Stability Problems in Symbolic Integration

TL;DR

This paper explores the stability of elementary functions in symbolic integration, analyzing their properties within differential fields to understand their dynamical behavior and classify stable functions.

Contribution

It introduces a dynamical perspective to symbolic integration by characterizing stability of elementary functions and D-finite series, proposing new directions for future research.

Findings

Characterization of stable elementary functions involving rational, logarithmic, and exponential functions.

Basic properties of stable elementary functions and D-finite power series established.

Proposed problems for future dynamical studies in differential and difference algebra.

Abstract

This paper aims to initialize a dynamical aspect of symbolic integration by studying stability problems in differential fields. We present some basic properties of stable elementary functions and D-finite power series that enable us to characterize three special families of stable elementary functions involving rational functions, logarithmic functions, and exponential functions. Some problems for future studies are proposed towards deeper dynamical studies in differential and difference algebra.