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On some series of functions, (1)

Published online by Cambridge University Press:  24 October 2008

R. E. A. C. Paley
Trinity College


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 series

which may be obtained from the standard series

by interchanging the signs of the terms in a quite arbitrary way.

Research Article
Copyright © Cambridge Philosophical Society 1930

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