Numerical Evaluation of Two-Dimensional Harmonic Polylogarithms
T. Gehrmann, E. Remiddi
Abstract
The two-dimensional harmonic polylogarithms (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 FORTRAN subroutine tdhpl to compute two-dimensional harmonic polylogarithms up to weight 4.
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