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Determinant formulas for the \(\tau\)-functions of the Painlevé equations of type \(A\). (English) Zbl 1134.33325

Explicit determinant formulas are presented for the \(\tau\)-functions of the generalized Painlevé equations of type \(A\). This result allows an interpretation of the \(\tau\)-functions as the Plücker coordinates of the universal Grassmann manifold.

MSC:

33E17 Painlevé-type functions
34M55 Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies

References:

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