Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2019
• Main Author: Kitaev, A.V.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2019
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210176
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin / A.V. Kitaev // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 13 назв. — англ.

We prove that there exists a unique odd meromorphic solution of dP3, u(τ), such that u(0) = 0, and study some of its properties, mainly: the coefficients of its Taylor expansion at the origin and asymptotic behaviour as τ→+∞.