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

被引：6

作者：

Shimomura, S ^{[1
]}

机构：

[1] Keio Univ, Dept Math, Yokohama, Kanagawa 2238522, Japan

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 2000年 / 82卷 / 1期

关键词：

Meromorphic Function; Simple Zero; Meromorphic Solution; Linear Ordinary Differential Equation; Transcendental Meromorphic Function;

D O I：

10.1007/BF02791233

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We examine value distribution properties of the first and the second Painleve transcendents. For every transcendental meromorphic solution phi (z) (resp. psi (z)) of the first (resp. second) Painleve equation, the deficiency delta (g, phi) (resp. delta (g, psi)) of a small function g(z) does not exceed 1/2. Furthermore, for phi (z), the ramification index satisfies v(g, phi) less than or equal to 5/12.

引用

页码：333 / 346

页数：14

共 50 条

[11] Lower estimates for the growth of the fourth and the second Painleve transcendents
Shimomura, S
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2004, 47 : 231 - 249
[12] ELLIPTIC ASYMPTOTICS OF THE FIRST AND THE 2ND PAINLEVE TRANSCENDENTS
KITAEV, AV
RUSSIAN MATHEMATICAL SURVEYS, 1994, 49 (01) : 81 - 150
[13] Value distribution of the Painlevé Transcendents
Norbert Steinmetz
Israel Journal of Mathematics, 2002, 128 : 29 - 52
[14] Tabulation of Painleve 6 transcendents
Guzzetti, Davide
NONLINEARITY, 2012, 25 (12) : 3235 - 3276
[15] EQUI-DISTRIBUTION OF VALUES FOR THE THIRD AND THE FIFTH PAINLEVE TRANSCENDENTS
Shimomura, Shun
NAGOYA MATHEMATICAL JOURNAL, 2008, 192 : 89 - 109
[16] Connection problem of the first Painleve transcendents with large initial data
Long, Wen-Gao
Li, Yu-Tian
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2023, 56 (17)
[17] A UNIFIED APPROACH TO THE PAINLEVE TRANSCENDENTS
Steinmetz, Norbert
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2017, 42 (01) : 17 - 49
[18] A method for calculating the Painleve transcendents
Abramov, A. A.
Yukhno, L. F.
APPLIED NUMERICAL MATHEMATICS, 2015, 93 : 262 - 269
[19] Growth results for Painleve transcendents
Hinkkanen, A
Laine, I
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2004, 137 : 645 - 655
[20] Generation of Painleve V transcendents
Bermudez, David
Fernandez, David J.
Negro, Javier
GEOMETRIC METHODS IN PHYSICS XXXVII, 2020, : 24 - 33

← 1 2 3 4 5 →