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

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