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Article

Локальные разложения решений пятого уравнения Пенлеве

Доклады Академии наук. 2011. Т. 438. № 4. С. 439-443.
Брюно А. Д., Парусникова А. В.

In this work, the methods of power geometry are used to find asymptotic expansions of solutions to the fifth Painlevй equation as x   0 for all values of its four complex parameters. We obtain 30 families of expansions, of which 22 are obtained from published expansions of solutions to the sixth Painlevй equation. Among the other eight families, one was previously known and two can be obtained from the expansions of solutions to the third Painlevй equation. Three families of half-exotic expansions and two families of complicated expansions are new.