Relations for Nielsen polylogarithms

• Jonathan M. Borwein ^[2] ; Armin Straub ^[1]
  1. [1] University of Illinois at Urbana Champaign

     University of Illinois at Urbana Champaign

     Township of Cunningham, Estados Unidos

     
  2. [2] University of Newcastle (Australia)
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 193, Nº 1 (May 2015), 2015, págs. 74-88
• Idioma: inglés
• DOI: 10.1016/j.jat.2013.07.003
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• Resumen

  • Polylogarithms appear in many diverse fields of mathematics. Herein, we investigate relations amongst the restricted class of Nielsen-type (essentially, height one) polylogarithms, both generic and at special arguments including the sixth roots of unity. Numerical computations suggest that the collected relations, partially motivated by a previous study of the authors on log-sine integrals, are complete except in the case when the argument is the fundamental sixth root of unity. For use in other applications, all our results are implemented and accessible for use in symbolic computation or to facilitate numeric computation. In particular, the relations are explicitly exhibited in the case of low weights.