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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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
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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.
AbstractList 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.
Author ErkuŞ-Duman, Esra
Choi, Junesang
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Cites_doi 10.4134/CKMS.2012.27.1.159
10.4134/CKMS.2003.18.4.781
10.1007/978-3-642-05014-5
10.2307/2371307
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10.14403/jcms.2012.25.2.253
10.1016/j.aml.2011.07.006
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10.18514/MMN.2018.2188
10.3836/tjm/1406552433
10.1007/978-1-4613-0071-7
10.1007/978-3-642-87682-0
ContentType Journal Article
Copyright 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
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SubjectTerms 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
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