PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 69(83), pp. 101--107 (2001)
TAYLOR SERIES OF THE NATURAL POWERS OF THE PICK FUNCTION AND APPLICATIONS
Pavel G. TodorovInstitute of Mathematics and Informatics Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
Abstract: 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
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© 2002 Mathematical Institute of the Serbian Academy of Science and Arts