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On truncations of entire transcendental functions

On truncations of entire transcendental functions In this paper it is shown that outside every circle, every finite value is assumed by some truncation of the Taylor series of an entire transcendental function (in fact, by every truncation of sufficiently high degree). This result differs from both Casorati-Weierstrass and Picard theorems inasmuch as the truncations actually assume the preassigned values and that there are no exceptional values. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

On truncations of entire transcendental functions

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Publisher
Springer Journals
Copyright
Copyright © 1982 by Sociedade Brasileira de Matemática
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/BF02584670
Publisher site
See Article on Publisher Site

Abstract

In this paper it is shown that outside every circle, every finite value is assumed by some truncation of the Taylor series of an entire transcendental function (in fact, by every truncation of sufficiently high degree). This result differs from both Casorati-Weierstrass and Picard theorems inasmuch as the truncations actually assume the preassigned values and that there are no exceptional values.

Journal

Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals

Published: Mar 3, 2007

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