Mesuma Atakishiyeva^*
Natig Atakishiyev^†

Abstract

We study a non-standard form of generating function for the three-parameter  continuous dual q-Hahn polynomials p n(x; a, b, c | 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 eq(z). ]]>
Keywords: q-scheme of Askey, generating function, q-exponential function of Jackson, dual q-Hahn polynomials.

Resumen

Estudiamos una forma no estándar de la función generatriz para una familia de polinomios duales continuos q-Hahn de tres parámetros p n( x; a, b, c | q ), que han surgido en un trabajo reciente de los autores en la construcción de operadores elevadores en q-diferencias del esquema de Askey de polinomios básicos  hipergeométricos. Demostramos que la función generatriz identidad resultante para  los polinomios q-Hahn duales continuos p n(x; a, b, c | q) puede ser expresada explícitamente en términos de las funciones q-exponenciales de Jackson eq(z).

Palabras clave: esquema q de Askey, función generatriz, polinomios duales q-Hahn, función q-exponencial de Jackson.

Mathematics Subject Classification: 33D45, 39A70, 47B39.

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Received: 18 Feb 2010; Revised: 22 Oct 2010; Accepted: 23 Nov 2010 ]]>