Geodesic
Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin
Symmetry, integrability and geometry: methods and applications, Tome 15 (2019) Cet article a éte moissonné depuis la source Math-Net.Ru

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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: asymptotic expansion, hypergeometric function, greatest common divisor.
Mots-clés : Painlevé equation, isomonodromy deformation 
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     author = {Alexander V. Kitaev},
     title = {Meromorphic {Solution} of the {Degenerate} {Third} {Painlev\'e} {Equation} {Vanishing} at the {Origin}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a45/}
}
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Alexander V. Kitaev. Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin. Symmetry, integrability and geometry: methods and applications, Tome 15 (2019). http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a45/

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