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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 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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},
     pages = {101 },
     year = {2001},
     volume = {_N_S_69},
     number = {83},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2001_N_S_69_83_a12/}
}
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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/