Gottlieb Polynomials and Their q-Extensions

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...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 9; no. 13; p. 1499
Main Authors: ErkuŞ-Duman, Esra, Choi, Junesang
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.07.2021
Subjects:
Calculus
Food science
Functions (mathematics)
generalized and generalized basic (or -q) hypergeometric function
generating functions
Gottlieb polynomials in several variables
Identities
Investigations
Lauricella’s multiple hypergeometric series in several variables
Mathematical analysis
Polynomials
Power series
q-binomial theorem
q-Gottlieb polynomials in several variables
Sequences
Theorems
Variables
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary: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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math9131499