A Non-Standard Generating Function for Continuous Dual $q$-Hahn polynomials
We study a non-standard form of generating function for the three-parameter continuous dual q-Hahn polynomials $p_{n} (x; a, b, | q)$, which has surfaced in a recent work of the present authors on the construction of lifting $q$-difference operators in the Askey scheme of basic hypergeometric polyno...
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Universidad de Costa Rica
2011-03-01
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| Series: | Revista de Matemática: Teoría y Aplicaciones |
| Online Access: | https://revistas.ucr.ac.cr/index.php/matematica/article/view/2117 |
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doaj-b732457b1baf450e99f30f1ebc1bfcfd2020-11-24T22:51:11ZspaUniversidad de Costa RicaRevista de Matemática: Teoría y Aplicaciones2215-33732011-03-0118111112010.15517/rmta.v18i1.21172015A Non-Standard Generating Function for Continuous Dual $q$-Hahn polynomialsMesuma Atakishiyeva0Natig Atakishiyev1Universidad Autónoma del Estado de Morelos, Facultad de CienciasUniversidad Nacional Autónoma deMéxico, Instituto de Matemáticas, Unidad CuernavacaWe study a non-standard form of generating function for the three-parameter continuous dual q-Hahn polynomials $p_{n} (x; a, b, | q)$, which has surfaced in a recent work of the present authors on the construction of lifting $q$-difference operators in the Askey scheme of basic hypergeometric polynomials. We show that the resulting generating function identity for the continuous dual q-Hahn polynomials $ p_{n} (x; a, b, c | q)$ can be explicitly stated in terms of Jackson’s $q$-exponential functions $e_{q} (z)$.https://revistas.ucr.ac.cr/index.php/matematica/article/view/2117 |
| collection |
DOAJ |
| language |
Spanish |
| format |
Article |
| sources |
DOAJ |
| author |
Mesuma Atakishiyeva Natig Atakishiyev |
| spellingShingle |
Mesuma Atakishiyeva Natig Atakishiyev A Non-Standard Generating Function for Continuous Dual $q$-Hahn polynomials Revista de Matemática: Teoría y Aplicaciones |
| author_facet |
Mesuma Atakishiyeva Natig Atakishiyev |
| author_sort |
Mesuma Atakishiyeva |
| title |
A Non-Standard Generating Function for Continuous Dual $q$-Hahn polynomials |
| title_short |
A Non-Standard Generating Function for Continuous Dual $q$-Hahn polynomials |
| title_full |
A Non-Standard Generating Function for Continuous Dual $q$-Hahn polynomials |
| title_fullStr |
A Non-Standard Generating Function for Continuous Dual $q$-Hahn polynomials |
| title_full_unstemmed |
A Non-Standard Generating Function for Continuous Dual $q$-Hahn polynomials |
| title_sort |
non-standard generating function for continuous dual $q$-hahn polynomials |
| publisher |
Universidad de Costa Rica |
| series |
Revista de Matemática: Teoría y Aplicaciones |
| issn |
2215-3373 |
| publishDate |
2011-03-01 |
| description |
We study a non-standard form of generating function for the three-parameter continuous dual q-Hahn polynomials $p_{n} (x; a, b, | q)$, which has surfaced in a recent work of the present authors on the construction of lifting $q$-difference operators in the Askey scheme of basic hypergeometric polynomials. We show that the resulting generating function identity for the continuous dual q-Hahn polynomials $ p_{n} (x; a, b, c | q)$ can be explicitly stated in terms of Jackson’s $q$-exponential functions $e_{q} (z)$. |
| url |
https://revistas.ucr.ac.cr/index.php/matematica/article/view/2117 |
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AT mesumaatakishiyeva anonstandardgeneratingfunctionforcontinuousdualqhahnpolynomials AT natigatakishiyev anonstandardgeneratingfunctionforcontinuousdualqhahnpolynomials AT mesumaatakishiyeva nonstandardgeneratingfunctionforcontinuousdualqhahnpolynomials AT natigatakishiyev nonstandardgeneratingfunctionforcontinuousdualqhahnpolynomials |
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