Numerical Evaluation of Harmonic Polylogarithms

Harmonic polylogarithms $\stackrel{˝}{(}\vec{a};x)$, a generalization of Nielsen’s polylogarithms $S_{n,p}(x)$, appear frequently in analytic calculations of radiative corrections in quantum field theory. We present an algorithm for the numerical evaluation of harmonic polylogarithms of arbitrary real argument. This algorithm is implemented into a {\tt FORTRAN} subroutine {\tt hplog} to compute harmonic polylogarithms up to weight 4.