General WP-Bailey Chains

Abstract

Motivated by a recent paper of Liu and Ma, we describe a number of general WP-Bailey chains. We show that many of the existing WP-Bailey chains (or branches of the WP-Bailey tree), including chains found by Andrews, Warnaar and Liu and Ma, arise as special cases of these general WP-Bailey chains. We exhibit three new branches of the WP-Bailey tree, branches which also follow as special cases of these general WP-Bailey chains. Finally, we describe a number of new transformation formulae for basic hypergeometric series which arise as consequences of these new WP-Bailey chains.

20 pages

References in corpus (1)

• Some Implications of the WP-Bailey Tree

Cited by in corpus (3)

• Some new Transformations for Bailey pairs and WP-Bailey Pairs
• A Reciprocity Relation for WP-Bailey Pairs
• General Multi-sum Transformations and Some Implications