HarmonicSums

The HarmonicSums package by Jakob Ablinger allows to deal with nested sums such as harmonic sums, S-sums, cyclotomic sums and cyclotmic S-sums as well as iterated integrals such as harmonic polylogarithms, multiple polylogarithms and cyclotomic polylogarithms in an algorithmic fashion. The package can calculte the Mellin transformation of the iterated integrals in terms of the nested sums and it can compute integral representations of the nested sums. The package can be used to compute algebraic and structural relations between the nested sums as well as between the the iterated integrals and connected to it the package can find relations between the nested sums at infinity and the iterated integrals at one. In addition the package provides algorithms to represent expressions involving the nested sums and iterated integrals in terms of basis representations. Moreover, the package allows to compute (asymptotic) expansions of the nested sums and iterated integrals and it contains an algorithm which rewrites certain types of nested sums into expressions in terms of cyclotomic S-sums


References in zbMATH (referenced in 23 articles )

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  1. Remiddi, Ettore; Tancredi, Lorenzo: Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral (2016)
  2. Schneider, Carsten: A difference ring theory for symbolic summation (2016)
  3. Ablinger, J.; Behring, A.; Blümlein, J.; De Freitas, A.; von Manteuffel, A.; Schneider, C.: The 3-loop pure singlet heavy flavor contributions to the structure function $F_2(x, Q^2)$ and the anomalous dimension (2015)
  4. Behring, A.; Blümlein, J.; De Freitas, A.; von Manteuffel, A.; Schneider, C.: The 3-loop non-singlet heavy flavor contributions to the structure function $g_1(x, Q^2)$ at large momentum transfer (2015)
  5. Bogner, Christian; Brown, Francis: Feynman integrals and iterated integrals on moduli spaces of curves of genus zero (2015)
  6. Panzer, Erik: Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals (2015)
  7. Ablinger, Jakob; Blümlein, Johannes; Raab, Clemens; Schneider, Carsten; Wißbrock, Fabian: Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms (2014)
  8. Ablinger, J.; Behring, A.; Blümlein, J.; De Freitas, A.; Hasselhuhn, A.; von Manteuffel, A.; Round, M.; Schneider, C.; Wißbrock, F.: The 3-loop non-singlet heavy flavor contributions and anomalous dimensions for the structure function $\mathrmF_2(\mathrmx, Q^\mathrm2)$ and transversity (2014)
  9. Ablinger, J.; Blümlein, J.; De Freitas, A.; Hasselhuhn, A.; von Manteuffel, A.; Round, M.; Schneider, C.: The $O(\alpha_s^3 T_F^2)$ contributions to the gluonic operator matrix element (2014)
  10. Ablinger, J.; Blümlein, J.; Raab, C.G.; Schneider, C.: Iterated binomial sums and their associated iterated integrals (2014)
  11. Abreu, Samuel; Britto, Ruth; Duhr, Claude; Gardi, Einan: From multiple unitarity cuts to the coproduct of Feynman integrals (2014)
  12. Beneke, M.; Piclum, J.; Rauh, T.: P-wave contribution to third-order top-quark pair production near threshold (2014)
  13. Ablinger, Jakob; Blümlein, Johannes: Harmonic sums, polylogarithms, special numbers, and their generalizations (2013)
  14. Ablinger, Jakob; Blümlein, Johannes; Schneider, Carsten: Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms (2013)
  15. Alday, Luis F.; Bissi, Agnese: Higher-spin correlators (2013)
  16. Leurent, Sébastien; Volin, Dmytro: Multiple zeta functions and double wrapping in planar $\mathcalN = 4$ SYM (2013)
  17. Ablinger, Jakob; Blümlein, Johannes; Hasselhuhn, Alexander; Klein, Sebastian; Schneider, Carsten; Wißbrock, Fabian: Massive 3-loop ladder diagrams for quarkonic local operator matrix elements (2012)
  18. Beneke, M.; Falgari, P.; Klein, S.; Schwinn, C.: Hadronic top-quark pair production with NNLL threshold resummation (2012)
  19. Blümlein, Johannes; Klein, Sebastian; Schneider, Carsten; Stan, Flavia: A symbolic summation approach to Feynman integral calculus (2012)
  20. Ablinger, Jakob; Blümlein, Johannes; Schneider, Carsten: Harmonic sums and polylogarithms generated by cyclotomic polynomials (2011)

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