Four classes of Rogers–Ramanujan identities with quintuple products

Abstract

Combining the finite form of Jacobi’s triple product identity with the $q$-Gauss summation theorem, we present a new and unified proof for the two transformation lemmas due to Andrews (1981). The same approach is then utilized to establish two further transformations from unilateral to bilateral series. They are employed to review forty identities of Rogers–Ramanujan type with quintuple products.