The WP-Bailey tree and its implications

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.