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.

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Bibliographic Details
Published in:Computational methods and function theory Vol. 23; no. 2; pp. 381 - 392
Main Authors: Hinkkanen, Aimo, Miles, Joseph
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2023
Subjects:
Analysis
Computational Mathematics and Numerical Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Primary 30D20
Entire function
Asymptotic value
Secondary 31A05
ISSN:1617-9447, 2195-3724
Online Access:Get full text
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Description
Summary: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.
ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-022-00464-2