Value distribution of the fifth Painlevé transcendents in sectorial domains
type: Item
instance of: scholarly article
title: Value distribution of the fifth Painlevé transcendents in sectorial domains
zbMATH Open document ID: 1133.34049
author: Yoshikatsu Sasaki
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-05-04T00:00:00Z
review text: Every solution of the fifth Painlevé equation is meromorphic on the universal covering of the domain \(\mathbb{C} \setminus \{0\},\) and, in general, it is many-valued around \(x=\infty\) and \(x=0.\) This paper is concerned with a value distribution property for any solution \(y(x)\) in a sector of the form \(| \arg x| <\phi,\) \(r<| x| <R\) as \(R \to\infty\) (respectively, \(r \to 0\)). Let \(N(y, \phi, r, R)\) denote the number of \(1\)-points of \(y(x)\) in this sector. It is shown that \(N(y,\phi, r, R) =O(R^C)\) as \(R\to \infty\) (respectively, \(N(y,\phi, r, R) =O(r^{-C})\) as \(r\to 0\)), where \(C\) is some positive number.
reviewed by: Shun Shimomura
Mathematics Subject Classification ID: 34M55
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 5149494
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.07.083
OpenAlex ID: W2069442721
cites work: Contribution à l'étude des solutions de l'équation (V) de Painleve
cites work: Solutions of a modified third Painlevé equation are meromorphic
cites work: Painlevé differential equations in the complex plane
cites work: Growth of modified Painlevé transcendents of the fifth and the third kind
cites work: Growth of the first, the second and the fourth Painlevé transcendents
cites work: Value distribution of painlevé transcendents of the third kind
DOI: 10.1016/J.JMAA.2006.07.083
description: scientific article; zbMATH DE number 5149494