New Parametric Polynomials of U-Charlier-Poisson Type: Properties and Szász-Type Operators Including These Polynomials (Contemporary Mathematics, 2025)
In this article, we introduce a new family of parametric U-Charlier-Poisson type polynomials, denoted by Gn[2+J] (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