Summability- (Z, p) and Sequences of Periodic Type

Abstract

We shall say that the sequence x = {sk} is summable- (Z, p) to the value s ifwhere p is a positive integer andIgnoring the values of n, 1 — p ≤ n < 0, which are clearly irrelevant, the transformation (Z, p) coincides with the regular Nörlund transformation defined by the sequence ( 1 , 1 , . . . , 1, 0, 0 , . . .) containing p initial 1's. This class of methods was first studied systematically by Silverman and Szász (8).