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We consider an ordinary differential equation (ODE) which can be written as apolynomial in variables and derivatives. Several types of asymptotic expansions ofits solutions can be found by algorithms of 2D Power Geometry. They are power,power-logarithmic, exotic, and complicated expansions. Here we develop 3D PowerGeometry and apply it for calculation power-elliptic expansions of solutions to anODE. Among them we select regular power-elliptic expansions and give a survey ofall such expansions in solutions of the Painlevé equations P1,…,P6

Power Geometry and Elliptic Expansions of Solutions to the Painlevé Equations