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Journal Article

On functional equations for Nielsen polylogarithms

MPS-Authors
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Charlton,  Steven
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons235289

Gangl,  Herbert
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons236038

Radchenko,  Danylo
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://dx.doi.org/10.4310/CNTP.2021.v15.n2.a4
(Publisher version)

https://doi.org/10.48550/arXiv.1908.04770
(Preprint)

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Citation

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


Cite as: https://hdl.handle.net/21.11116/0000-0008-BD73-2
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.