Distribution of partial sums of the Taylor development of rational functions
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- by V. Nestoridis PDF
- Trans. Amer. Math. Soc. 346 (1994), 283-295 Request permission
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.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- 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