Series-To-Series Quasi-Hausdorff Transformations

Let U = ^∞∑_{I =0} u_i be a series, convergent or not, and let (a_nk) be an infinite square matrix. If for n = 0,1, 2 , . . . The series ∑a_nk u_k converges to some value v_n, and if also the series ∑ v_n converges, then U is said to be summable by the series-to-series transformation A = (a_nk) to the sum ∑ v_n.