With the methods of power geometry we obtained those asymptotic expansions of solutions to the equation P6 near its singular point x=0, which have the order of the first term less one. These expansions are named base expansions. They organize 19 families and include expansions of four types: power, power-logarithmic, complicated and exotic. All other asymptotic expansions of solutions to the equation P6 near its singular points x=0, x=1 and x=∞ compute from the base expansions by means of symmetries of the equation. The most of these expansions are new.

Mathematical problems and theory of numerical methods