Deformed Bivariate $q$-Appell Polynomials

TL;DR

This paper introduces and studies deformed bivariate q-Appell polynomials, exploring their algebraic properties, relations, and specific examples like Bernoulli, Euler, and Genocchi types.

Contribution

It presents the first systematic study of deformed bivariate q-Appell polynomials, including their algebraic structure, characterizations, and related operators.

Findings

Established relations with deformed homogeneous polynomials

Derived Mehler's and Rogers-type formulas for these polynomials

Provided examples including Bernoulli, Euler, and Genocchi types

Abstract

In this paper, we introduce bivariate polynomial sets of deformed $q$-Appell type, and we study the algebraic properties of these sets. We show the relation between deformed bivariate $q$-Appell polynomials and deformed homogeneous polynomials. Next, we give some of their characterizations and algebraic structure. Then, we introduce the deformed $q$-Appell operators and obtain Mehler's and Rogers-type formulas of quasi-$q$-Appell polynomials. Finally, some examples of polynomial sequences of deformed $q$-Appell type are given: Bernoulli, Euler, and Genocchi types.