Research on Some New Results Arising from Multiple q-Calculus

Ugur Duran, Mehmet Acikgoz, Serkan Araci


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.

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