Numerical evaluation of two-dimensional harmonic polylogarithms

2001/11/21 by T. Gehrmann, E. Remiddi · 6 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Analytic Number Theory Research #Mathematical functions and polynomials #hep-ph

paper · pdf · doi:10.1016/s0010-4655(02)00139-x

published as Comput.Phys.Commun. 144 (2002) 200-223 · 22 pages, LaTeX

arxiv created 2001/11/21 · openalex publication_date 2002/04/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The two-dimensional harmonic polylogarithms \G(a(z);y), a generalization of the harmonic polylogarithms, themselves a generalization of Nielsen's polylogarithms, appear in analytic calculations of multi-loop radiative corrections in quantum field theory. We present an algorithm for the numerical evaluation of two-dimensional harmonic polylogarithms, with the two arguments y,z varying in the triangle 0≤ y ≤ 1, 0≤ z ≤ 1, 0≤ (y+z) ≤ 1. This algorithm is implemented into a \tt FORTRAN subroutine \tt tdhpl to compute two-dimensional harmonic polylogarithms up to weight 4.

Citations

• Multiple polylogarithms and mixed Tate motives
• Harmonic Polylogarithms

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