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Studies of the Painlevé equations. I: Sixth Painlevé equation \(P_{VI}\). (English) Zbl 0637.34019

The author studies birational canonical transformations of the Hamiltonian system \({\mathfrak H}\) associated with the sixth Painlevé equation. Solutions of \({\mathfrak H}\), which can be written by use of hypergeometric functions are studied in details.
Reviewer: P.Bolley

MSC:

34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
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