Generalized 2D Extension of the q-Bessel polynomials

Abstract

The article aims at introducing a generalized 2D extension of the q-Bessel polynomials. The generating equation, series expansion and determinant form for the generalized 2D q-Bessel polynomials are established. An example providing the continuous 2D q-Hermite--Bessel polynomials is considered. The recurrence relation and other properties for the continuous 2D q-Hermite--Bessel polynomials are derived. The graphs and plots depicting the behaviour of the continuous 2D Hermite polynomials, continuous 2D Hermite--Bessel polynomials and continuous 2D q-Hermite--Bessel polynomials are drawn. The distribution of zeros for these polynomials is also presented.