The Relationship of Borel Distribution and Horadam Polynomials Leads to Analytical Bi-Univalent Functions

The Borel distribution is a practical and applicable model for a wide range of real-world applications. Using the Borel distribution as a foundation, we create a novel subclass of analytic bi-univalent functions in this study. We employ these functions, which involve the ultraspherical polynomials, to create our new subclass. For functions that fall within the constructed class,we investigate alternative estimations of the Maclaurin coefficients and solve the Fekete-Szego functional problem.