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Computational Methods and Function Theory 8 (2008), No. 1, 199--202
Copyright Heldermann Verlag 2008

A Jentzsch-Type-Theorem

Wolfgang Luh
luh@uni-trier.de , Universität Trier, Fachbereich IV Mathematik, 54286 Trier, Germany.

[Abstract-pdf] [Abstract-ps]

Suppose that $\sum_{\nu=0}^{\infty} a_\nu z^\nu$ is a power series with radius of convergence $1$ and denote by $s_n(z)=\sum_{\nu=0}^{n} a_\nu z^\nu$ its partial sums. In this paper, we investigate properties of the mapping $w=s_n(z)$.

Keywords: Power series, distribution of zeros, Jentzsch-theorems.

MSC 2000: 30B10, 30C15.

[FullText-pdf (193 K)] [FullText-ps (327 K)]