Comparison of products of methods of summability
Ralph Palmer Agnew · Transactions of the American Mathematical Society · 1938
AB, is the method which associates with a given sequence the A transform of its B transform, that is,Thus 5" is summable ^4P to L if lim Un = L.The composition product is also at times denoted by AB; it is the method whose matrix is the product AB (which we denote by AB) of the matrices A and B. Thus we write 00 CO (AB) Vn = 5Z 23 anpbpksk, k=x p=x and s" is summable ^4 P to P if F"->P.We observe that Un and F" are, if they exist, respectively the "sum by rows" and the "sum by columns" of the double series(1.4) + a"3b3Xsx + a"3b32s2 + an3b33s3 + • • -+.