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

Abstract

This paper addresses a new characterization of $(\mathcal{R},p,q)-$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 $(\mathcal{R},p,q)-$deformed Hermite polynomials and their recurrence relation are also deduced. Novel relations are provided and discussed.

References in corpus (1)

• Two-parameter quantum algebras, twin-basic numbers, and associated generalized hypergeometric series