On identities of the Rogers-Ramanujan type

A generalized Bailey pair, which contains several special cases considered by Bailey (Proc. London Math. Soc. (2), 50, 421-435 (1949)), is derived and used to find a number of new Rogers-Ramanujan type identities. Consideration of associated q-difference equations points to a connection with a mild extension of Gordon's combinatorial generalization of the Rogers-Ramanujan identities (Amer. J. Math., 83, 393-399 (1961)). This, in turn, allows the formulation of natural combinatorial interpretations of many of the identities in Slater's list (Proc. London Math. Soc. (2) 54, 147-167 (1952)), as well as the new identities presented here. A list of 26 new double sum-product Rogers-Ramanujan type identities are included as an Appendix.