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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Autores Principales: Atakishiyeva, Mesuma, Atakishiyev, Natig
Formato: Artículo
Idioma: Español
Publicado: 2015
Acceso en línea: http://revistas.ucr.ac.cr/index.php/matematica/article/view/2117
http://hdl.handle.net/10669/12988
Sumario: 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 $e_{q} (z)$.