On functional equations for Nielsen polylogarithms

Charlton, Steven; Gangl, Herbert; Radchenko, Danylo

Abstract

We derive new functional equations for Nielsen polylogarithms. We show that, when viewed moduloLi5 and products of lower weight functions, the weight 5 Nielsen polylogarithm S3,2 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.

Citation

Charlton, S., Gangl, H., & Radchenko, D. (2021). On functional equations for Nielsen polylogarithms. Communications in Number Theory and Physics, 15(2), 363-454. https://doi.org/10.4310/cntp.2021.v15.n2.a4

• Journal Article Type: Article
• Acceptance Date: Jan 13, 2021
• Online Publication Date: Jun 18, 2021
• Publication Date: 2021
• Deposit Date: Oct 29, 2021
• Publicly Available Date: Oct 29, 2021
• Journal: Communications in Number Theory and Physics
• Print ISSN: 1931-4523
• Electronic ISSN: 1931-4531
• Publisher: International Press
• Peer Reviewed: Peer Reviewed
• Volume: 15
• Issue: 2
• Pages: 363-454
• DOI: https://doi.org/10.4310/cntp.2021.v15.n2.a4
• Public URL: https://durham-repository.worktribe.com/output/1227026