%0 Unpublished work %T EXPANSION OF GENERALIZED STIELTJES CONSTANTS IN TERMS OF DERIVATIVES OF HURWITZ ZETA-FUNCTIONS %+ Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville (LMPA) %A Prévost, Marc %8 2023-05-01 %D 2023 %Z 2305.15806 %K Stieltjes constants %K Riemann zeta function %K Hurwitz zeta function %K Laurent expansion %K Stirling numbers of the first kind. %Z 2020 Mathematics Subject Classification Primary: 11Y60, 41A21; 2020 Mathematics Subject Classification Secondary: 41A60 %Z Computer Science [cs]/Numerical Analysis [cs.NA]Preprints, Working Papers, ... %X 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. %G English %2 https://ulco.hal.science/hal-04105596/document %2 https://ulco.hal.science/hal-04105596/file/Stieltjes%20constants%20V17.pdf %L hal-04105596 %U https://ulco.hal.science/hal-04105596 %~ UNIV-LITTORAL %~ LMPA-JL