Gottlieb Polynomials and Their <i>q</i>-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 <i>q</i>-extensions of these polynomials...
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MDPI AG
2021-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/13/1499 |
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| author | Esra ErkuŞ-Duman Junesang Choi |
| author_facet | Esra ErkuŞ-Duman Junesang Choi |
| author_sort | Esra ErkuŞ-Duman |
| collection | DOAJ |
| description | 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 <i>q</i>-extensions of these polynomials to provide certain <i>q</i>-generating functions for three sequences associated with a finite power series whose coefficients are products of the known <i>q</i>-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 <i>q</i>-Gottlieb polynomials to highlight certain connections with several other known <i>q</i>-polynomials, and provide its <i>q</i>-integral representation. Furthermore, we conclude this paper by disclosing our future investigation plan. |
| first_indexed | 2024-03-10T10:02:00Z |
| format | Article |
| id | doaj.art-cde7b89e5bbc42f088a2c2395a08a1cb |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T10:02:00Z |
| publishDate | 2021-06-01 |
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| series | Mathematics |
| spelling | doaj.art-cde7b89e5bbc42f088a2c2395a08a1cb2023-11-22T01:50:46ZengMDPI AGMathematics2227-73902021-06-01913149910.3390/math9131499Gottlieb Polynomials and Their <i>q</i>-ExtensionsEsra ErkuŞ-Duman0Junesang Choi1Department of Mathematics, Faculty of Science, Gazi University, Teknikokullar, TR-06500 Ankara, TurkeyDepartment of Mathematics, Dongguk University, Gyeongju 38066, KoreaSince 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 <i>q</i>-extensions of these polynomials to provide certain <i>q</i>-generating functions for three sequences associated with a finite power series whose coefficients are products of the known <i>q</i>-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 <i>q</i>-Gottlieb polynomials to highlight certain connections with several other known <i>q</i>-polynomials, and provide its <i>q</i>-integral representation. Furthermore, we conclude this paper by disclosing our future investigation plan.https://www.mdpi.com/2227-7390/9/13/1499Gottlieb polynomials in several variables<i>q</i>-Gottlieb polynomials in several variablesgenerating functionsgeneralized and generalized basic (or -<i>q</i>) hypergeometric functionLauricella’s multiple hypergeometric series in several variables<i>q</i>-binomial theorem |
| spellingShingle | Esra ErkuŞ-Duman Junesang Choi Gottlieb Polynomials and Their <i>q</i>-Extensions Mathematics Gottlieb polynomials in several variables <i>q</i>-Gottlieb polynomials in several variables generating functions generalized and generalized basic (or -<i>q</i>) hypergeometric function Lauricella’s multiple hypergeometric series in several variables <i>q</i>-binomial theorem |
| title | Gottlieb Polynomials and Their <i>q</i>-Extensions |
| title_full | Gottlieb Polynomials and Their <i>q</i>-Extensions |
| title_fullStr | Gottlieb Polynomials and Their <i>q</i>-Extensions |
| title_full_unstemmed | Gottlieb Polynomials and Their <i>q</i>-Extensions |
| title_short | Gottlieb Polynomials and Their <i>q</i>-Extensions |
| title_sort | gottlieb polynomials and their i q i extensions |
| topic | Gottlieb polynomials in several variables <i>q</i>-Gottlieb polynomials in several variables generating functions generalized and generalized basic (or -<i>q</i>) hypergeometric function Lauricella’s multiple hypergeometric series in several variables <i>q</i>-binomial theorem |
| url | https://www.mdpi.com/2227-7390/9/13/1499 |
| work_keys_str_mv | AT esraerkusduman gottliebpolynomialsandtheiriqiextensions AT junesangchoi gottliebpolynomialsandtheiriqiextensions |