EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 69(83), pp. 101--107 (2001)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home

EMIS Home

 		 

TAYLOR SERIES OF THE NATURAL POWERS OF THE PICK FUNCTION AND APPLICATIONS

Pavel G. Todorov

Institute 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

Full text of the article:

Electronic fulltext finalized on: 5 Feb 2002. This page was last modified: 5 Feb 2002.

© 2002 Mathematical Institute of the Serbian Academy of Science and Arts
© 2002 ELibM for the EMIS Electronic Edition