Modular relations for the nonic analogues of the Rogers-Ramanujan functions with applications to partitions

We define the nonic Rogers-Ramanujan-type functions D(q), E(q) and F(q) and establish several modular relations involving these functions, which are analogous to Ramanujan's well known forty identities for the Rogers-Ramanujan functions. We also extract partition theoretic results from some of these relations.