Certain properties and characterizations of a novel family of bivariate 2D-q Hermite polynomials

Abstract

Abstract This study presents a novel family of bivariate 2D- q q Hermite polynomials. We derive explicit forms and q q -partial differential equations and investigate numerical aspects associated with these polynomials. Furthermore, we deduce the monomiality principle and other key properties of the bivariate 2D- q q Hermite polynomials, including q q -recurrence relations and q q -difference equations. In addition, the graphical representations for the bivariate 2D- q q Hermite polynomials and q q -Hermite polynomials are explored for different values of indices.