Numerical evaluation of two-dimensional harmonic polylogarithms. T. Gehrmann, E. Remiddi.

PROGRAM SUMMARY
Title of program: tdhpl version 1.0, release 1
Catalogue identifier: ADPU
Ref. in CPC: 144(2002)200
Distribution format: tar gzip file
Operating system: Linux
High speed store required: 1144K words
Number of bits in a word: 32
Number of lines in distributed program, including test data, etc: 34971
Keywords: Harmonic polylogarithms, Feynman integrals, General purpose, Function.
Programming language used: Fortran
Computer: Pentium III/600MHz PC .

CPC Program Library subprograms used:

 Cat. Id.  Title                             Ref. in CPC
 ADPG      hplog version 1.0                  141(2001)296                   
 

Nature of physical 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.

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

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

Typical 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.