On the reduction of generalized polylogarithms to ${\text{Li}}_n$ and ${\text{Li}}_{2,2}$ and on the evaluation thereof

Abstract

We give expressions for all generalized polylogarithms up to weight four in terms of the functions log, ${\text{Li}}_n$, and ${\text{Li}}_{2,2}$, valid for arbitrary complex variables. Furthermore we provide algorithms for manipulation and numerical evaluation of ${\text{Li}}_n$ and ${\text{Li}}_{2,2}$, and add codes in Mathematica and C++ implementing the results. With these results we calculate a number of previously unknown integrals, which we add in App. C.

35 pages, 4 figures. Ancillary files are attached. Published version with small typos fixed and an extra formula added in App A