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

Abstract

This study presents a novel family of bivariate 2D-qq Hermite polynomials. We derive explicit forms and qq-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-qq Hermite polynomials, including qq-recurrence relations and qq-difference equations. In addition, the graphical representations for the bivariate 2D-qq Hermite polynomials and qq-Hermite polynomials are explored for different values of indices.

Keywords

• q-special polynomials
• q-calculus
• monomiality principle
• explicit form
• numerical representation
• 33e20
• 33c45
• 33b10
• 33e30
• 11t23