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.
The Ramanujan Journal
McLaughlin, J., & Zimmer, P. (2012). A Reciprocity Relation for WP-Bailey Pairs. The Ramanujan Journal, 28(2), 155-173. Retrieved from https://digitalcommons.wcupa.edu/math_facpub/73
Preprint version is available here.