Growth of modified Painlevé transcendents of the fifth and the third kind. (English) Zbl 1058.34127

The author considers alternative versions of the third and fifth Painlevé equations. His aim is to estimate the magnitude of the characteristic function \(T(r,f)\) of the Nevanlinna theory for solutions of these two equations. He also comments on the classical work of P. Boutroux [Acta Math. 28, 97–224 (1904; JFM 35.0411.02)] in the case of the alternative version of the third Painlevé equation.


34M55 Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
33E17 Painlevé-type functions


JFM 35.0411.02
Full Text: DOI


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