Some theorems on absolute Cesàro summability

Abstract

1. It is convenient to begin with a brief statement of the notation which will be used throughout this paper.Let k be any positive number and letwhere is the coefficient of xn in the formal expansion of (1 – x )–k–1, and letThen the series Σαn is said to be summable(C, k) if is convergent, that is, if tends to a limit, and absolutely summable (C, k), or summable |C, k|, if is absolutely convergent.