Let sn=1+1/2+cdots, three dots, centered+1/(n−1)−logn. In 1995, the author has found a series transformation of the type image with integer coefficients μn,k,τ, from which geometric convergence to Eulerʹs constant γ for τ=O(n) results. In recently published papers T. Rivoal and Kh. & T. Hessami Pilehrood have generalized this result. In this paper we introduce a series transformation image with two parameters τ1 and τ2 and integer coefficients μn,k,τ1. By applying the analysis of the ψ-function, we prove a sharp upper bound for S−γ. A similar result holds for generalized Stieltjes constants.