This article is cited in 1 paper

Non-formal solutions to ODE

A. D. Bruno, I. V. Goryuchkina


Abstract: Here we prove theorem on sufficient condition of convergence of whole series, which is formal solution to ordinary differential equation of the $n$ order. For that we construct majorant series and prove its convergence. In the second section we prove convergence of series on example of formal expansion of solution to the third Painlevé equation and show construction of majorant series.

UDC: 517.91