A Reciprocity Relation for WP-Bailey Pairs

Abstract

We derive a new general transformation for WP-Bailey pairs by considering the a certain limiting case of a WP-Bailey chain previously found by the authors, and examine several consequences of this new transformation. These consequences include new summation formulae involving WP-Bailey pairs. Other consequences include new proofs of some classical identities due to Jacobi, Ramanujan and others, and indeed extend these identities to identities involving particular specializations of arbitrary WP-Bailey pairs.

17 pages

References in corpus (4)

• General WP-Bailey Chains
• Some identities between basic hypergeometric series deriving from a new Bailey-type transformation
• Some new Transformations for Bailey pairs and WP-Bailey Pairs
• A New Summation Formula for WP-Bailey Pairs