Some infinite series related to Feynman diagrams

  • Authors:

  • Odd Magne Ogreid;Per Osland

  • Affiliations:

  • Department of Physics, University of Bergen, Allégaten 55, N5007 Bergen, Norway;Department of Physics, University of Bergen, Allégaten 55, N5007 Bergen, Norway

  • Venue:
  • Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
  • Year:
  • 2002

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Abstract

Results are presented for some infinite series appearing in Feynman diagram calculations, many of which are similar to the Euler series. These include both one-, two- and three-dimensional series. The sums of these series can be evaluated with the help of various integral representations for hypergeometric functions, and expressed in terms of ζ(2), ζ(3), the Catalan constant G and Cl2(π/3) where Cl2(θ) is Clausen's function.