This thesis introduces a new generalized conjuagate Bailey pair and infinite families of conjugate Bailey pairs. We discuss the applications of each in conjuction with the Bailey transform. Results range over many different applications: generalized Lambert series, infinite products, Ramanujan-like identities, partitions, indefinite quadratics forms and sums of triangular numbers.
We close with some partition-related remarks on two of the identities which appear in previous chapters, and use this interpretation to prove generalizations and finite forms of each of the identities.
