Harmonic Polylogarithms

  title={Harmonic Polylogarithms},
  author={Ettore Remiddi and J. A. M. Vermaseren},
The harmonic polylogarithms (hpl’s) are introduced. They are a generalization of Nielsen’s polylogarithms, satisfying a product algebra (the product of two hpl’s is in turn a combination of hpl’s) and forming a set closed under the transformation of the arguments x = 1/z and x = (1−t)/(1+t). The coefficients of their expansions and their Mellin transforms are harmonic sums. AMS(1991) subject classification: Primary 33B99, 33E99, Secondary 11Y60 

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  • J. M. Borwein, D. M. Bradley, D. J. Broadhurst
  • The Electronic Journal of Combinatorics, Vol. 4…
  • 1997
Highly Influential
4 Excerpts


  • D. J. Broadhurst, D. Kreimer Phys
  • B393
  • 1997
1 Excerpt

Symbolic Manipulation with FORM

  • J.A.M. Vermaseren
  • version 2, Computer Algebra Nederland, Amsterdam
  • 1991
2 Excerpts

Dilogarithms and Associated Functions, North Holland 1958; Polylogarithms and Associated Functions

  • L. Lewin
  • 1981
1 Excerpt

On Nielsen’s generalized polylogarithms and their numerical calculation

  • K. S. Kölbig, J. A. Mignaco, E. Remiddi
  • B.I.T. 10, 38 (1970); see also the Appendices of…
  • 1972
2 Excerpts

Sopra l’irradiazione nell’urto di particelle veloci

  • G. Racah
  • Nuovo Cimento 11,461
  • 1934
1 Excerpt

Der Eulersche Dilogarithmus und seine Verallgemeinerungen

  • N. Nielsen
  • Nova Acta Leopoldina (Halle) 90
  • 1909
2 Excerpts

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