Investigating the Properties and Diverse Applications of Special Polynomials Linked to Appell Sequences

Abstract

This paper presents a study that builds upon existing research by generating novel results by applying the monomiality principle. The primary focus of this work is the construction and analysis of Tangent-based Appell polynomials, with a detailed exploration of their properties, including their explicit and determinant forms, as well as their compliance with the monomiality principle. The study further investigates specific classes of Appell polynomials, namely the Tangent-based Bernoulli, Euler, and Genocchi polynomials, deriving key outcomes for each. In addition, numerical and graphical representations of the Tangent-based Bernoulli, Euler, and Genocchi polynomials are provided, facilitating a deeper understanding of their characteristics. This research contributes to the broader field of special polynomials and their applications in various mathematical and scientific contexts.