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Wiman-Valiron method for difference equations

Published online by Cambridge University Press:  22 January 2016

K. Ishizaki  and
N. Yanagihara
K. Ishizaki
Affiliation:
Department of Mathematics, Nippon Institute of Technology, 4-1 Gakuendai Miyashiro, Minamisaitama, Saitama-ken, 345-0826, Japan, ishi@nit.ac.jp
N. Yanagihara
Affiliation:
Minami-Iwasaki 671-18, Ichihara-City, Chiba-ken 290-0244, Japan, yanagihara-nm@icntv.ne.jp
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Abstract

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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 χ < 1/2, then we have log M (r, f) = Lrχ(1 + o(1)) with a constant L > 0.

Keywords

39B1030D35
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 175 , 2004 , pp. 75 - 102
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2004

References

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