EvaluateMultiSums

Simplifying multiple sums in difference fields. In this survey article, we present difference field algorithms for symbolic summation. Special emphasize is put on new aspects in how the summation problems are rephrased in terms of difference fields, how the problems are solved there, and how the derived results in the given difference field can be reinterpreted as solutions of the input problem. The algorithms are illustrated with the Mathematica package Sigma by discovering and proving new harmonic number identities extending those from Paule and Schneider, 2003. In addition, the newly developed package EvaluateMultiSums is introduced that combines the presented tools. In this way, large scale summation problems for the evaluation of Feynman diagrams in QCD (Quantum ChromoDynamics) can be solved completely automatically.


References in zbMATH (referenced in 25 articles , 1 standard article )

Showing results 1 to 20 of 25.
Sorted by year (citations)

1 2 next

  1. Ablinger, Jakob: Extensions of the AZ-algorithm and the package multiintegrate (2021)
  2. Abramov, Sergei A.; Bronstein, Manuel; Petkovšek, Marko; Schneider, Carsten: On rational and hypergeometric solutions of linear ordinary difference equations in (\Pi\Sigma^\ast)-field extensions (2021)
  3. Blümlein, J.; De Freitas, A.; Schönwald, K.: The QED initial state corrections to the forward-backward asymmetry of (e^+ e^- \to\gamma^\ast/ Z^0^\ast) to higher orders (2021)
  4. Blümlein, J.; Marquard, P.; Schneider, C.; Schönwald, K.: The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements (2021)
  5. Heinrich, Gudrun: Collider physics at the precision frontier (2021)
  6. Schneider, Carsten: The absent-minded passengers problem: a motivating challenge solved by computer algebra (2021)
  7. Ablinger, J.; Behring, A.; Blümlein, J.; De Freitas, A.; von Manteuffel, A.; Schneider, C.; Schönwald, K.: The three-loop single mass polarized pure singlet operator matrix element (2020)
  8. Ablinger, J.; Blümlein, J.; De Freitas, A.; Schönwald, K.: Subleading logarithmic QED initial state corrections to (e^+ e^- \to\gamma^\ast/ Z^0^\ast) to (O(\alpha^6 L^5)) (2020)
  9. Krattenthaler, Christian; Schneider, Carsten: Evaluation of binomial double sums involving absolute values (2020)
  10. Aumüller, Martin; Dietzfelbinger, Martin; Heuberger, Clemens; Krenn, Daniel; Prodinger, Helmut: Dual-pivot quicksort: optimality, analysis and zeros of associated lattice paths (2019)
  11. Behring, A.; Blümlein, J.; De Freitas, A.; Goedicke, A.; Klein, S.; von Manteuffel, A.; Schneider, C.; Schönwald, K.: The polarized three-loop anomalous dimensions from on-shell massive operator matrix elements (2019)
  12. Stenlund, David; Wan, James G.: Some double sums involving ratios of binomial coefficients arising from urn models (2019)
  13. Ablinger, Jakob; Schneider, Carsten: Algebraic independence of sequences generated by (cyclotomic) harmonic sums (2018)
  14. Blümlein, Johannes; Round, Mark; Schneider, Carsten: Refined holonomic summation algorithms in particle physics (2018)
  15. de Hon, Bastiaan P.; Floris, Sander J.; Arnold, John M.: No-neighbours recurrence schemes for space-time Green’s functions on a 3D simple cubic lattice (2018)
  16. Ablinger, J.; Behring, A.; Blümlein, J.; De Freitas, A.; von Manteuffel, A.; Schneider, C.: The three-loop splitting functions (P_q g^(2)) and (P_g g^(2, \operatornameN_\operatornameF)) (2017)
  17. Chen, Shaoshi; Kauers, Manuel: Some open problems related to creative telescoping (2017)
  18. Schneider, Carsten: Summation theory. II: Characterizations of (R \Pi\Sigma^\ast)-extensions and algorithmic aspects (2017)
  19. Schneider, Carsten; Sulzgruber, Robin: Asymptotic and exact results on the complexity of the Novelli-Pak-Stoyanovskii algorithm (2017)
  20. Ablinger, J.; Behring, A.; Blümlein, J.; De Freitas, A.; von Manteuffel, A.; Schneider, C.: Calculating three loop ladder and (V)-topologies for massive operator matrix elements by computer algebra (2016)

1 2 next