

Kargın, LEVENT; Dil, AYHAN; Cenkci, MEHMET; Can, MÜMÜN

doi:10.1016/j.jmaa.2023.127302

On the Stieltjes constants with respect to harmonic zeta functions

Kargın L., Dil A., Cenkci M., Can M.

Journal of Mathematical Analysis and Applications, vol.525, no.2, 2023 (SCI-Expanded)

Publication Type: Article / Article
Volume: 525 Issue: 2
Publication Date: 2023
Doi Number: 10.1016/j.jmaa.2023.127302
Journal Name: Journal of Mathematical Analysis and Applications
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
Keywords: Euler sum, Harmonic numbers, Laurent expansion, Stieltjes constant, Zeta values
Akdeniz University Affiliated: Yes

Abstract

The aim of this paper is to investigate harmonic Stieltjes constants occurring in the Laurent expansions of the function [Formula presented] which we call harmonic Hurwitz zeta function. In particular evaluation formulas for the harmonic Stieltjes constants γH(m,1/2) and γH(m,1) are presented.