TTP99-08 Harmonic Polylogarithms

The harmonic polylogarithms (hpl's) are introduced. They are a generalization of Nielsen's polylogarithms, satisfying a product algebra (the product of two hpl's is in turn a combination of hpl's) and forming a set closed under the transformation of the arguments \( x=1/z \) and \( x=(1-t)/(1+t) \). The coefficients of their expansions and their Mellin transforms are harmonic sums.