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2004 Wiman-Valiron method for difference equations
K. Ishizaki, N. Yanagihara
Nagoya Math. J. 175: 75-102 (2004).

Abstract

Let $f(z)$ be an entire function of order less than $1/2.$ We consider an analogue of the Wiman-Valiron theory rewriting power series of $f(z)$ into binomial series. As an application, it is shown that if a transcendental entire solution $f(z)$ of a linear difference equation is of order $\chi < 1/2,$ then we have %$\chi$ is obtained from the Newton polygon for the equation, and $\log M(r,f) = Lr^{\chi}(1 + o(1))$ with a constant $L > 0.$

Citation

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K. Ishizaki. N. Yanagihara. "Wiman-Valiron method for difference equations." Nagoya Math. J. 175 75 - 102, 2004.

Information

Published: 2004
First available in Project Euclid: 27 April 2005

zbMATH: 1070.39002
MathSciNet: MR2085312

Subjects:
Primary: 39A05
Secondary: 30D35

Rights: Copyright © 2004 Editorial Board, Nagoya Mathematical Journal

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Vol.175 • 2004
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