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Asymptotic Values of Entire Functions of Infinite Order

Asymptotic Values of Entire Functions of Infinite Order We prove that there exists an entire function for which every complex number is an asymptotic value and whose growth is arbitrarily slow subject only to the necessary condition that the function is of infinite order. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Asymptotic Values of Entire Functions of Infinite Order

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-022-00464-2
Publisher site
See Article on Publisher Site

Abstract

We prove that there exists an entire function for which every complex number is an asymptotic value and whose growth is arbitrarily slow subject only to the necessary condition that the function is of infinite order.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Aug 18, 2022

Keywords: Entire function; Asymptotic value; Primary 30D20; Secondary 31A05

References