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@ARTICLE{Blmlein:598863,
      author       = {Blümlein, Johannes and Saragnese, Marco and Schneider,
                      Carsten},
      title        = {{H}ypergeometric {S}tructures in {F}eynman {I}ntegrals},
      journal      = {Annals of mathematics and artificial intelligence},
      volume       = {91},
      number       = {5},
      issn         = {1012-2443},
      address      = {Dordrecht [u.a.]},
      publisher    = {Springer Science + Business Media B.V},
      reportid     = {PUBDB-2023-07057, arXiv:2111.15501. DESY-21-071. DO-TH
                      21/16. RISC Report Series 21-17. SAGEX-21-10-E},
      pages        = {591 - 649},
      year         = {2023},
      note         = {55 pages, several anc. files},
      abstract     = {Hypergeometric structures in single and multiscale Feynman
                      integrals emerge in a wide class of topologies. Using
                      integration-by-parts relations, associated master or scalar
                      integrals have to be calculated. For this purpose it appears
                      useful to devise an automated method which recognizes the
                      respective (partial) differential equations related to the
                      corresponding higher transcendental functions. We solve
                      these equations through associated recursions of the
                      expansion coefficient of the multivalued formal Taylor
                      series. The expansion coefficients can be determined using
                      either the package ${\tt$ Sigma} in the case of linear
                      difference equations or by applying heuristic methods in the
                      case of partial linear difference equations. In the present
                      context a new type of sums occurs, the Hurwitz harmonic
                      sums, and generalized versions of them. The code ${\tt$
                      HypSeries} transforming classes of differential equations
                      into analytic series expansions is described. Also partial
                      difference equations having rational solutions and rational
                      function solutions of Pochhammer symbols are considered, for
                      which the code ${\tt$ solvePartialLDE} is designed.
                      Generalized hypergeometric functions, Appell-,~Kampé de
                      Fériet-, Horn-, Lauricella-Saran-, Srivasta-, and
                      Exton--type functions are considered. We illustrate the
                      algorithms by examples.},
      keywords     = {differential equations (INSPIRE) / Feynman graph (INSPIRE)
                      / structure (INSPIRE) / mathematical methods (INSPIRE) /
                      Taylor expansion (INSPIRE) / topology (INSPIRE) / master
                      integral (INSPIRE) / computer: algebra (INSPIRE) / numerical
                      methods (INSPIRE)},
      cin          = {$Z_ZPPT$},
      ddc          = {004},
      cid          = {$I:(DE-H253)Z_ZPPT-20210408$},
      pnm          = {611 - Fundamental Particles and Forces (POF4-611)},
      pid          = {G:(DE-HGF)POF4-611},
      experiment   = {EXP:(DE-588)4276505-5},
      typ          = {PUB:(DE-HGF)16},
      eprint       = {2111.15501},
      howpublished = {arXiv:2111.15501},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2111.15501;\%\%$},
      UT           = {WOS:000962572700001},
      doi          = {10.1007/s10472-023-09831-8},
      url          = {https://bib-pubdb1.desy.de/record/598863},
}