ANZIAM  J.  44 (2002), 1-9
Taming the movable singularities

Jarmo Hietarinta
  Department of Physics
  University of Turku
  FIN-20014 Turku

We have finally obtained for each of the 6 Painlevés an expression of $z$, $w$, $w'$ that behaves as $1/(z-z_0)+O(1)$ 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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