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.

Two-Variable q-Hermite-Based Appell Polynomials and Their Applications

“…In certain cases, we additionally reference published findings. (Check, over the instance [6,8,9,[36][37][38][39][40][41]).…”

“…Multiple researchers have recently investigated and studied a few strange polynomials connected by q-calculus. (See for example [2][3][4][5][6][7][8][9][10]).…”