New proofs of some double sum Rogers–Ramanujan type identities

Abstract

Recently, Rosengren utilized an integral method to prove a number of conjectural identities found by Kanade and Russell. Using this integral method, we give new proofs to some double sum identities of Rogers–Ramanujan type. These identities were earlier proved by approaches such as combinatorial arguments or using q-difference equations. Our proofs are based on streamlined calculations, which relate these double sum identities to some known Rogers–Ramanujan type identities with single sums. Moreover, we prove a conjectural identity of Andrews and Uncu which was earlier confirmed by Chern.