Gottlieb Polynomials and Their q -Extensions

Esra ErkuŞ-Duman and Junesang Choi
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Esra ErkuŞ-Duman: Department of Mathematics, Faculty of Science, Gazi University, Teknikokullar, TR-06500 Ankara, Turkey
Junesang Choi: Department of Mathematics, Dongguk University, Gyeongju 38066, Korea

Mathematics, 2021, vol. 9, issue 13, 1-15

Abstract: Since Gottlieb introduced and investigated the so-called Gottlieb polynomials in 1938, which are discrete orthogonal polynomials, many researchers have investigated these polynomials from diverse angles. In this paper, we aimed to investigate the q -extensions of these polynomials to provide certain q -generating functions for three sequences associated with a finite power series whose coefficients are products of the known q -extended multivariable and multiparameter Gottlieb polynomials and another non-vanishing multivariable function. Furthermore, numerous possible particular cases of our main identities are considered. Finally, we return to Khan and Asif’s q -Gottlieb polynomials to highlight certain connections with several other known q -polynomials, and provide its q -integral representation. Furthermore, we conclude this paper by disclosing our future investigation plan.

Keywords: Gottlieb polynomials in several variables; q -Gottlieb polynomials in several variables; generating functions; generalized and generalized basic (or - q ) hypergeometric function; Lauricella’s multiple hypergeometric series in several variables; q -binomial theorem; q -exponential functions; q -calculus; q -Jacobi polynomials; q -Meixner polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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