SIGMA

Sigma is a Mathematica package that can handle multisums in terms of indefinite nested sums and products. The summation principles of Sigma are: telescoping, creative telescoping and recurrence solving. The underlying machinery of Sigma is based on difference field theory. The package has been developed by Carsten Schneider, a member of the RISC Combinatorics group.


References in zbMATH (referenced in 47 articles , 3 standard articles )

Showing results 1 to 20 of 47.
Sorted by year (citations)

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  1. Schneider, Carsten; Sulzgruber, Robin: Asymptotic and exact results on the complexity of the Novelli-Pak-Stoyanovskii algorithm (2017)
  2. Brent, Richard P.; Krattenthaler, Christian; Warnaar, Ole: Discrete analogues of Macdonald-Mehta integrals (2016)
  3. Schneider, Carsten: A difference ring theory for symbolic summation (2016)
  4. Wang, Jun; Wei, Chuanan: Derivative operator and summation formulae involving generalized harmonic numbers (2016)
  5. Hou, Qing-Hu; Wang, Rong-Hua: An algorithm for deciding the summability of bivariate rational functions (2015)
  6. Kim, Seon-Hong: On some integrals involving Chebyshev polynomials (2015)
  7. Buchta, Christian: Exact formulae for variances of functionals of convex hulls (2013)
  8. Choi, Byoung Kyu; Kang, Donghun: Modeling and simulation of discrete event systems (2013)
  9. Schneider, Carsten: Simplifying multiple sums in difference fields (2013)
  10. Zima, Eugene V.: Accelerating indefinite summation: simple classes of summands (2013)
  11. Amdeberhan, Tewodros; Koutschan, Christoph; Moll, Victor H.; Rowland, Eric S.: The iterated integrals of $\ln (1 + x^n)$ (2012)
  12. Blümlein, Johannes; Klein, Sebastian; Schneider, Carsten; Stan, Flavia: A symbolic summation approach to Feynman integral calculus (2012)
  13. Chen, Shaoshi; Kauers, Manuel: Trading order for degree in creative telescoping (2012)
  14. Chu, Wenchang: Infinite series identities on harmonic numbers (2012)
  15. Blümlein, Johannes: The QCD coupling and parton distributions at high precision (2011)
  16. Chen, William Y.C.; Hou, Qing-Hu; Jin, Hai-Tao: The Abel-Zeilberger algorithm (2011)
  17. Prodinger, Helmut; Schneider, Carsten; Wagner, Stephan: Unfair permutations (2011)
  18. Chen, Xiaojing; Chu, Wenchang: Dixon’s $_3F_2(1)$-series and identities involving harmonic numbers and the Riemann zeta function (2010)
  19. Garoufalidis, Stavros; Sun, Xinyu: The non-commutative $A$-polynomial of twist knots (2010)
  20. Garoufalidis, Stavros; Sun, Xinyu: A new algorithm for the recursion of hypergeometric multisums with improved universal denominator (2010)

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Further publications can be found at: http://www.risc.jku.at/people/cschneid/Sigma/Sigma.html