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arXiv · hep-ph/0111255

Numerical Evaluation of Two-Dimensional Harmonic Polylogarithms

T. Gehrmann·E. Remiddi
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Abstract

The two-dimensional harmonic polylogarithms $\G(\vec{a}(z);y)$, 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.

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T. Gehrmann, E. Remiddi. 2001-11-21. Numerical Evaluation of Two-Dimensional Harmonic Polylogarithms. https://doi.org/10.1016/s0010-4655(02)00139-x

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