For the first Painlevé equation, it is proved that every meromorphic solution satisfies T(r, w) = O(r5/2). In showing this estimate, we employ two types of auxiliary function, one of which is crucial in the proof of the Painlevé property. Our method is also applicable to the second (resp. the fourth) Painlevé transcendents, and we obtain T(r, w) = O(r3) (resp. O(r4)).
|Number of pages||11|
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|Publication status||Published - 2003 Mar|
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