# On functional equations for Nielsen polylogarithms

## TL;DR

This paper derives new functional equations for Nielsen polylogarithms, revealing their relations to classical polylogarithm identities and extending known results up to weight 8.

## Contribution

It introduces novel functional equations for Nielsen polylogarithms and connects them to classical polylogarithm relations, especially at weight 5 and higher.

## Key findings

- Weight 5 Nielsen polylogarithm satisfies the dilogarithm five-term relation modulo lower weight functions.
- Functional equations and evaluations are provided for weights up to 8.
- General families of identities are established for higher weights.

## Abstract

We derive new functional equations for Nielsen polylogarithms. We show that, when viewed modulo $\mathrm{Li}_5$ and products of lower weight functions, the weight $5$ Nielsen polylogarithm $S_{3,2}$ satisfies the dilogarithm five-term relation. We also give some functional equations and evaluations for Nielsen polylogarithms in weights up to 8, and general families of identities in higher weight.

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Source: https://tomesphere.com/paper/1908.04770