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Preprints of the Keldysh Institute of Applied Mathematics, 2006, 013, 32 pp. (Mi ipmp561)  

Expansions of solutions to the sixth Painlevé equation near singular points $x=0$ и $x=\infty$

A. D. Bruno, I. V. Goryuchkina
Abstract: We consider the sixth Painlevé equation in the case $a,b\ne0$. By the methods of Power Geometry, near the singular points $x=0$ and $x=\infty$, we have found all power, power-logarithmic and complicated expansions of its solutions. Near $x=0$ we have obtained 15 families of expansions, sixth of them are complicated. Using a symmetry of the equation, near $x=\infty$ we have obtained again 15 families of expansions, including 6 complicated.
Document Type: Preprint
Language: Russian
Citation: A. D. Bruno, I. V. Goryuchkina, “Expansions of solutions to the sixth Painlevé equation near singular points $x=0$ и $x=\infty$”, Keldysh Institute preprints, 2006, 013, 32 pp.
Citation in format AMSBIB
\Bibitem{BruGor06}
\by A.~D.~Bruno, I.~V.~Goryuchkina
\paper Expansions of solutions to the sixth Painlev\'e equation near singular points $x=0$ и $x=\infty$
\jour Keldysh Institute preprints
\yr 2006
\papernumber 013
\totalpages 32
\mathnet{http://mi.mathnet.ru/ipmp561}
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