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 34 articles )

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  1. Ablinger, Jakob; Schneider, Carsten: Algebraic independence of sequences generated by (cyclotomic) harmonic sums (2018)
  2. Ablinger, J.; Blümlein, J.; De Freitas, A.; Goedicke, A.; Schneider, C.; Schönwald, K.: The two-mass contribution to the three-loop gluonic operator matrix element $A_g g, Q^(3)$ (2018)
  3. Ablinger, J.; Blümlein, J.; De Freitas, A.; Schneider, C.; Schönwald, K.: The two-mass contribution to the three-loop pure singlet operator matrix element (2018)
  4. Blümlein, Johannes; Schneider, Carsten: Analytic computing methods for precision calculations in quantum field theory (2018)
  5. Lee, R. N.; Onishchenko, A. I.: ABJM quantum spectral curve and Mellin transform (2018)
  6. Sofo, Anthony: General order Euler sums with multiple argument (2018)
  7. 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)
  8. Mafra, Carlos R.; Schlotterer, Oliver: Non-abelian $Z$-theory: Berends-Giele recursion for the $\alpha^'$-expansion of disk integrals (2017)
  9. 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)
  10. Bogner, Christian: MPL -- a program for computations with iterated integrals on moduli spaces of curves of genus zero (2016)
  11. Remiddi, Ettore; Tancredi, Lorenzo: Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral (2016)
  12. Schneider, Carsten: A difference ring theory for symbolic summation (2016)
  13. 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)
  14. 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)
  15. Bogner, Christian; Brown, Francis: Feynman integrals and iterated integrals on moduli spaces of curves of genus zero (2015)
  16. Broedel, Johannes; Mafra, Carlos R.; Matthes, Nils; Schlotterer, Oliver: Elliptic multiple zeta values and one-loop superstring amplitudes (2015)
  17. Panzer, Erik: Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals (2015)
  18. 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)
  19. 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)
  20. 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)

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