Elementary proofs of some \(q\)-identities of Jackson and Andrews--Jain

DOI10.1016/j.disc.2005.03.001zbMath1080.33015OpenAlexW2109996873MaRDI QIDQ556837

Victor J. W. Guo

Publication date: 23 June 2005

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2005.03.001

zbMATH Keywords

basic hypergeometric series\(q\)-analogue of Clausen's formulaJackson

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Related Items (7)

Proof of Andrews' conjecture on a₄φ₃summation ⋮ Abel's method on summation by parts and terminating well-poised \(q\)-series identities ⋮ Short proofs of summation and transformation formulas for basic hypergeometric series ⋮ Summation formulae for \(q\)-Watson type \(4\phi 3\)-series ⋮ Some further \(q\)-series identities related to divisor functions ⋮ Some new formulas involving \(\Gamma_q\) functions ⋮ Contiguous relations and summation and transformation formulae for basic hypergeometric series

Cites Work

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• Parameter augmentation for basic hypergeometric series. II
• \(q\)-identities from Lagrange and Newton interpolation
• A combinatorial proof of a symmetric \(q\)-Pfaff-Saalschütz identity
• On some \(q\)-identities related to divisor functions
• Some operator identities and \(q\)-series transformation formulas
• Some formulas of F. H. Jackson
• On the q-analog of Kummer's theorem and applications
• The Basic Analogues of Identities of the Cayley-Orr Type
• q-Series Identities and Reducibility of Basic Double Hypergeometric Functions
• A Nonterminating q-Clausen Formula and Some Related Product Formulas
• Some Transformations of Basic Hypergeometric Functions. Part II
• On q-Analogues of the Watson and Whipple Summations
• q-Extensions of Clausen’s Formula and of the Inequalities Used by de Branges in His Proof of the Bieberbach, Robertson, and Milin Conjectures
• THE q^θ EQUATIONS WHOSE SOLUTIONS ARE PRODUCTS OF SOLUTIONS OF qθ EQUATIONS OF LOWER ORDER
• ON THE ANALOGUE OF DIXON'S THEOREM FOR BILATERAL BASIC HYPERGEOMETRIC SERIES
• ON THE SUM OF A TERMINATING ₂F₂(1)
• A NOTE ON CERTAIN q-IDENTITIES
• CERTAIN q-IDENTITIES

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