The WP - Bailey Tree and its Implications

Our object is a thorough analysis of the WP-Bailey tree, a recent extension of classical Bailey chains. We begin by observing how the WP-Bailey tree naturally entails a finite number of classical q-hypergeometric transformation formulas. We then show how to move beyond this closed set of results and in the process we explicate heretofore mysterious identities of D. Bressoud. Next, we use WP-Bailey pairs to provide a new proof of recent formula of A. Kirillov. Finally, we discuss the relation between our approach and that of W. Burge.