On Nielsen's generalized polylogarithms and their numerical calculation

@article{Klbig1970OnNG,
  title={On Nielsen's generalized polylogarithms and their numerical calculation},
  author={Kurt Siegfried K{\"o}lbig and Juan A. Mignaco and Ettore Remiddi},
  journal={BIT Numerical Mathematics},
  year={1970},
  volume={10},
  pages={38-73}
}
The generalized polylogarithms of Nielsen are studied, in particular their functional relations. New integral expressions are obtained, and relations for function values of particular arguments are given. An Algol procedure for calculating 10 functions of lowest order is presented. The numerical values of the Chebyshev coefficients used in this procedure are tabulated. A table of the real zeros of these functions is also given. 
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TLDR
Comment finds the roots x = r[1, k]-4-sqrt(-1) X r[2, k] arranged in order (k= 1, 2) of ascending modulus, of the quadra-tic equation.