Nagoya Mathematical Journal

Wiman-Valiron method for difference equations

K. Ishizaki and N. Yanagihara

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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 $\chi < 1/2,$ 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 $L > 0.$

Article information

Nagoya Math. J., Volume 175 (2004), 75-102.

First available in Project Euclid: 27 April 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 39A05: General theory
Secondary: 30D35: Distribution of values, Nevanlinna theory


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

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