Iterated Binomial Sums and their Associated Iterated Integrals

@article{Ablinger2014IteratedBS,
  title={Iterated Binomial Sums and their Associated Iterated Integrals},
  author={Jakob Ablinger and Johannes Blumlein and Clemens G. Raab and Carsten Schneider},
  journal={arXiv: High Energy Physics - Theory},
  year={2014}
}
We consider finite iterated generalized harmonic sums weighted by the binomial $\binom{2k}{k}$ in numerators and denominators. A large class of these functions emerges in the calculation of massive Feynman diagrams with local operator insertions starting at 3-loop order in the coupling constant and extends the classes of the nested harmonic, generalized harmonic and cyclotomic sums. The binomially weighted sums are associated by the Mellin transform to iterated integrals over square-root valued… 

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