Power expansions of solutions to the fifth Painlevé equation

By means of Power Geometry, shortly presented in § 1, in the generic case we compute all power expansions of solutions to the fifth Painlevé equation at points and $z=0$ and $z=\infty$. Exept known expansions being power series, we have found expansions with a more complicate set of power exponents. In particularly, we have found a family for which expansions begin from arbitrary power of the independent variable with arbitrary constant coefficient.