On q-Hermite Polynomials with Three Variables: Recurrence Relations, q-Differential Equations, Summation and Operational Formulas

Abstract

In the present study, we use several identities from the q-calculus to define the concept of q-Hermite polynomials with three variables and present their associated formalism. Many properties and new results of q-Hermite polynomials of three variables are established, including their generation function, series description, summation equations, recurrence relationships, q-differential formula and operational rules.