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On the Stieltjes constants with respect to harmonic zeta functions (2304.03517v1)
Published 7 Apr 2023 in math.NT and math.CV
Abstract: The aim of this paper is to investigate harmonic Stieltjes constants occurring in the Laurent expansions of the function [ \zeta_{H}\left( s,a\right) =\sum_{n=0}{\infty}\frac{1}{\left( n+a\right) {s}}\sum_{k=0}{n}\frac{1}{k+a},\text{ }\operatorname{Re}\left( s\right) >1, ] which we call harmonic Hurwitz zeta function. In particular evaluation formulas for the harmonic Stieltjes constants $\gamma_{H}\left( m,1/2\right) $ and $\gamma_{H}\left( m,1\right) $ are presented.