Characterization of $({\cal R},p,q)-$deformed Rogers-Szeg\"o polynomials: associated quantum algebras, deformed Hermite polynomials and relevant properties

J D Bukweli Kyemba; M N Hounkonnou

arxiv: 1204.4705 · v1 · pith:VLS4EM3Vnew · submitted 2012-04-20 · 🧮 math-ph · math.MP

Characterization of ({cal R},p,q)-deformed Rogers-Szeg\"o polynomials: associated quantum algebras, deformed Hermite polynomials and relevant properties

J D Bukweli Kyemba , M N Hounkonnou This is my paper

classification 🧮 math-ph math.MP

keywords deformedpolynomialsassociatedcharacterizationhermitequantumrecurrencerelation

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This paper addresses a new characterization of $({\cal R},p,q)-$deformed Rogers-Szeg\"o 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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