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

Shun Shimomura

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


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)).

Original languageEnglish
Pages (from-to)259-269
Number of pages11
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number2
Publication statusPublished - 2003 Mar

ASJC Scopus subject areas

  • Mathematics(all)


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