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NewZeil.m

Sharp upper bounds for the orders of the recurrences output by the Zeilberger and $q$-Zeilberger algorithms We do what the title promises, and as a bonus, we get much simplified versions of these algorithms, that do not make any explicit mention of Gosper’s algorithm.

Keywords for this software

Anything in here will be replaced on browsers that support the canvas element

  • hypergeometric identities
  • Zeilberger’s algorithm
  • symbolic summation
  • (q)-analog
  • differential algebra
  • height
  • symbolic integration
  • hypergeometric summands and integrands
  • hyperexponential terms
  • computer algebra
  • numerical verification
  • multi-sum summation
  • creative telescoping
  • basic hypergeometric series
  • hypergeometric functions
  • Ore algebras
  • summability
  • (q)-Dixon sum
  • definite integration
  • Abel pairs
  • Zeilberger-Bressoud theorem
  • bivariate rational function
  • degree
  • Symbolic summation
  • (q)-Dyson conjecture
  • Gosper pairs
  • linear operators
  • (q)-Gosper algorithm
  • Gosper’s algorithm
  • Abel lemma

  • URL: home.dimacs.rutgers.ed...
  • InternetArchive
  • Authors: Andrew Sills
  • Dependencies: Mathematica

  • Add information on this software.


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References in zbMATH (referenced in 9 articles , 1 standard article )

Showing results 1 to 9 of 9.
y Sorted by year (citations)

  1. Chen, Shaoshi; Kauers, Manuel: Some open problems related to creative telescoping (2017)
  2. Hou, Qing-Hu; Wang, Rong-Hua: An algorithm for deciding the summability of bivariate rational functions (2015)
  3. Kauers, Manuel; Yen, Lily: On the length of integers in telescopers for proper hypergeometric terms (2015)
  4. Chen, Shaoshi; Kauers, Manuel: Trading order for degree in creative telescoping (2012)
  5. Guo, Qiang-Hui; Hou, Qing-Hu; Sun, Lisa H.: Proving hypergeometric identities by numerical verifications (2008)
  6. Apagodu, Moa; Zeilberger, Doron: Multi-variable Zeilberger and Almkvist-Zeilberger algorithms and the sharpening of Wilf-Zeilberger theory (2006)
  7. Chen, Vincent Y. B.; Chen, William Y. C.; Gu, Nancy S. S.: The Abel lemma and the (q)-Gosper algorithm (2006)
  8. Sills, Andrew V.: Disturbing the Dyson conjecture, in a generally GOOD way (2006)
  9. Mohammed, Mohamud; Zeilberger, Doron: Sharp upper bounds for the orders of the recurrences output by the Zeilberger and (q)-Zeilberger algorithms (2005)

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  • MSC classification / top
    • Top MSC classes
      • 05 Combinatorics
      • 11 Number theory
      • 33 Special functions
      • 65 Numerical analysis
      • 68 Computer science

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