Numerical implementation of harmonic polylogarithms to weight w=8

被引：35

作者：

Ablinger, J. ^{[1
]}

Bluemlein, J. ^{[2
]}

Round, M. ^{[1
,2
]}

Schneider, C. ^{[1
]}

机构：

[1] Johannes Kepler Univ Linz, RISC, Altenbergerstr 69, A-4040 Linz, Austria

[2] DESY, Deutsch Elektronen Synchrotron, Platanenallee 6, D-15738 Zeuthen, Germany

来源：

COMPUTER PHYSICS COMMUNICATIONS | 2019年 / 240卷

基金：

奥地利科学基金会;

关键词：

Harmonic polylogarithms; Numeric representation; Cyclotomic harmonic polylogarithms; MELLIN TRANSFORMS; ANALYTIC CONTINUATION; SUMS; INTEGRALS;

D O I：

10.1016/j.cpc.2019.02.005

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We present the FORTRAN-code HPOLY. f for the numerical calculation of harmonic polylogarithms up to w = 8 at an absolute accuracy of similar to 10(-15) or better. Using algebraic and argument relations the numerical representation can be limited to the range x is an element of [0, root 2-1 ]. We provide replacement files to map all harmonic polylogarithms to a basis and the usual range of arguments x is an element of ] -infinity, +infinity[ to the above interval analytically. We also briefly comment on a numerical implementation of real valued cyclotomic harmonic polylogarithms. Program Summary Program title: HPOLY.f Program Files doi http://dx.doi.org/10.17632/vnc3fc79cr.1 Licensing provisions: CC by NC 3.0 Programming Language: Fortran Nature of problem: Harmonic polylogarithms form key building blocks in the analytic calculation of many multi-loop and multi-leg calculations in high energy physics and other disciplines of modern physics. Their numerical representation is provided. Solution method: Bernoulli-improvement of series expansions, Ref. [1]. Additional comments: Program obtainable from https://www-zeuthen.desy.dei-blumleini References: [1] G. 't Hooft and M.J.G. Veltman, Scalar One Loop Integrals, Nucl. Phys. B 153 (1979) 365. (C) 2019 Elsevier B.V. All rights

引用

页码：189 / 201

页数：13

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