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Explicit formulas for the coefficients of Faber polynomials with respect to univalent functions of the class $ \Sigma $


Author: Pavel G. Todorov
Journal: Proc. Amer. Math. Soc. 82 (1981), 431-438
MSC: Primary 30C50; Secondary 30D30
DOI: https://doi.org/10.1090/S0002-9939-1981-0612735-4
MathSciNet review: 612735
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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$ [6].


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DOI: https://doi.org/10.1090/S0002-9939-1981-0612735-4
Keywords: Faber polynomial, Grunsky coefficient, Faà di Bruno formula for the $ n$th derivative of composite functions
Article copyright: © Copyright 1981 American Mathematical Society