XI.—On q-Functions and a certain Difference Operator

Abstract

In this paper my object is, primarily, to investigate the properties of a certain operative symbol which appears to be of great utility in discussing q-functions. The first part of the paper will consist of an investigation into the various forms ofand the nature of the inverse operations symbolised by Δ−n. With certain restrictions as to continuity, etc., φ(x) will denote an arbitrary function of x.