Symbolic integration in the spirit of Liouville, Abel and Lie

TL;DR

This paper develops a Liouville principle for integrating functions using elliptic integrals, incorporating Lie theoretic perspectives and modern notation to deepen understanding of classical integration methods.

Contribution

It introduces a Liouville principle for elliptic integrals, blending Abel, Liouville, and Lie theoretic approaches with modern notation.

Findings

Establishes a Liouville principle for elliptic integrals.

Highlights Lie theoretic aspects of classical integration.

Provides a modern reinterpretation of Abel and Liouville's methods.

Abstract

We provide a Liouville principle for integration in terms of elliptic integrals. Our methods are essentially those of Abel and Liouville changed to modern notation. We expose Lie theoretic aspect of Liouville's work.