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

Hjalte Frellesvig; Damiano Tommasini; Christopher Wever

doi:10.1007/jhep03(2016)189

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arXiv · 1601.02649

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

Hjalte Frellesvig·Damiano Tommasini·Christopher Wever

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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.

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Hjalte Frellesvig, Damiano Tommasini, Christopher Wever. 2016-01-11. On the reduction of generalized polylogarithms to $\text{Li}_n$ and $\text{Li}_{2,2}$ and on the evaluation thereof. https://doi.org/10.1007/jhep03(2016)189

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