Expansion of Euler’s constant in terms of Zeta numbers

Many formulas involving Euler’s constant have been proved by different authors. Some of these expressions concern the expansion of Euler’s constant in terms of the Zeta function evaluated at integers. In this paper, using the Padé approximation, we prove a general formula depending on three parameters which contains as particular cases Euler’s, Euler–Stieltjes, Flajolet–Vardi and some new formulas. The last section contains similar formulas for generalized Euler constants.