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.