On functional equations for Nielsen polylogarithms

Charlton, Steven; Gangl, Herbert; Radchenko, Danylo

doi:10.4310/cntp.2021.v15.n2.a4

On functional equations for Nielsen polylogarithms

Charlton, Steven; Gangl, Herbert; Radchenko, Danylo

Authors

Steven Charlton

Professor Herbert Gangl herbert.gangl@durham.ac.uk
Professor

Danylo Radchenko

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

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Copyright © International Press. First published in Communications in Number Theory and Physics in 15:2 (2021), published by International Press.