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arXiv · 1809.07084

Numerical Implementation of Harmonic Polylogarithms to Weight w = 8

J. Ablinger·J. Blümlein·M. Round·C. Schneider
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Abstract

We present the FORTRAN-code HPOLY.f for the numerical calculation of harmonic polylogarithms up to w = 8 at an absolute accuracy of $\sim 4.9 \cdot 10^{-15}$ or better. Using algebraic and argument relations the numerical representation can be limited to the range $x \in [0, \sqrt{2}-1]$. 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.

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J. Ablinger, J. Blümlein, M. Round, C. Schneider. 2018-09-19. Numerical Implementation of Harmonic Polylogarithms to Weight w = 8. https://doi.org/10.1016/j.cpc.2019.02.005

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