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@ARTICLE{Ablinger:207123,
      author       = {Ablinger, J. and Blümlein, J. and Raab, Clemens and
                      Schneider, C.},
      title        = {{I}terated {B}inomial {S}ums and their {A}ssociated
                      {I}terated {I}ntegrals},
      journal      = {Journal of mathematical physics},
      volume       = {55},
      number       = {11},
      issn         = {1089-7658},
      address      = {College Park, Md.},
      publisher    = {American Inst. of Physics},
      reportid     = {PUBDB-2015-01108, DESY-14-021. DO-TH-13/22. SFB/CPP-14-35.
                      LPN 14-082. arXiv:1407.1822},
      pages        = {112301},
      year         = {2014},
      note         = {OA},
      abstract     = {We consider finite iterated generalized harmonic sums
                      weighted by the binomial $\left( \frac{2k}k \right)$ 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 alphabets. The values of the sums for $N \rightarrow
                      \infty$ and the iterated integrals at x = 1 lead to new
                      constants, extending the set of special numbers given by the
                      multiple zeta values, the cyclotomic zeta values and special
                      constants which emerge in the limit $N \rightarrow \infty$
                      of generalized harmonic sums. We develop algorithms to
                      obtain the Mellin representations of these sums in a
                      systematic way. They are of importance for the derivation of
                      the asymptotic expansion of these sums and their analytic
                      continuation to $N \in C$ . The associated convolution
                      relations are derived for real parameters and can therefore
                      be used in a wider context, as, e.g., for multi-scale
                      processes. We also derive algorithms to transform iterated
                      integrals over root-valued alphabets into binomial sums.
                      Using generating functions we study a few aspects of
                      infinite (inverse) binomial sums.},
      cin          = {ZEU-THEO},
      ddc          = {530},
      cid          = {I:(DE-H253)ZEU-THEO-20120731},
      pnm          = {514 - Theoretical Particle Physics (POF2-514)},
      pid          = {G:(DE-HGF)POF2-514},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000345643100017},
      eprint       = {1407.1822},
      howpublished = {arXiv:1407.1822},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:1407.1822;\%\%$},
      doi          = {10.1063/1.4900836},
      url          = {https://bib-pubdb1.desy.de/record/207123},
}