Difference equations of q-Appell polynomials

TL;DR

This paper investigates properties of q-Appell polynomials, deriving recurrence relations and q-difference equations that extend classical results and apply to various special cases like q-Bernoulli and q-Euler polynomials.

Contribution

It introduces new q-difference equations and recurrence relations for q-Appell polynomials and their special cases, expanding the theoretical framework of q-polynomial families.

Findings

Derived q-difference equations for q-Appell polynomials

Established recurrence relations for q-Bernoulli, q-Euler, and q-Genocchi polynomials

Introduced q-Hermite polynomials as a new special case

Abstract

In this paper, we study some properties of the q-Appell polynomials, including the recurrence relations and the q-difference equations which extend some known calssical (q=1) results. We also provide the recurrence relations and the q-difference equations for q-Bernoulli polynomials, q-Euler polynomials, q-Genocchi polynomials and for newly defined q-Hermite polynomials, as special cases of q-Appell polynomials