Geodesic
Taylor Series of the Natural Powers of the Pick Function and Applications
Publications de l'Institut Mathématique, _N_S_69 (2001) no. 83, p. 101 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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.
Classification : 30B10 30C50 30C10 33C05 33C20
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. 
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     author = {Pavel G. Todorov},
     title = {Taylor {Series} of the {Natural} {Powers} of the {Pick} {Function} and {Applications}},
     journal = {Publications de l'Institut Math\'ematique},
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     number = {83},
     year = {2001},
     language = {en},
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Pavel G. Todorov. Taylor Series of the Natural Powers of the Pick Function and Applications. Publications de l'Institut Mathématique, _N_S_69 (2001) no. 83, p. 101 . http://geodesic.mathdoc.fr/item/PIM_2001_N_S_69_83_a12/