Open AccessResearch on some new results arising from multiple q-calculus
Author(s) -
Uğur Duran,
Serkan Aracı,
Mehmet Açıkgöz
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.