Here are written methods and results of power geometry which are used to research asymptotic expansions of solutions to the six Panlev'e equation. The methods of power geometry are aplied to very wide class of equations and systems. The equations of Painlev'e relate to comparatively narrow class of equations with their specific character. Particular, this specific character shows up in that the power asymptotic forms have no more than one critical value and multiple logarithms are lacking in expansions. Thats why here is written only cases corresponding to no more than one critical value and logarithm.

Mathematical problems and theory of numerical methods