Abstract

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

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