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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:
30D35Distribution of values (one complex variable); Nevanlinna theory
References:
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