# On the convergence of an exotic formal series solution of an ODE

## TL;DR

This paper establishes a sufficient condition for the convergence of a special type of formal series solution, with complex exponents, to a general ordinary differential equation.

## Contribution

It introduces a new convergence criterion for exotic formal series solutions of ODEs, expanding understanding of their analytical properties.

## Key findings

- Proposes a sufficient condition for convergence.
- Applies to a broad class of ODEs.
- Enhances theoretical understanding of exotic series solutions.

## Abstract

A sufficient condition of the convergence of an exotic formal series (a kind of power series with complex exponents) solution to an ODE of a general form is proposed.