A new summation formula for WP-bailey pairs

Abstract

Let (αn(a,k), βn(a,k)) be a WP-Bailey pair. Assuming the limits exist, let be the derived WP-Bailey pair. By considering a particular limiting case of a transformation due to George Andrews, we derive new basic hypergeometric summation and transformation formulae involving derived WP-Bailey pairs. We then use these formulae to derive new identities for various theta series/products which are expressible in terms of certain types of Lambert series.