The Abel Lemma and the $q$-Gosper Algorithm

DOI10.1090/S0025-5718-07-01968-0zbMath1134.33012OpenAlexW2001466252WikidataQ125029736 ScholiaQ125029736MaRDI QIDQ5444318

Vincent Y. B. Chen, Nancy S. S. Gu, William Y. C. Chen

Publication date: 25 February 2008

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-07-01968-0

zbMATH Keywords

basic hypergeometric series\(q\)-Gosper algorithmAbel pairsGosper pairsAbel Lemma

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items (1)

A common recursive formula for Ramanujan’s ₁𝜓₁ and Bailey’s very-well-poised ₆𝜓₆ summation formulas

Uses Software

• ZEILBERGER
• qZEILBERGER
• pqTelescope

Cites Work

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• An algorithmic proof theory for hypergeometric (ordinary and ``\(q\)) multisum/integral identities
• A simple proof of Ramanujan's summation of the \(_1\Psi_1\)
• On Zeilberger's algorithm and its \(q\)-analogue
• Short and easy computer proofs of the Rogers-Ramanujan identities and of identities of similar type
• A generalization of Gosper's algorithm to bibasic hypergeometric summation
• \(q\)-hypergeometric solutions of \(q\)-difference equations
• Inversion of bilateral basic hypergeometric series
• A \textit{Mathematica} version of Zeilberger's algorithm for proving binomial coefficient identities
• Algorithms for \(q\)-hypergeometric summation in computer algebra
• Sharp upper bounds for the orders of the recurrences output by the Zeilberger and \(q\)-Zeilberger algorithms
• Bailey's very well-poised \(_6\psi_6\)-series identity
• Abel-Rothe Type Generalizations of Jacobi's Triple Product Identity
• Non-Terminating Basic Hypergeometric Series and the q-Zeilberger Algorithm
• Shorter Notes: A Simple Proof of Ramanujan's 1 Ψ 1 Sum
• Shorter Notes: On Ramanujan's Summation of 1 ψ 1 (a; b; z)
• On a Transformation of Bilateral Series with Applications
• SERIES OF HYPERGEOMETRIC TYPE WHICH ARE INFINITE IN BOTH DIRECTIONS
• Über Polynome, die gleichzeitig zwei verschiedenen Orthogonalsystemen angehören
• On Lerch's Transcendant and the Basic Bilateral Hypergeometric Series ₂ ψ₂

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