Gosper summability of rational multiples of hypergeometric terms

DOI10.1080/10236198.2021.2007903zbMath1494.41013arXiv2105.05567OpenAlexW3216998191MaRDI QIDQ5023848

Qing-Hu Hou, Guo-jie Li

Publication date: 25 January 2022

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2105.05567

zbMATH Keywords

hypergeometric termBauer's seriesGosper representationGosper summablesuper-congruence

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Combinatorial inequalities (05A20) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) General theorems on summability (40D05)

Related Items (2)

Polynomial reduction for holonomic sequences and applications in \(\pi\)-series and congruences ⋮ \(q\)-rational reduction and \(q\)-analogues of series for \(\pi\)

Cites Work

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• The extended Zeilberger algorithm with parameters
• On Zeilberger's algorithm and its \(q\)-analogue
• \(q\)-analogues of three Ramanujan-type formulas for \(1/\pi\)
• New series for powers of \(\pi\) and related congruences
• Polynomial reduction and supercongruences
• \(q\)-analogues of some series for powers of \(\pi\)
• A Modified Abramov-Petkovsek Reduction and Creative Telescoping for Hypergeometric Terms
• A $p$-adic supercongruence conjecture of van Hamme
• Decision procedure for indefinite hypergeometric summation

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