Numerical Evaluation of Two-Dimensional Harmonic Polylogarithms

Abstract

The two-dimensional harmonic polylogarithms $\text{G}(\vec{a}(z);y)$, 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 $0\le y\le 1$, $0\le z\le 1$, $0\le (y+z)\le 1$. This algorithm is implemented into a {\tt FORTRAN} subroutine {\tt tdhpl} to compute two-dimensional harmonic polylogarithms up to weight 4.

Comments: 22 pages, LaTeX