摘要
In this paper, we prove modular identities involving cubes of the Rogers-Ramanujan functions. Applications are given to proving relations for the Rogers-Ramanujan continued fraction. Some of our identities are new. We establish analogous results for the Ramanujan-G枚llnitz-Gordon functions and the Ramanujan-G枚llnitz-Gordon continued fraction. Finally, we offer applications to the theory of partitions.