\(q\)-binomial sums toward Euler's pentagonal number theorem

DOI10.1007/s40840-022-01279-zOpenAlexW4226190564WikidataQ113891886 ScholiaQ113891886MaRDI QIDQ2147597

Chu, Wenchang

Publication date: 20 June 2022

Published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40840-022-01279-z

zbMATH Keywords

generating functionquintuple product identitybasic hypergeometric seriesEuler's pentagonal number theoremRamanujan's \(_1\psi_1\)-series

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Partition identities; identities of Rogers-Ramanujan type (11P84)

Related Items (1)

Some supercongruences on \(q\)-trinomial coefficients

Cites Work

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• Summation formulae for a class of terminating balanced \(q\)-series
• Some observations on Dyson's new symmetries of partitions
• The number of solutions of \(X^ 2 = 0\) in triangular matrices over \(GF(q)\)
• \(q\)-hypergeometric proofs of polynomial analogues of the triple product identity, Lebesgue's identity and Euler's pentagonal number theorem
• Abel's lemma on summation by parts and Ramanujan's \(_1\psi_1\)-series identity
• Some finite generalizations of Euler's pentagonal number theorem
• THE QUINTUPLE PRODUCT IDENTITY
• Evaluating a class of balanced q -series

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