All asymptotic expansions of solutions to the equation P6 are obtained from base ones

A. D. Bruno, I. V. Goryuchkina


Abstract: By means of two symmetries of the equation P6 from base expansions of solutions in the case $a\cdot b\ne0$ (Preprint No 62 of the Keldysh Institute of Applied Mathematics of RAS, 2007) we obtain all other expansions of solutions near singular points of equation $x=0$ and $x=\infty$ existed in this case. Asymptotic expansions of solutions to the equation P6 near its singular point $x=1$ computed by means its third symmetry from expansions of solutions near other its singular point $x=0$.