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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Vydáno v:Computational methods and function theory Ročník 23; číslo 2; s. 381 - 392
Hlavní autoři: Hinkkanen, Aimo, Miles, Joseph
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2023
Témata:
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
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Popis
Shrnutí: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