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On Nielsen's generalized polylogarithms and their numerical calculation

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Abstract

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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Authors and Affiliations

  1. CERN, Geneva, Switzerland

    K. S. Kölbig, J. A. Mignaco & E. Remiddi

  2. University of Geneva, Switzerland

    K. S. Kölbig, J. A. Mignaco & E. Remiddi

Authors
  1. K. S. Kölbig
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  2. J. A. Mignaco
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  3. E. Remiddi
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Shortened version of CERN preprint DD/CO/69/5.

Supported by Swiss National Research Fund. On leave from Consejo Nacional de Investigaciones de la Republica Argentina.

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Kölbig, K.S., Mignaco, J.A. & Remiddi, E. On Nielsen's generalized polylogarithms and their numerical calculation. BIT 10, 38–73 (1970). https://doi.org/10.1007/BF01940890

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  • DOI: https://doi.org/10.1007/BF01940890

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