Proceedings of the Japan Academy, Series A, Mathematical Sciences

Finite order meromorphic solutions of linear difference equations

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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 87, Number 5 (2011), 73-76.

Dates
First available in Project Euclid: 26 April 2011

https://projecteuclid.org/euclid.pja/1303825550

Digital Object Identifier
doi:10.3792/pjaa.87.73

Mathematical Reviews number (MathSciNet)
MR2803894

Zentralblatt MATH identifier
1226.30032

Citation

Li, Sheng; Gao, Zong-Sheng. Finite order meromorphic solutions of linear difference equations. Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 5, 73--76. doi:10.3792/pjaa.87.73. https://projecteuclid.org/euclid.pja/1303825550

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