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Functions of Finite Logarithmic Order in the Unit Disc, Part II

Functions of Finite Logarithmic Order in the Unit Disc, Part II Part I of this paper illustrates how the concept of logarithmic order in the unit disc, defined in terms of the Nevanlinna characteristic, gives a natural growth scale for meromorphic functions of unbounded characteristic but of zero (usual) order of growth. Part II deals with the analytic case, where the logarithmic order can be defined in terms of the maximum modulus as well as in terms of Wiman–Valiron indices. Given an analytic function $$f$$ f , these logarithmic orders are related to the Taylor coefficients of $$f$$ f . Part II culminates in revealing a refinement of Wiman–Valiron theory. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Functions of Finite Logarithmic Order in the Unit Disc, Part II

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Publisher
Springer Journals
Copyright
Copyright © 2014 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-014-0089-4
Publisher site
See Article on Publisher Site

Abstract

Part I of this paper illustrates how the concept of logarithmic order in the unit disc, defined in terms of the Nevanlinna characteristic, gives a natural growth scale for meromorphic functions of unbounded characteristic but of zero (usual) order of growth. Part II deals with the analytic case, where the logarithmic order can be defined in terms of the maximum modulus as well as in terms of Wiman–Valiron indices. Given an analytic function $$f$$ f , these logarithmic orders are related to the Taylor coefficients of $$f$$ f . Part II culminates in revealing a refinement of Wiman–Valiron theory.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Sep 5, 2014

References