Power series and nonpower asymptotics of solutions to the second Painlevé equation

By means of Power Geometry, shortly presented in § 1, in the generic case we compute all power expansions of solutions to the second Painlevé equation at points $z=0$, $z=\infty$ (§ 2) and $z=z_0\ne0$ (§ 3). Analogously for $a=0$ we compute all power expansions of solutions and of logarithm of solutions (§ 4). We have found new fine properties of some of these expansions.