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

Abstract

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