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 58 articles )

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  1. Ablinger, Jakob: Discovering and proving infinite Pochhammer sum identities (2022)
  2. Ablinger, Jakob: Extensions of the AZ-algorithm and the package multiintegrate (2021)
  3. Behring, A.; Blümlein, J.; De Freitas, A.; von Manteuffel, A.; Schönwald, K.; Schneider, C.: The polarized transition matrix element (A_gq(N)) of the variable flavor number scheme at (O(\alpha_s^3)) (2021)
  4. 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)
  5. Raab, Clemens G.: Nested integrals and rationalizing transformations (2021)
  6. Wang, Weiping; Xu, Ce: Alternating multiple zeta values, and explicit formulas of some Euler-Apéry-type series (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.; Goedicke, A.; Saragnese, M.; Schneider, C.; Schönwald, K.: The two-mass contribution to the three-loop polarized gluonic operator matrix element (A_gg, Q^(3)) (2020)
  9. Ablinger, J.; Blümlein, J.; De Freitas, A.; Saragnese, M.; Schneider, C.; Schönwald, K.: The three-loop polarized pure singlet operator matrix element with two different masses (2020)
  10. 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)
  11. Blümlein, J.; De Freitas, A.; Raab, C. G.; Schönwald, K.: The (O(\alpha^2)) initial state QED corrections to (e^+ e^- \to\gamma^\ast/ Z_0^\ast) (2020)
  12. Blümlein, Johannes: Large scale analytic calculations in quantum field theories (2020)
  13. Ferrero, Pietro; Ghosh, Kausik; Sinha, Aninda; Zahed, Ahmadullah: Crossing symmetry, transcendentality and the Regge behaviour of 1d CFTs (2020)
  14. Wang, Weiping; Chen, Yao: Explicit formulas of sums involving harmonic numbers and Stirling numbers (2020)
  15. Xu, Ce; Wang, Weiping: Explicit formulas of Euler sums via multiple zeta values (2020)
  16. Ablinger, J.; Blümlein, J.; Marquard, P.; Rana, N.; Schneider, C.: Automated solution of first order factorizable systems of differential equations in one variable (2019)
  17. Blümlein, J.; De Freitas, A.; Raab, C. G.; Schönwald, K.: The unpolarized two-loop massive pure singlet Wilson coefficients for deep-inelastic scattering (2019)
  18. Blümlein, J.; Marquard, P.; Rana, N.; Schneider, C.: The heavy fermion contributions to the massive three loop form factors (2019)
  19. Joubat, Mohammad; Prygarin, Alexander: The analytic structure of the BFKL equation and reflection identities of harmonic sums at weight five (2019)
  20. Prygarin, Alex: BFKL eigenvalue and maximal alternation of harmonic sums (2019)

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