Deformed Bivariate $q$-Appell Polynomials
Combinatorics
2025-05-29 v1
Abstract
In this paper, we introduce bivariate polynomial sets of deformed -Appell type, and we study the algebraic properties of these sets. We show the relation between deformed bivariate -Appell polynomials and deformed homogeneous polynomials. Next, we give some of their characterizations and algebraic structure. Then, we introduce the deformed -Appell operators and obtain Mehler's and Rogers-type formulas of quasi--Appell polynomials. Finally, some examples of polynomial sequences of deformed -Appell type are given: Bernoulli, Euler, and Genocchi types.
Cite
@article{arxiv.2505.22500,
title = {Deformed Bivariate $q$-Appell Polynomials},
author = {Ronald Orozco López},
journal= {arXiv preprint arXiv:2505.22500},
year = {2025}
}