XSummer - transcendental functions and symbolic summation in form. Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums, where the harmonic sums and their generalizations appear as building blocks, originating for example, from the expansion of generalized hypergeometric functions around integer values of the parameters. In this paper we discuss the implementation of several algorithms to solve these sums by algebraic means, using the computer algebra system Form. (Source: http://cpc.cs.qub.ac.uk/summaries/)

References in zbMATH (referenced in 30 articles , 1 standard article )

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  1. Heinrich, Gudrun: Collider physics at the precision frontier (2021)
  2. Abreu, Samuel; Britto, Ruth; Duhr, Claude; Gardi, Einan; Matthew, James: From positive geometries to a coaction on hypergeometric functions (2020)
  3. Bargheer, Till; Chestnov, Vsevolod; Schomerus, Volker: The multi-Regge limit from the Wilson loop OPE (2020)
  4. Blümlein, Johannes: Large scale analytic calculations in quantum field theories (2020)
  5. Bytev, Vladimir V.; Kniehl, Bernd A.: Derivatives of any Horn-type hypergeometric functions with respect to their parameters (2020)
  6. Wang, Weiping; Chen, Yao: Explicit formulas of sums involving harmonic numbers and Stirling numbers (2020)
  7. Xu, Ce; Wang, Weiping: Explicit formulas of Euler sums via multiple zeta values (2020)
  8. Blümlein, Johannes; Schneider, Carsten: Analytic computing methods for precision calculations in quantum field theory (2018)
  9. Del Duca, Vittorio; Druc, Stefan; Drummond, James; Duhr, Claude; Dulat, Falko; Marzucca, Robin; Papathanasiou, Georgios; Verbeek, Bram: The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy (2018)
  10. Adams, Luise; Bogner, Christian; Schweitzer, Armin; Weinzierl, Stefan: The kite integral to all orders in terms of elliptic polylogarithms (2016)
  11. Del Duca, Vittorio; Druc, Stefan; Drummond, James; Duhr, Claude; Dulat, Falko; Marzucca, Robin; Papathanasiou, Georgios; Verbeek, Bram: Multi-Regge kinematics and the moduli space of Riemann spheres with marked points (2016)
  12. Bogner, Christian; Brown, Francis: Feynman integrals and iterated integrals on moduli spaces of curves of genus zero (2015)
  13. Ochman, Michał; Riemann, Tord: \textttMBsums-- a \textttMathematicapackage for the representation of Mellin-Barnes integrals by multiple sums (2015)
  14. Panzer, Erik: Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals (2015)
  15. Boels, Rutger H.: On the field theory expansion of superstring five point amplitudes (2013)
  16. Huang, Zhi-Wei; Liu, Jueping: NumExp: numerical epsilon expansion of hypergeometric functions (2013)
  17. Bierenbaum, Isabella; Czakon, Michał; Mitov, Alexander: The singular behavior of one-loop massive QCD amplitudes with one external soft gluon (2012)
  18. Grozin, A. G.: Massless two-loop self-energy diagram: historical review (2012)
  19. Rottmann, Paulo A.; Reina, Laura: Z-Sum approach to loop integrals using Taylor expansion (2011)
  20. Del Duca, Vittorio; Duhr, Claude; Nigel Glover, E. W.; Smirnov, Vladimir A.: The one-loop pentagon to higher orders in (\varepsilon) (2010)

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