EXPANSION OF GENERALIZED STIELTJES CONSTANTS IN TERMS OF DERIVATIVES OF HURWITZ ZETA-FUNCTIONS

Marc Prévost (1)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

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.

Mots clés: Stieltjes constants; Riemann zeta function; Hurwitz zeta function; Laurent expansion; Stirling numbers of the first kind.

Domaines: Analyse numérique [cs.NA]

Marc Prévost. EXPANSION OF GENERALIZED STIELTJES CONSTANTS IN TERMS OF DERIVATIVES OF HURWITZ ZETA-FUNCTIONS. 2023. ⟨hal-04105596⟩