On Certain New Modular Relations for the Rogers-Ramanujan Type Functions of Order Ten and Applications to Partitions

Abstract

In this paper, we consider the Rogers-Ramanujan type functions J(q) and K(q) of order ten and establish several modular relations involving these identities, which are analogues to Ramanujan’s forty identities for the Rogers-Ramanujan functions. Furthermore, we give partition theoretic interpretations of some of our modular relations.