Tauberian Constants and Quasi-Hausdorff Series-to-Series Transformations

It is the object of this paper to obtain the best estimate, in a certain sense, of |σ_n-S_m| where s_m is the partial sum of a series satisfying the Tauboerian condition u_n=0(1/n) and σ_n is the partial Sum of Σv_n where v_n is the Quasi-Hausdorff series-to-series transform of Σu_n by the regular matrix (H^*, μ.).