Applicability of the \(q\)-analogue of Zeilberger's algorithm

DOI10.1016/j.jsc.2004.09.002zbMath1126.33008arXivmath/0410222OpenAlexW1998769190MaRDI QIDQ2456539

Qing-Hu Hou, Yan-Ping Mu, William Y. C. Chen

Publication date: 19 October 2007

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0410222

zbMATH Keywords

Zeilberger's algorithm\(q\)-hypergeometric terms

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items (10)

Some open problems related to creative telescoping ⋮ Refined telescoping algorithms in RΠΣ -extensions to reduce the degrees of the denominators✱ ⋮ Telescopers for differential forms with one parameter ⋮ Residues and telescopers for bivariate rational functions ⋮ The Ore-Sato theorem and shift exponents in the \(q\)-difference case ⋮ How to Generate All Possible Rational Wilf-Zeilberger Pairs? ⋮ On the existence of telescopers for mixed hypergeometric terms ⋮ Proof of the Wilf-Zeilberger conjecture for mixed hypergeometric terms ⋮ On the existence of telescopers for rational functions in three variables ⋮ Efficient \(q\)-integer linear decomposition of multivariate polynomials

Uses Software

• qZeil

Cites Work

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• Rational normal forms and minimal decompositions of hypergeometric terms
• An algorithmic proof theory for hypergeometric (ordinary and ``\(q\)) multisum/integral identities
• The method of creative telescoping
• On Zeilberger's algorithm and its \(q\)-analogue
• \(q\)-hypergeometric solutions of \(q\)-difference equations
• When does Zeilberger's algorithm succeed?
• A criterion for the applicability of Zeilberger's algorithm to rational functions
• On the structure of multivariate hypergeometric terms.
• \(k\)-free recurrences of double hypergeometric terms
• Algorithms for \(q\)-hypergeometric summation in computer algebra
• Theory of prehomogeneous vector spaces (algebraic part)—the English translation of Sato’s lecture from Shintani’s note
• General hypergeometric systems of equations and series of hypergeometric type

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