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.