Orthogonal polynomials have been studied extensively by Legendre in 1784. They are representatively related to typically real functions, which played an important role in the geometric function theory, and its role of estimating coefficient bounds. This chapter associates certain bi-univalent functions with certain orthogonal polynomials, such as Gegnbauer polynomials and Horadam polynomials, and then explores some properties of the subclasses in hand. This chapter is concerned with the connection between orthogonal polynomials and bi-univalent functions. Our purpose is to introduce certain classes of bi-univalent functions by means of Gegenbauer polynomials and Hordam polynomials. Bounds for the initial coefficients of
Part of the book: Recent Research in Polynomials