Abstract

AbstractWe have finally obtained for each of the 6 Painlevés an expression of z, w, w′ that behaves as 1/(z − Z0) + O(1) at each kind of movable singular point. This expression is polynomial in w′ (at most quadratic), and rational in w and z. After it is integrated and exponentiated it yields a function that has a simple zero at each of the singular points.

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