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May 2011 Finite order meromorphic solutions of linear difference equations
Sheng Li, Zong-Sheng Gao
Proc. Japan Acad. Ser. A Math. Sci. 87(5): 73-76 (May 2011). DOI: 10.3792/pjaa.87.73

Abstract

In this paper, we mainly investigate the growth and the value distribution of meromorphic solutions of the linear difference equation \begin{equation*} a_{n}(z)f(z+n)+…+a_{1}(z)f(z+1)+a_{0}(z)f(z)=b(z), \end{equation*} where $a_{0}(z),a_{1}(z),\cdots,a_{n}(z),b(z)$ are entire functions such that $a_{0}(z)a_{n}(z)\not\equiv 0$. For a finite order meromorphic solution $f(z)$, some interesting results on the relation between $\rho=\rho(f)$ and $\lambda_{f}=\max\{\lambda(f),\lambda(1/f)\}$, are proved. And examples are provided for our results.

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Sheng Li. Zong-Sheng Gao. "Finite order meromorphic solutions of linear difference equations." Proc. Japan Acad. Ser. A Math. Sci. 87 (5) 73 - 76, May 2011. https://doi.org/10.3792/pjaa.87.73

Information

Published: May 2011
First available in Project Euclid: 26 April 2011

zbMATH: 1226.30032
MathSciNet: MR2803894
Digital Object Identifier: 10.3792/pjaa.87.73

Subjects:
Primary: 30D35 , 39A13 , 39A22

Keywords: difference equations , Finite order , value distribution

Rights: Copyright © 2011 The Japan Academy

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Vol.87 • No. 5 • May 2011
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