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Value distribution of meromorphic solutions of certain difference Painlevé equations. (English) Zbl 1183.30026
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:
 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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##### References:
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