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Preprints of the Keldysh Institute of Applied Mathematics, 2006, 013, 32 pp.
(Mi ipmp561)
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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.
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.
Linking options:
https://www.mathnet.ru/eng/ipmp561 https://www.mathnet.ru/eng/ipmp/y2006/p13
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