Large z Asymptotics for Special Function Solutions of Painlevé II in the Complex Plane

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2018
• Main Author: Deaño, A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209850
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Large z Asymptotics for Special Function Solutions of Painlevé II in the Complex Plane / A. Deaño // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 35 назв. — англ.

In this paper, we obtain large z asymptotic expansions in the complex plane for the tau function corresponding to special function solutions of the Painlevé II differential equation. Using the fact that these tau functions can be written as n × n Wronskian determinants involving classical Airy funct...