Expansion of generalized Stieltjes constants in terms of derivatives of Hurwitz zeta-functions

05/25/2023

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by   M Prévost, et al.

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Generalized Stieltjes constants γ n (a) are the coecients in the Laurent series for the Hurwitz-zeta function ζ(s, a) at the pole s = 1. Many authors proved formulas for these constants. In this paper, using a recurrence between (ζ(s + j, a)) j and proved by the author, we prove a general result which contains some of these formulas as particular cases.