The package HarmonicSums: Computer Algebra and Analytic aspects of Nested Sums

TL;DR

The HarmonicSums package provides advanced computer algebra tools for manipulating nested sums and iterated integrals like harmonic polylogarithms, facilitating analytic computations and representations in mathematical research.

Contribution

It introduces comprehensive functionality for nested sums and iterated integrals, bridging algebraic and analytic aspects within a unified computational framework.

Findings

Efficient manipulation of harmonic sums and polylogarithms

Illustration of the interplay between sums and integrals

Concrete examples demonstrating analytic capabilities

Abstract

This paper summarizes the essential functionality of the computer algebra package HarmonicSums. On the one hand HarmonicSums can work with nested sums such as harmonic sums and their generalizations and on the other hand it can treat iterated integrals of the Poincare and Chen-type, such as harmonic polylogarithms and their generalizations. The interplay of these representations and the analytic aspects are illustrated by concrete examples.