Properties of Orthogonal Polynomials and Typically Real Functions

The book is concerned with the connection between orthogonal polynomials and typically real functions, both strictly related to the Koebe function. Orthogonal polynomials appear in many areas of mathematics and have been the subject of interest of many mathematicians. In recent years this interest has often arisen from outside the subject of orthogonal polynomials, after their connection with the class of analytic functions. Our purpose is to investigate mathematical properties of some generalization of Koebe function, which is associated to the generalized Chebyshev polynomials of the second kind, as well as to the class of typically real functions that is defined by extended Koebe function. We approach the problem from both perspectives. By looking for a generating function of orthogonal polynomials and by using orthogonal polynomials as a tool to describe the properties of a class of functions.