Preprint Article Version 1 This version is not peer-reviewed

Research on Some New Results Arising from Multiple q-Calculus

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

A peer-reviewed article of this Preprint also exists.

Duran, U.; Acikgoz, M.; Araci, S. Research on Some New Results Arising from Multiple q-Calculus. FILOMAT 2018, 32, 1-9. Duran, U.; Acikgoz, M.; Araci, S. Research on Some New Results Arising from Multiple q-Calculus. FILOMAT 2018, 32, 1-9.

Journal reference: Filomat 2018, 32
DOI: 10.2298/FIL1801001D

Abstract

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.

Subject Areas

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

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