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