On the convergence of generalized power series satisfying an algebraic ODE

TL;DR

This paper establishes a sufficient condition for the convergence of generalized power series that formally satisfy algebraic ordinary differential equations, using the majorant method to prove the result.

Contribution

It introduces a new convergence criterion for generalized power series solving algebraic ODEs, expanding understanding of their analytic properties.

Findings

Provides a sufficient condition for convergence of generalized power series

Utilizes the majorant method for the proof

Enhances theoretical understanding of algebraic ODE solutions

Abstract

We propose a sufficient condition of the convergence of a generalized power series formally satisfying an algebraic (polynomial) ordinary differential equation. The proof is based on the majorant method.