Integro-difference equations and umbral study for q-Appell-Hermite polynomials

Abstract

In this paper, we present q-Appell-Hermite polynomials and explore their various intriguing properties and traits using the factorization method. We also determine partial difference equations, pure difference equations, and integro-difference equations for the q-Appell-Hermite polynomials. Furthermore, we extend these findings to the q-Bernoulli-Hermite polynomials and q-Euler-Hermite polynomials. Finally, graphical representations of these polynomials are provided as concluding remarks. The proposed technique is umbral and factorization method.