Value distribution of Painlevé transcendents of the first and the second kind

Shun Shimomura

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We examine value distribution properties of the first and the second Painlevé transcendents. For every transcendental meromorphic solution φ(z) (resp. ψ(z)) of the first (resp. second) Painlevé equation, the deficiency δ(g, φ) (resp. δ(g, ψ)) of a small function g(z) does not exceed 1/2. Furthermore, for φ(z), the ramification index satisfies script v sign(g, φ) ≤ 5/12.

Original languageEnglish
Pages (from-to)333-346
Number of pages14
JournalJournal d'Analyse Mathematique
Publication statusPublished - 2000 Jan 1


ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)

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