On functional equations for Nielsen polylogarithms

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.