Numerical evaluation of two-dimensional harmonic polylogarithms Original Research Article

The two-dimensional harmonic polylogarithms G(a→(z);y), a generalization of the harmonic polylogarithms, themselves a generalization of Nielsenʹs 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.