Laurent expansion of harmonic zeta functions

“…A complete evaluation of the sums R 1,p , R p,1 , and R p,p is then given for each positive integer p. This allows us to provide a number of relations similar (though more complicated) to the classical relations mentioned above (see Propositions 1 to 4). Several interesting applications of these formulas are given in [4] and [8].…”

Section: Introductionmentioning

confidence: 99%

On some formulae related to Euler sums

Coppo

Candelpergher

2022

Lith Math J

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“…Hence, (12) follows from ( 13) and (14). We are ready to give the aforementioned representation for the constants γ h (r) (m) .…”

Section: Alternative Representations For Hyperharmonic Stieltjes Cons...mentioning

confidence: 99%

“…and give explicitly the coefficient a 0 when b = 0 and b = 1 − 2j, j ∈ N. Recently, using the Ramanujan summation method, Candelpergher and Coppo [12] record that the harmonic Stieltjes constants γ H (m) defined by the Laurent expansion…”

Section: Introductionmentioning

confidence: 99%

Stieltjes constants appearing in the Laurent expansion of the hyperharmonic zeta function

Can¹,

Dil²,

Kargın³

2021

Preprint

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In this paper, we consider meromorphic extension of the function(which we call hyperharmonic zeta function) where h (r) n are the hyperharmonic numbers. We establish certain constants, denoted γ h (r) (m), which naturally occur in the Laurent expansion of ζ h (r) (s). Moreover, we show that the constants γ h (r) (m) and integrals involving generalized exponential integral can be written as a finite combination of some special constants.

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