Multiple Series Identities of the Rogers-Ramanujan Type for Overpartition Pairs

The Rogers-Ramanujan identities, which were first introduced by Rogers and then rediscovered by Ramanujan, have attracted a lot of attention. In 1961, Gordon considered the combinatorial generalization of these two identities. Then, in view of the q-difference equations for certain basic hypergeometric series, Andrews derived an analytic version of Gordon's theorem involving multiple series. Later, Bressoud established a companion for even moduli. Then, subsequent research has been focused on overpartition analogues. In this paper, with the aid of some q-difference equations, we establish the overpartition pair analogues of the aforementioned two theorems due to Gordon and Bressoud. Meanwhile, the corresponding multiple series identities of the Rogers-Ramanujan type are derived by the Bailey pair method. Furthermore, we use the Gordon markings of overpartition pairs to give the combinatorial interpretations of the multiple series.