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Numerical Evaluation of Harmonic Polylogarithms

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arxiv hep-ph/0107173 v2 pith:FFN6R2RG submitted 2001-07-16 hep-ph

T.Gehrmann , E. Remiddi This is my paper
classification hep-ph
keywords polylogarithmsharmonicalgorithmevaluationnumericalanalyticappeararbitrary
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

Harmonic polylogarithms $\H(\vec{a};x)$, 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.

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Cited by 2 Pith papers

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  1. The variable flavor number scheme to three-loop order

    hep-ph 2026-07 accept novelty 6.0 of 10

    The variable flavor number scheme is completed to three-loop order with single- and two-mass effects, validated by renormalization-group analysis to match asymptotic heavy-flavor corrections, plus numerical Wilson-coe...

  2. IterInt: Evaluating iterated integrals via differential equations

    hep-ph 2026-06 unverdicted novelty 5.0 of 10

    IterInt package evaluates iterated integrals by transforming them into solvable differential equation systems with built-in regularization.

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