Comparison of Products of Methods of Summability*

determined by the matrix A =(a„fc) of real or complex constants, if the transform S» exists and limn^S„ = L. The matrix A (and method of summability A) is called row-finite if for each n, a„k = 0 for all sufficiently great k; and is called triangular if an* = 0 for k>n. The method A is regular if sn—>L implies Sn-*L. Necessary and sufficient conditions that A be regular are, by the Silverman-Toeplitz theorem,