On Modular Relations for the Göllnitz-Gordon Functions with Applications to Partitions

In a manuscript of Ramanujan, published with his Lost Notebook [21, pp. 236-237], there are forty identities involving the Rogers-Ramanujan functions. According to G. N. Watson, the beauty of these identities are comparable to that of the Rogers- Ramanujan identities. In the paper, we establish modular relations involving the Göllnitz-Gordon functions which are analogous to Ramanujan's forty identities. Furthermore, we extract interesting partition results from some of the modular relations.