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Entire Functions of Small Order of Growth

Entire Functions of Small Order of Growth Let f and F be transcendental entire functions. We are concerned with a growth estimate of F ∘ f when F satisfies the condition $$\log M(r,F)=K(\log r)^p(1+O(1)),$$ where K is a positive constant and p > 1. It is shown that $$\log\log M(r,F(f))=p\log\log M(r,f)(1+O(1)).$$ We give an application to a certain functional equation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Entire Functions of Small Order of Growth

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References (7)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321804
Publisher site
See Article on Publisher Site

Abstract

Let f and F be transcendental entire functions. We are concerned with a growth estimate of F ∘ f when F satisfies the condition $$\log M(r,F)=K(\log r)^p(1+O(1)),$$ where K is a positive constant and p > 1. It is shown that $$\log\log M(r,F(f))=p\log\log M(r,f)(1+O(1)).$$ We give an application to a certain functional equation.

Journal

Computational Methods and Function Theory – Springer Journals

Published: Feb 12, 2011

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