On some series of functions, (1)

Abstract

Let c0, c1,…, cn,…be a sequence of real constants, and ƒ0(x), ƒ1(x),…, ƒn(x),… a sequence of functions defined, for example, in the interval (0, 1). In this paper we shall investigate some of the properties of the serieswhich may be obtained from the standard seriesby interchanging the signs of the terms in a quite arbitrary way.