The \(q\)-WZ method for infinite series

DOI10.1016/j.jsc.2008.11.005zbMath1173.33317arXiv0806.2491OpenAlexW1994849056MaRDI QIDQ1023261

William Y. C. Chen, Ernest X. W. Xia

Publication date: 11 June 2009

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

Full work available at URL: https://arxiv.org/abs/0806.2491

zbMATH Keywords

basic hypergeometric seriesthe \(q\)-Gosper algorithmthe \(q\)-WZ methodthe \(q\)-Zeilberger algorithm

Mathematics Subject Classification ID

Generalized hypergeometric series, ({}_pF_q) (33C20) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items

A family of WZ pairs and \(q\)-identities, The leading root of the partial theta function

Uses Software

• MarkovWZ
• MarkovAZ
• ContMarkovWZ

Cites Work

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• An algorithmic proof theory for hypergeometric (ordinary and ``\(q\)) multisum/integral identities
• A fast algorithm for proving terminating hypergeometric identities
• Ramanujan's ``lost notebook. I: Partial Theta-functions
• \(q\)-Apéry irrationality proofs by \(q\)-WZ pairs
• Identities of nonterminating series by Zeilberger's algorithm
• On Zeilberger's algorithm and its \(q\)-analogue
• A generalization of Kummer's identity.
• The Markov-WZ method
• Finding identities with the WZ method
• The product of partial theta functions
• Rational Functions Certify Combinatorial Identities
• Non-Terminating Basic Hypergeometric Series and the q-Zeilberger Algorithm
• Decision procedure for indefinite hypergeometric summation
• Towards a WZ Evolution of the Mehta Integral
• Partial Theta Functions. I. Beyond the Lost Notebook
• Towards computerized proofs of identities