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

Symmetry Integrability and Geometry-Methods and Applications

article

Alexander V. Kitaev¹ 

[1] Steklov Mathematical Institute

关键词: Painlev´e equation;    asymptotic expansion;    hypergeometric function;    isomonodromy deformation;    greatest common divisor;   

DOI  :  10.3842/SIGMA.2019.046

来源: National Academy of Science of Ukraine

【 摘 要 】

We prove that there exists the unique odd meromorphic solution of dP3, $u(\tau)$ such that $u(0)=0$, and study some of its properties, mainly: the coefficients of its Taylor expansion at the origin andasymptotic behaviour as $\tau\to+\infty$.

【 授权许可】

Unknown