Explicit formulas for the coefficients of Faber polynomials with respect to univalent functions of the class Σ

Abstract

In this note, we obtain three natural explicit formulas for the coefficients of the Faber polynomials with respect to the univalent functions of the class ∑ \sum . As an application, we obtain two new explicit formulas for the Grunsky coefficients of functions in ∑ \sum ; these formulas are simpler than those due to Schur [2] and Hummel [4]. The method used in this paper is different from the one that we used to obtain explicit expressions for the Grunsky coefficients for functions of the class S S [6].