On some series of functions, (1)

Abstract

Let c 0 , c 1 ,…, c n ,…be a sequence of real constants, and ƒ 0 ( x ), ƒ 1 ( x ),…, ƒ n ( 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 series which may be obtained from the standard series by interchanging the signs of the terms in a quite arbitrary way.