Distribution of partial sums of the Taylor development of rational functions

Nestoridis, V.

doi:10.1090/S0002-9947-1994-1264150-4

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 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 . We investigate the angular distribution of the sequence ${S_N}(z),\;N = 0,1,2, \ldots$ , around . We show that for all in the plane, except a denumerable union of straight lines passing through 0, this angular distribution exists and is uniform.

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