BIT Numerical Mathematics

, Volume 10, Issue 1, pp 38-73

First online:

On Nielsen's generalized polylogarithms and their numerical calculation

  • K. S. KölbigAffiliated withCERNUniversity of Geneva
  • , J. A. MignacoAffiliated withCERNUniversity of Geneva
  • , E. RemiddiAffiliated withCERNUniversity of Geneva

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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.