Analytical properties of Δ h -hybrid Laguerre-Appell polynomials and their applications in computer modeling

This work thoroughly investigates a new class of polynomials, the \(Δ_h\) Laguerre-Appell polynomials, which combine certain operational strategies with the principle of monomiality. By using an innovative approach, this study adds to previous research on the subject and presents discoveries. Since these polynomials are essential for simulating entropy in quantum systems, their significance is especially clear in quantum mechanics. In-depth derivations of explicit formulas and an analysis of important characteristics and links to well-known polynomial families are given. Through an examination of the special characteristics and uses of \(Δ_h\) Laguerre-Appell polynomials, this work greatly expands their theoretical knowledge and increases their prospective applications in a variety of mathematical and scientific contexts.