Research on Some New Results Arising from Multiple q-Calculus

Uğur Duran; Mehmet Acikgoz; Serkan Araci

doi:10.20944/preprints201712.0148.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 20 December 2017 / Approved: 21 December 2017 / Online: 21 December 2017 (04:31:25 CET)

In this paper, we develop the theory of the multiple q-analogue of the Heine’s binomial formula, chain rule and Leibnitz’s rule. We also derive many useful definitions and results involving multiple q-antiderivative and multiple q-Jackson’s integral. Finally, we list here multiple q-analogue of some elementary functions including trigonometric functions and hyperbolic functions. This may be a good consideration in developing the multiple q-calculus in combinatorics, number theory and other fields of mathematics.

quantum calculus; multiple quantum calculus; trigonometric functions; hyperbolic functions; Jackson’s integral

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Research on Some New Results Arising from Multiple q-Calculus

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