Investigating the Properties and Diverse Applications of Special Polynomials Linked toAppell Sequences

This paper presents a study that builds upon existing research by applying the monomialityprinciple to generate novel results. The study primarily focuses on the construction and analysis of tangent-based Appell polynomials, exploring their properties in detail, including their explicit and determinant forms,and their compliance with the monomiality principle. The study also investigates specific classes of Appellpolynomials — namely, the tangent-based Bernoulli, Euler and Genocchi polynomials — and derives key out-comes for each. Additionally, the paper provides numerical and graphical representations of these polynomials,facilitating a deeper understanding of their characteristics. This research contributes to the broader field ofspecial polynomials and their applications in various mathematical and scientific contexts.