Generalized Harmonic, Cyclotomic, and Binomial Sums, their Polylogarithms and Special Numbers

@article{Ablinger2014GeneralizedHC,
  title={Generalized Harmonic, Cyclotomic, and Binomial Sums, their Polylogarithms and Special Numbers},
  author={J. Ablinger and J. Blumlein and C. Schneider},
  journal={arXiv: Mathematical Physics},
  year={2014},
  volume={523},
  pages={012060}
}
  • J. Ablinger, J. Blumlein, C. Schneider
  • Published 2014
  • Physics, Mathematics
  • arXiv: Mathematical Physics
  • A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of special numbers. Starting with harmonic sums and polylogarithms we discuss recent extensions of these quantities as cyclotomic, generalized (cyclotomic), and binomially weighted sums, associated iterated integrals and special constants and their relations. 

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