PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 69(83), pp. 101107 (2001) 

TAYLOR SERIES OF THE NATURAL POWERS OF THE PICK FUNCTION AND APPLICATIONSPavel G. TodorovInstitute of Mathematics and Informatics Bulgarian Academy of Sciences, 1113 Sofia, BulgariaAbstract: We find the simplest forms of the Taylor series of the natural powers of the Pick function. As an application we give a new proof of our formula (13) which throws a bridge over the de Branges proof and the Weinstein proof of the Bieberbach conjecture. Keywords: Pick function, Koebe function, natural powers of the Pick function, Taylor series, Gauss and Goursat hypergeometric polynomials, de Branges functions, Bieberbach conjecture, de Branges proof, Weinstein proof. Classification (MSC2000): 30B10, 30C50; 30C10, 33C05, 33C20 Full text of the article:
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