paper

Numerical Implementation of Harmonic Polylogarithms to Weight w = 8

arXiv:1809.07084 · doi:10.1016/j.cpc.2019.02.005

Abstract

We present the FORTRAN-code HPOLY.f for the numerical calculation of harmonic polylogarithms up to w = 8 at an absolute accuracy of $\sim 4.9 \cdot 1 0^{- 15}$ or better. Using algebraic and argument relations the numerical representation can be limited to the range $x \in [0, 2 - 1]$ . We provide replacement files to map all harmonic polylogarithms to a basis and the usual range of arguments $x \in] - \infty, + \infty [$ to the above interval analytically. We also briefly comment on a numerical implementation of real valued cyclotomic harmonic polylogarithms.

19 pages LATEX, 3 Figures, ancillary data