What question did this study set out to answer?

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

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

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Investigates inverse operations related to q-functions, suggesting significant mathematical utility.

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.

F. H. Jackson (1909) studied this question.

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