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

[21] THE CONNECTION PROBLEM FOR PAINLEVE TRANSCENDENTS
JOSHI, N
KRUSKAL, MD
PHYSICA D, 1986, 18 (1-3): : 215 - 216
[22] MATRIX GENERALIZATION OF PAINLEVE TRANSCENDENTS
SADOVNIKOV, BI
INOZEMTSEVA, NG
PHYSICA A, 1990, 162 (02): : 255 - 260
[23] Hankel determinants for a singular complex weight and the first and third Painleve transcendents
Xu, Shuai-Xia
Dai, Dan
Zhao, Yu-Qiu
JOURNAL OF APPROXIMATION THEORY, 2016, 205 : 64 - 92
[24] A truncation for obtaining all the first degree birational transformations of the Painleve transcendents
Conte, R
Musette, M
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2002, 9 (Suppl 1) : 14 - 28
[25] Meromorphic Painleve transcendents at a fixed singularity
Kaneko, Kazuo
Ohyama, Yousuke
MATHEMATISCHE NACHRICHTEN, 2013, 286 (8-9) : 861 - 875
[26] The meromorphic nature of the sixth painleve transcendents
Hinkkanen, A
Laine, I
JOURNAL D ANALYSE MATHEMATIQUE, 2004, 94 (1): : 319 - 342
[27] SELF-DUALITY AND THE PAINLEVE TRANSCENDENTS
MASON, LJ
WOODHOUSE, NMJ
NONLINEARITY, 1993, 6 (04) : 569 - 581
[28] Uniqueness Theorems for Solutions of Painleve Transcendents
Zhang, X. B.
Han, Y.
Xu, J. F.
JOURNAL OF CONTEMPORARY MATHEMATICAL ANALYSIS-ARMENIAN ACADEMY OF SCIENCES, 2016, 51 (04): : 208 - 214
[29] ON THE STRUCTURE OF PAINLEVE TRANSCENDENTS WITH A LARGE PARAMETER
KAWAI, T
TAKEI, Y
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1993, 69 (07) : 224 - 229
[30] Painleve transcendents and Einstein's equation
Calvert, G
Woodhouse, NMJ
CLASSICAL AND QUANTUM GRAVITY, 1996, 13 (04) : L33 - L39

← 1 2 3 4 5 →