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arXiv · 2304.03517

On the Stieltjes constants with respect to harmonic zeta functions

Levent Kargın·Ayhan Dil·Mehmet Cenkci·Mümün Can
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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.

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Levent Kargın, Ayhan Dil, Mehmet Cenkci, Mümün Can. 2023-04-07. On the Stieltjes constants with respect to harmonic zeta functions. https://doi.org/10.1016/j.jmaa.2023.127302

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