Modular relations for the Rogers-Ramanujan-Slater type functions of order fifteen and its applications to partitions

Abstract

In a manuscript of Ramanujan, published with his Lost Notebook [20] there are forty identities involving the Rogers-Ramanujan functions. In this paper, we establish several modular relations involving the Rogers-Ramanujan functions and the Rogers-Ramanujan-Slater type functions of order fifteen which are analogues to Ramanujan’s well known forty identities. Furthermore, we give partition theoretic interpretations of two modular relations.

Keywords

• Rogers-Ramanujan functions
• theta functions
• product identity
• partitions
• colored partitions
• modular relations.