On a new $q$-analogue of Appell polynomials

TL;DR

This paper introduces a novel $q$-analogue of Appell polynomial sequences, along with their generalizations, and derives new $q$-analogues of Bernoulli and Euler polynomials and numbers, including their key representations.

Contribution

The paper presents a new $q$-analogue of Appell polynomials and their generalizations, expanding the framework of $q$-calculus in polynomial theory.

Findings

New $q$-analogue of Appell polynomials introduced

Main characterizations of these polynomials proved

New $q$-analogues of Bernoulli and Euler polynomials and numbers derived

Abstract

A new $q$-analogue of Appell polynomial sequences and their generalizations are introduced and their main characterizations are proved. As consequences new $q$-analogue of Bernoulli and Euler polynomials and numbers is introduced, their main representations are given.