On the reduction of generalized polylogarithms to Lin and Li2,2 and on the evaluation thereof

Abstract

Abstract: We give expressions for all generalized polylogarithms up to weight four in terms of the functions log, Lin, and Li2,2, valid for arbitrary complex variables. Furthermore we provide algorithms for manipulation and numerical evaluation of Lin and Li2,2, 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 appendix C.