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Symmetry, Integrability and Geometry: Methods and Applications, 2019, Volume 15, 046, 53 pp.
DOI: https://doi.org/10.3842/SIGMA.2019.046 (Mi sigma1482) 		 
This article is cited in 4 scientific papers (total in 4 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
Full-text PDF (960 kB) Citations (4)
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DOI: https://doi.org/10.3842/SIGMA.2019.046
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.
Received: November 13, 2018; in final form May 30, 2019; Published online June 18, 2019
Bibliographic databases:
Document Type: Article
MSC: 34M40, 33E17, 34M50, 34M55, 34M60
Language: English
Citation: Alexander V. Kitaev, “Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin”, SIGMA, 15 (2019), 046, 53 pp.
Citation in format AMSBIB
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\by Alexander~V.~Kitaev
\paper Meromorphic Solution of the Degenerate Third Painlev\'e Equation Vanishing at the Origin
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
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