Applications and Properties for Bivariate Bell-Based Frobenius-Type Eulerian Polynomials

Abstract

In this study, we introduce sine and cosine Bell-based Frobenius-type Eulerian polynomials, and by presenting several relations and applications, we analyze certain properties. Our first step is to obtain diverse relations and formulas that cover summation formulas, addition formulas, relations with earlier polynomials in the literature, and differentiation rules. Finally, after determining the first few zero values of the Eulerian polynomials, we draw graphical representations of these zero values.