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...
| Main Authors: | , |
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| Format: | Article |
| Language: | Spanish |
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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 |
| Summary: | 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 $e_{q} (z)$. |
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| ISSN: | 2215-3373 |