Numerical evaluation of two-dimensional harmonic polylogarithms

The two-dimensional harmonic polylogarithms G((a) over bar (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 less than or equal to y less than or equal to 1, 0 less than or equal to z less than or equal to 1, 0 less than or equal to (y + z) less than or equal to 1. This algorithm is implemented into a FORTRAN subroutine tdhp1 to compute two-dimensional harmonic polylogarithms up to weight 4. (C) 2002 Elsevier Science B.V. All rights reserved.