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THE WP-BAILEY TREE AND ITS IMPLICATIONS

Published online by Cambridge University Press:  24 March 2003

GEORGE ANDREWS  and
ALEXANDER BERKOVICH
GEORGE ANDREWS
Affiliation:
Department of Mathematics, Pennsylvania State University, University Park, PA 16802, [email protected]
ALEXANDER BERKOVICH
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL 32611, [email protected]
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Abstract

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.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 66 , Issue 3 , December 2002 , pp. 529 - 549
Copyright
© The London Mathematical Society, 2002

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