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The WP‐Bailey Tree and its Implications
Author(s) -
Andrews George,
Berkovich Alexander
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003617
Subject(s) - tree (set theory) , extension (predicate logic) , mathematics , relation (database) , transformation (genetics) , set (abstract data type) , object (grammar) , algebra over a field , pure mathematics , computer science , combinatorics , linguistics , philosophy , programming language , biochemistry , chemistry , database , gene
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.