Power Expansions of Solutions to the fifth Painleve' Equation.
By means of Power Geometry, shortly presented in §1, in the generic case we compute all power expansions of solutions to the fifth Painleve' equation at points and z=0 and z = ∞. 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.
Mathematical problems and theory of numerical methods