This article is cited in 2 papers

All base asymptotic expansions of solutions to the equation P6 in the case $a\cdot b\ne0$

A. D. Bruno, I. V. Goryuchkina


Abstract: 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 $x=\infty$ compute from the base expansions by means of symmetries of the equation. The most of these expansions are new.

UDC: 517.91