The meromorphic nature of the sixth Painlevé transcendents

DOI10.1007/BF02789052zbMath1115.34084OpenAlexW2094808978MaRDI QIDQ2565887

Aimo Hinkkanen, Ilpo Laine

Publication date: 28 September 2005

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02789052

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Meromorphic functions of one complex variable (general theory) (30D30) Painlevé-type functions (33E17)

Related Items (6)

Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations ⋮ Takasaki’s rational fourth Painlevé-Calogero system and geometric regularisability of algebro-Painlevé equations ⋮ On Hamiltonian structures of quasi-Painlevé equations ⋮ Exceptional solutions to the Painlevé VI equation ⋮ Polygons of Petrović and Fine, algebraic ODEs, and contemporary mathematics ⋮ Algebro-geometric approach to an Okamoto transformation, the Painlevé VI and Schlesinger equations

Cites Work

• Solutions of a modified third Painlevé equation are meromorphic
• On a system of non-linear ordinary differential equations containing a parameter. II.
• On Painlevé's equations I, II and IV
• Solutions of the first and second Painlevé equations are meromorphic
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