Constructive Approximation

, Volume 39, Issue 1, pp 75–83 | Cite as

Relations Between Linear Equations and Painlevé’s Equations

  • S. Y. Slavyanov


Painlevé equations are studied on the basis of linear equations, which are generic for them. Different possible approaches are compared to each other. Formulas binding these approaches are derived. Symmetries demonstrated in the equations are also a subject of discussion.


Heun equation Heun deformed equation Apparent singularity 2×2 Fuchsian linear system Painlevé equation Antiquantization Euler integral transform 

Mathematics Subject Classification

32S99 33E17 33E99 34B30 81R12 



The author is grateful to A.Ya. Kazakov for long cooperation and to M.V. Babich for useful discussions.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.St-Petersburg State UniversitySt-PetersburgRussia

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