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