New convergent sequences of approximations to Stieltjes' constants

Stieltjes' constants γn are the coefficients in Laurent series for zeta function ζ(s) at pole s=1 (Euler's constant γ0 is term of this expansion). The main result paper construction new sequences approximations any one γn. rests on a generalization “remainder Padé approximants” method introduced by first named author 1996. We also focus γ1 which we construct faster using ordinary remainder approximants.