This article is cited in 2 papers

Power-exponential expansions of solutions to an ODE

A. D. Bruno


Abstract: We consider an ordinary differential equation of a very general form. For it, we introduce the notion of a power-exponential expansion of its solutions and give a method of calculation of the expansion. We show that the second Painlevé equation has not got such expansion of solution, but the fourth Painlevé equation has them.