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Distribution of partial sums of the Taylor development of rational functions


Author: V. Nestoridis
Journal: Trans. Amer. Math. Soc. 346 (1994), 283-295
MSC: Primary 30B10; Secondary 26C15
DOI: https://doi.org/10.1090/S0002-9947-1994-1264150-4
MathSciNet review: 1264150
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Abstract: Let $ f$ be a rational function regular at 0, which is not a polynomial; let $ {S_N}(z),\;N = 0,1,2, \ldots ,z \in \mathbb{C}$, denote the partial sums of the Taylor development of $ f$. We investigate the angular distribution of the sequence $ {S_N}(z),\;N = 0,1,2, \ldots $, around $ f(z)$. We show that for all $ z$ in the plane, except a denumerable union of straight lines passing through 0, this angular distribution exists and is uniform.


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DOI: https://doi.org/10.1090/S0002-9947-1994-1264150-4
Article copyright: © Copyright 1994 American Mathematical Society

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