2025/05/28 by López, Ronald Orozco
#05A30 #11B68 #11B83 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2505.22500
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.