Research on some new results arising from multiple q-calculus | Zendy

Uğur Duran | Zendy; Mehmet Açíkgöz | Zendy; Serkan Aracı | Zendy

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Research on some new results arising from multiple q-calculus

Author(s) -

Uğur Duran,

Mehmet Açíkgöz,

Serkan Aracı

Publication year - 2018

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1801001d

Subject(s) - mathematics , trigonometry , calculus (dental) , chain rule (probability) , binomial theorem , binomial (polynomial) , binomial coefficient , number theory , algebra over a field , trigonometric functions , discrete mathematics , pure mathematics , mathematical analysis , probability distribution , regular conditional probability , medicine , statistics , geometry , dentistry , probability mass function

In this paper, we develop the theory of the multiple q-analogue of the Heine?s binomial formula, chain rule and Leibniz?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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