Summation formulae for a class of terminating balanced \(q\)-series

DOI10.1016/J.JMAA.2017.02.035zbMath1358.05032OpenAlexW2591097660MaRDI QIDQ517970

Xiaojing Chen, Chu, Wenchang

Publication date: 28 March 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2017.02.035

zbMATH Keywords

basic hypergeometric seriescontiguous relationspolynomial argument\(q\)-Pfaff-Saalschütz theoremBailey's well-poised \(_6\psi_6\) series identityCarlitz inversions

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Basic hypergeometric functions (33D99)

Related Items (9)

\(q\)-binomial sums toward Euler's pentagonal number theorem ⋮ Divided differences and well-poised q-series ⋮ TERMINATING ALMOST POISED <i>q</i>-DIXON SUMS ⋮ Evaluating a class of balanced q -series ⋮ Full \(q\)-analogue for an identity of \(\lambda\)-extended Catalan numbers ⋮ Q-analogues of five difficult hypergeometric evaluations ⋮ Quadratic sums of Gaussian \(q\)-binomial coefficients and Fibonomial coefficients ⋮ Some q-transformation formulas and Hecke type identities ⋮ Terminating balanced \({}_4\phi_3\)-series and very well-poised \({}_8\phi_7\)-series

Cites Work

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• Some inverse relations
• \(q\)-hypergeometric proofs of polynomial analogues of the triple product identity, Lebesgue's identity and Euler's pentagonal number theorem
• Bailey's very well-poised \(_6\psi_6\)-series identity
• Applications of q-Lagrange Inversion to Basic Hypergeometric Series
• Basic hypergeometric identities: An introductory revisiting through the Carlitz inversions
• SERIES OF HYPERGEOMETRIC TYPE WHICH ARE INFINITE IN BOTH DIRECTIONS

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