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Growth of the first, the second and the fourth Painlevé transcendents

Published online by Cambridge University Press:  01 May 2003

SHUN SHIMOMURA
SHUN SHIMOMURA
Affiliation:
Department of Mathematics, Keio University, 3-14-1, Hiyoshi, Yokohama 223-8522, Japan. e-mail: shimomur@math.keio.ac.jp
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Abstract

For the first Painlevé equation, it is proved that every meromorphic solution satisfies T(r, w) = O(r$^{\frac {5}{2}}$). 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)).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 134 , Issue 2 , March 2003 , pp. 259 - 269
Copyright
2003 Cambridge Philosophical Society

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