Contemporary Mathematics https://ojs.wiserpub.com/index.php/CM/ Research Article New Parametric Polynomials of U -Charlier-Poisson Type: Properties and Szász-Type Operators Including These Polynomials Cesarano Clemente 1* , Alejandro Urieles 2 , Javier Villa 2 , María José Ortega 3 1 Section of Mathematics, UniNettuno University, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy 2 Mathematics Program, University of the Atlantic, Km 7 Via Pto. Colombia, Barranquilla, Colombia 3 Department of Natural and Exact Sciences, University of the Coast, Barranquilla, Colombia E-mail: c.cesarano@uninettunouniversity.net Received: 6 June 2025; Revised: 16 July 2025; Accepted: 24 July 2025 Abstract: In this article, we introduce a new family of parametric U -Charlier-Poisson type polynomials, denoted by G [2+J] n (x; α , β , λ ). Then, some properties are studied, such as its explicit representation, the orthogonality relationship, and its connection with the derivative of the harmonic function. Subsequently, Szász-type operators are applied to the new family of polynomials to study convergence properties using Korovkin’s theorem. Keywords: Charlier polynomials, Korovkin theorem, Brenke type operators MSC: 11B68, 11B83, 11B39, 05A19 1. Introduction Throughout this article, N will mean the set of natural numbers; N 0 = N ∪{0}, likewise R, R + , and C will denote the set of real numbers, positive real numbers, and the set of complex numbers. As usual, will denote by C[0, ∞) the set of all functions f continuous in the interval [0, ∞). The notation UC[0, ∞) will denote the space of functions uniformly continuous on [0, ∞). The space of all polynomials in one variable with real coefficients is denoted by P, and log(z) denotes the principal value of the multi-valued logarithm function. In [1], a famous theorem about linear operators is published, known as the Korovkin theorem, which states that a sequence of linear operators under certain conditions converges uniformly in each subset of the locally compact domain. Korovkin theorem, in its many applications, was also used to demonstrate the convergence of Szász operators, which are defined by (see [2, p.239, Eq. (2)]): S n ( f ; x): = e −nx ∞ ∑ k=0 (nx) k k! f  k n  , (1) where f ∈ C[0, ∞), n ∈ N, and x ≥ 0. The generalizations of Szász operators by using polynomials, especially defined via generating functions, have been frequently studied lately. These kinds of generalizations provide a range of new sequences Copyright ©2025 Cesarano Clemente, et al. DOI: https://doi.org/10.37256/cm.6420257391 This is an open-access article distributed under a CC BY license (Creative Commons Attribution 4.0 International License) https://creativecommons.org/licenses/by/4.0/ Volume 6 Issue 4|2025| 5293 Contemporary Mathematics