The Maillet--Malgrange type theorem for generalized power series

TL;DR

This paper extends the Maillet--Malgrange theorem to generalized power series with complex exponents, providing insights into the growth behavior of their coefficients when satisfying algebraic differential equations.

Contribution

It introduces a new theorem for generalized power series with complex exponents, detailing the growth of coefficients in algebraic differential equations.

Findings

The theorem characterizes coefficient growth for complex exponent series.

It applies to series satisfying algebraic differential equations.

Provides a framework for analyzing generalized power series.

Abstract

There is proposed the Maillet--Malgrange type theorem for a generalized power series (having complex power exponents) formally satisfying an algebraic ordinary differential equation. The theorem describes the growth of the series coefficients.