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Zbl 1183.30026
Chen, Zong-Xuan; Shon, Kwang Ho
Value distribution of meromorphic solutions of certain difference Painlevé equations. (English)
[J] J. Math. Anal. Appl. 364, No. 2, 556-566 (2010). ISSN 0022-247X

Summary: The Borel exceptional value and the exponents of convergence of poles, zeros, and fixed points of finite order transcendental meromorphic solutions for difference Painlevé $I$ and $II$ equations are estimated. The forms of rational solutions of the difference Painlevé $II$ equation and the autonomous difference Painlevé $I$ equation are also given. It is also proved that the non-autonomous difference Painlevé $I$ equation has no rational solution.

MSC 2000:: *30D35 Distribution of values (one complex variable)

Keywords: difference Painlevé equation; Borel exceptional value; rational solution

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