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

Shun Shimomura

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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
Volume82
Publication statusPublished - 2000

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Small Function
Meromorphic Solution
Value Distribution
Transcendental
Ramification
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ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis

Cite this

Value distribution of Painlevé transcendents of the first and the second kind. / Shimomura, Shun.

In: Journal d'Analyse Mathematique, Vol. 82, 2000, p. 333-346.

Research output: Contribution to journalArticle

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