2014
DOI: 10.1016/j.cpc.2014.05.022
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CHAPLIN—Complex Harmonic Polylogarithms in Fortran

Abstract: We present a new Fortran library to evaluate all harmonic polylogarithms up to weight four numerically for any complex argument. The algorithm is based on a reduction of harmonic polylogarithms up to weight four to a minimal set of basis functions that are computed numerically using series expansions allowing for fast and reliable numerical results. PACS: 12.38.Bx, Perturbative calculations

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Cited by 61 publications
(52 citation statements)
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“…, a n } that are equal to 1. Software to evaluate HPLs numerically in a fast and accurate way (at least up to weight four) is publicly available [37][38][39][40][41]. Due to the magnitude of the expressions obtained for the functions Σ reg X (x; ǫ) we refrain from stating them here explicitly and make them publicly available together with the arXiv submission of this article and on the web-page [42].…”
Section: Jhep12(2013)088mentioning
confidence: 99%
“…, a n } that are equal to 1. Software to evaluate HPLs numerically in a fast and accurate way (at least up to weight four) is publicly available [37][38][39][40][41]. Due to the magnitude of the expressions obtained for the functions Σ reg X (x; ǫ) we refrain from stating them here explicitly and make them publicly available together with the arXiv submission of this article and on the web-page [42].…”
Section: Jhep12(2013)088mentioning
confidence: 99%
“…Furthermore, to cross-check our results, a second implementation was programmed in C++, where the convolutions of splitting kernels and partonic cross sections were performed numerically. For both codes, the numerical evaluation of HPLs was performed using the library Chaplin [60]. The two implementations agreed for all parameter configurations that were tested.…”
Section: Numerical Results For the Gluon Fusion Scale Variation At N mentioning
confidence: 99%
“…For more comprehensive information about harmonic polylogarithms, we refer to [54][55][56][57][58][59][60]. Any convolution involving a delta function trivially returns the other convolutant (whether it be another delta function, a plus distribution or a regular function),…”
Section: Computation Of the Convolutionsmentioning
confidence: 99%
“…It was realised that many Feynman integrals can be evaluated in terms of multiple polylogarithms [1][2][3]. These functions are by now well understood, including their analytic continuation to arbitrary kinematic regions and their efficient numerical evaluation for arbitrary complex arguments [4][5][6][7].…”
Section: Introductionmentioning
confidence: 99%