Nonterminating well–poised hypergeometric series

DOI10.15672/hujms.548103zbMath1488.33019OpenAlexW3037475990MaRDI QIDQ5163721

Chu, Wenchang

Publication date: 8 November 2021

Published in: Hacettepe Journal of Mathematics and Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.15672/hujms.548103

zbMATH Keywords

Abel's lemma on summation by partsPfaff-Saalschütz theoremclassical hypergeometric seriesDougall's formulae for \(_2H_2\)-series and \(_5H_5\)-series

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Generalized hypergeometric series, ({}_pF_q) (33C20)

Cites Work

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• A short proof for Gosper's \(_7F_6\)-series conjecture
• Evaluation of nonterminating \({}_3F_2\left(\frac{3}{4}\right)\)-series
• \(q\)-extensions of Dougall's bilateral \(_2H_2\)-series
• Asymptotic method for Dougall's bilateral hypergeometric sums
• Extensions of the classical theorems for very well-poised hypergeometric functions
• Abel's lemma on summation by parts and basic hypergeometric series
• Bailey's very well-poised \(_6\psi_6\)-series identity
• Abel's lemma on summation by parts and Ramanujan's \(_1\psi_1\)-series identity
• The modified Abel lemma on summation by parts and terminating hypergeometric series identities
• A nonterminating 7F6-series evaluation
• Closed formulae for a class of terminating 3F2(4)-series
• Terminating ₃F₂(4)-series extended with three integer parameters
• Abel's method on summation by parts and hypergeometric series
• SERIES OF HYPERGEOMETRIC TYPE WHICH ARE INFINITE IN BOTH DIRECTIONS
• A Note on the Sum of a Particular Well-Poised ₆ H ₆ with Argument - 1

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