Numerical implementation of harmonic polylogarithms to weight w = 8

We present the FORTRAN-code HPOLY.f for the numerical calculation of harmonic polylogarithms up to w = 8 at an absolute accuracy of ~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 to x in ]-infty, +infty [ the above interval analytically. We also briefly comment on a numerical implementation of real valued cyclotomic harmonic polylogarithms.

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CC BY 4.0