On Generalized Cesàro-Based Apostol Type Special Polynomials


Nejla Özmen, Esra Erkuş-Duman




We define a new and generalized family of polynomials based on a Cesàro-type generating function. This new class, called the generalized Cesàro-based special polynomials, includes several well-known families such as Bernoulli, Euler, and Genocchi polynomials as special cases. Although these classical polynomials are well studied, we provide new definitions for their Cesàro-based versions by using our general formulation. The generating function involves multiple parameters, allowing a wide range of flexibility and generalization. We study important properties of these polynomials, including recurrence relations, addition formulas, and generating function identities. Our results offer a unified approach to classical special polynomials and open new directions for further research in number theory, combinatorics, and approximation theory.