Quantum algebra from generalized q-Hermite polynomials

Abstract

In this paper, we discuss new results related to the generalized discrete $q$-Hermite II polynomials ${\tilde{h}}_{n,\alpha }(x;q)$, introduced by Mezlini et al. in 2014. Our aim is to give a continuous orthogonality relation, a $q$-integral representation and an evaluation at unity of the Poisson kernel, for these polynomials. Furthermore, we introduce $q$-Schrödinger operators and give the raising and lowering operator algebra corresponding to these polynomials. Our results generate a new explicit realization of the quantum algebra ${\mathsf{su}}_q(1,1)$, using the generators associated with a $q$-deformed generalized para-Bose oscillator.

References in corpus (1)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue

Cited by in corpus (1)

• Mean value theorem for quantum integral operator with application to sharp Ostrowski inequality