Note on the truncated generalizations of Gauss's square exponent theorem

DOI10.1216/RMJ-2018-48-7-2211zbMath1454.11044arXiv1803.09738OpenAlexW2962798261WikidataQ128783352 ScholiaQ128783352MaRDI QIDQ1755470

Shane Chern

Publication date: 10 January 2019

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.09738

zbMATH Keywords

\(q\)-binomial coefficientsmultiple summationstruncated identitiesGauss's square exponent theorem

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Related Items (1)

Truncations of Gauss' square exponent theorem

Uses Software

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Cites Work

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• The truncated pentagonal number theorem
• A truncated Jacobi triple product theorem
• Proofs of two conjectures on truncated series
• Bilateral truncated Jacobi's identity
• Shifted versions of the Bailey and well-poised Bailey lemmas
• Truncated series from the quintuple product identity
• Multiple extensions of a finite Euler's pentagonal number theorem and the Lucas formulas
• \texttt{qMultiSum} -- a package for proving \(q\)-hypergeometric multiple summation identities
• Truncated theta series and a problem of Guo and Zeng
• Some finite generalizations of Gauss's square exponent identity
• Some observations on Dyson's new symmetries of partitions
• The number of solutions of \(X^ 2 = 0\) in triangular matrices over \(GF(q)\)
• Two truncated identities of Gauss
• \(q\)-hypergeometric proofs of polynomial analogues of the triple product identity, Lebesgue's identity and Euler's pentagonal number theorem
• Another approach to the Truncated Pentagonal Number Theorem
• Some finite generalizations of Euler's pentagonal number theorem

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