Systematic Exploration of q‐Truncated‐Fubini–Appell Polynomials with Computational Applications

This article systematically investigates a new family of ‐special functions: the ‐truncated‐Fubini–Appell polynomials. We first define the fundamental ‐truncated‐Fubini polynomials through their generating function and establish their basic properties. For the extended family, we then develop explicit series representations, ‐recurrence relations, ‐integral formulas, quasi‐monomial properties, differential equations, and a determinant representation. Applying this general theory yields specific results for notable cases such as the ‐truncated‐Fubini–Bernoulli and Euler polynomials. Finally, a computational study using Mathematica offers visual and numerical analysis of the polynomials' zero distributions, providing support for the theoretical results.