The WP‐Bailey Tree and its Implications

By George E. Andrews, Alexander Berkovich. 2001

52 citations recorded by the source corpus.

The object of the paper is a thorough analysis of the WP‐Bailey tree, a recent extension of classical Bailey chains. The paper begins by observing how the WP‐Bailey tree naturally requires a finite number of classical q‐hypergeometric transformation formulas. It then shows how to move beyond this closed set of results, and in the process, heretofore mysterious identities of Bressoud are explicated. Next, WP‐Bailey pairs are used to provide a new proof of a recent formula of Kirillov. Finally, the relation between the approach in the paper and that of Burge is discussed.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/6fad1d46d484a80e295d7024ac0e418572a78c15

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In Algebra and Number Theory

In Computational Theory and Mathematics

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Citations in the corpus

A Bailey Tree for Integrals (2003, background): “Evidently, our Theorem 2 should have a series analogue as well which would lead to an elliptic Bailey tree for series (its analogue for q-hypergeometric series would be qualitatively different from the tree considered in [1], [4]).”
Positivity preserving transformations for $q$-binomial coefficients (2003, background): “The Bailey lemma is the following powerful mechanism for generating new Bailey pairs [6, 7, 9, 13, 39, 52].”
Extensions of the well-poised and elliptic well-poised Bailey lemma (2003, background): “Shortly after [2] and [3] appeared, Spiridonov [19] pointed out that part of the programme carried out by Andrews and Berkovich can be formulated at the level of elliptic functions, leading to new results for elliptic or modular hypergeometric series.”