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Manuscript Title: Numerical evaluation of two-dimensional harmonic polylogarithms.
Authors: T. Gehrmann, E. Remiddi
Program title: tdhpl version 1.0, release 1
Catalogue identifier: ADPU_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 144(2002)200
Programming language: Fortran.
Computer: Pentium III/600MHz PC.
Operating system: Linux.
RAM: 1144K words
Word size: 32
Keywords: Harmonic polylogarithms, Feynman integrals, General purpose, Function.
Classification: 4.7.

Subprograms used:
Cat Id Title Reference
ADPG_v1_0 hplog version 1.0 CPC 141(2001)296

Nature of problem:
Numerical evaluation of the two-dimensional harmonic polylogarithms up to weight 4 for real arguments restricted to 0 <= y <= 1, 0 <= z <= (1-y). These functions are emerging in Feynman graph integrals involving three mass scales.

Solution method:
For small values of the argument: series representation with expansion coefficients depending on the second argument; other values of the argument: transformation formulae.

Limited to 2dHPLs of up to weight 4, the algorithms used here can be extended to higher weights without further modification.

Running time:
On average 1.8 ms (both arguments varied)/0.5 ms (only one argument varied) for the evaluation of all two-dimensional harmonic polylogarithms up to weight 4 on a Pentium III/600 MHz Linux PC.