Some modular relations analogues to the Ramanujan's forty identities with its applications to partitions

Recently, the authors have established a large class of modular relations involving the Rogers-Ramanujan type functions J(q) and K(q) of order ten. In this paper, we establish further modular relations connecting these two functions with Rogers-Ramanujan functions, Göllnitz-Gordon functions and cubic functions, which are analogues to the Ramanujan's forty identities for Rogers-Ramanujan functions. Furthermore, we give partition theoretic interpretations of some of our modular relations