1204.4705 (J D Bukweli Kyemba et al.)

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

J D Bukweli Kyemba, M N Hounkonnou

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.

View original: http://arxiv.org/abs/1204.4705