This article is cited in 6 papers

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

Alexander V. Kitaev

Steklov Mathematical Institute, Fontanka 27, St. Petersburg, 191023, Russia

Abstract: 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 and asymptotic behaviour as $\tau\to+\infty$.

Keywords: Painlevé equation, asymptotic expansion, hypergeometric function, isomonodromy deformation, greatest common divisor.

MSC: 34M40, 33E17, 34M50, 34M55, 34M60

Received: November 13, 2018; in final form May 30, 2019; Published online June 18, 2019

Language: English

DOI: 10.3842/SIGMA.2019.046

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ArXiv: 1809.00122