Characterization of (\cal R,p,q)-deformed Rogers-Szegö polynomials: associated quantum algebras, deformed Hermite polynomials and relevant properties

2012/04/20 by Joseph Désiré Bukweli Kyemba, Kyemba, J D Bukweli, Mahouton Norbert Hounkonnou +1
Mathematics · #Algebraic structures and combinatorial models #Advanced Mathematical Identities #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.1204.4705

Abstract

This paper addresses a new characterization of (\cal R,p,q)-deformed Rogers-Szegö polynomials by providing their three-term recurrence relation and the associated quantum algebra built with corresponding creation and annihilation operators. The whole construction is performed in a unified way, generalizing all known relevant results which are straightforwardly derived as particular cases. Continuous (\cal R,p,q)-deformed Hermite polynomials and their recurrence relation are also deduced. Novel relations are provided and discussed.

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