On the convergence of formal power-log series solutions of an algebraic ODE

TL;DR

This paper establishes a sufficient condition for the convergence of power-log series solutions to algebraic ordinary differential equations of any order, analyzing the properties of their functional coefficients.

Contribution

It provides a general convergence criterion for formal power-log series solutions of algebraic ODEs, expanding understanding of their functional coefficients.

Findings

Derived a sufficient convergence condition for power-log series

Analyzed properties of the functional coefficients

Applicable to algebraic ODEs of arbitrary order

Abstract

We propose a sufficient condition of the convergence of a power-log series that formally satisfies an algebraic ordinary differential equation (ODE) of arbitrary order. A general form and properties of the functional coefficients of such a series are established.