What question did this study set out to answer?

The aim is to explore the properties of an operative symbol useful for q-functions.

January 1, 1909

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

Key Points

The aim is to explore the properties of an operative symbol useful for q-functions.
Investigate forms and nature of the difference operator Δ−n.
Examine inverse operations with considerations of continuity.
Analyze an arbitrary function φ(x) of x.
Establishes the various forms of inverse operations relating to the difference operator.
Identifies the utility of the operative symbol in analyzing q-functions.

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 of and 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 .

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

Key Points

Abstract

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