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On the Proximate Order of Growth of Generating Functions of Pólya Frequency Sequences

On the Proximate Order of Growth of Generating Functions of Pólya Frequency Sequences We study the possible growth of Pólya frequency sequence generating functions analytic in the unit disk and describe the proximate orders of growth of these functions. Some classical function theory results concerning orders of growth are generalized to the case of proximate orders. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

On the Proximate Order of Growth of Generating Functions of Pólya Frequency Sequences

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Publisher
Springer Journals
Copyright
Copyright © 2001 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/BF03321001
Publisher site
See Article on Publisher Site

Abstract

We study the possible growth of Pólya frequency sequence generating functions analytic in the unit disk and describe the proximate orders of growth of these functions. Some classical function theory results concerning orders of growth are generalized to the case of proximate orders.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 7, 2013

References