The Koebe Radius for Certain Class of Polynomials

Explore the intricacies of close-to-convex polynomials with zeros of derivative in the unit circle in this 26-minute conference talk from the HyperComplex Seminar 2023. Delve into the determination of minimal and maximal discs containing images of the unit disc D through polynomials of degrees 3 and 4, including the identification of extremal functions. Examine the solution for polynomials of degree 5 and consider the hypothesis proposed for polynomials of odd degree. Gain insights from the joint work of Maciej Parol and Szymon Ignaciuk on the Koebe radius for specific polynomial classes within the context of holomorphic functions of one variable.