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 19 articles , 1 standard article )

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  1. Adams, Luise; Bogner, Christian; Schweitzer, Armin; Weinzierl, Stefan: The kite integral to all orders in terms of elliptic polylogarithms (2016)
  2. Bogner, Christian; Brown, Francis: Feynman integrals and iterated integrals on moduli spaces of curves of genus zero (2015)
  3. Panzer, Erik: Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals (2015)
  4. Boels, Rutger H.: On the field theory expansion of superstring five point amplitudes (2013)
  5. Huang, Zhi-Wei; Liu, Jueping: NumExp: numerical epsilon expansion of hypergeometric functions (2013)
  6. Bierenbaum, Isabella; Czakon, Michał; Mitov, Alexander: The singular behavior of one-loop massive QCD amplitudes with one external soft gluon (2012)
  7. Grozin, A.G.: Massless two-loop self-energy diagram: historical review (2012)
  8. Rottmann, Paulo A.; Reina, Laura: Z-Sum approach to loop integrals using Taylor expansion (2011)
  9. Del Duca, Vittorio; Duhr, Claude; Nigel Glover, E.W.; Smirnov, Vladimir A.: The one-loop pentagon to higher orders in $\varepsilon $ (2010)
  10. Del Duca, Vittorio; Duhr, Claude; Smirnov, Vladimir A.: A two-loop octagon Wilson loop in $\mathcalN = 4$ SYM (2010)
  11. Del Duca, Vittorio; Duhr, Claude; Smirnov, Vladimir A.: An analytic result for the two-loop hexagon Wilson loop in $ \mathcalN = 4 $ SYM (2010)
  12. Del Duca, Vittorio; Duhr, Claude; Smirnov, Vladimir A.: The two-loop hexagon Wilson loop in $\mathcalN=4$ SYM (2010)
  13. Bierenbaum, Isabella; Blümlein, Johannes; Klein, Sebastian; Schneider, Carsten: Two-loop massive operator matrix elements for unpolarized heavy flavor production to $O(\epsilon)$ (2008)
  14. Huber, Tobias; Ma{^i}tre, Daniel: Hypexp 2, expanding hypergeometric functions about half-integer parameters (2008)
  15. Gluza, J.; Kajda, K.; Riemann, T.: AMBRE - a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals (2007)
  16. Bekavac, Stefan: Calculation of massless Feynman integrals using harmonic sums (2006)
  17. Czakon, M.; Gluza, J.; Riemann, T.: The planar four-point master integrals for massive two-loop Bhabha scattering (2006)
  18. Marquard, P.; Piclum, J.H.; Seidel, D.; Steinhauser, M.: Fermionic corrections to the three-loop matching coefficient of the non-relativistic vector current (2006)
  19. Moch, S.; Uwer, P.: XSummer -- transcendental functions and symbolic summation in form (2006)