Expansions of solutions to the fifth Painlevé equation near its nonsingular point
By applying methods of power geometry, we find all asymptotic expansions of solutions to the fifth Painlevé equation near its nonsingular point for all values of its four complex parameters. More specifically, 10
families of expansions of solutions to the equation areobtained, of which one was not previously known.
Three expansions are Laurent series, while the remaining seven expansions are Taylor series. All of them converge in a (deleted) neighborhood of the nonsingular point.