On Modular Relations for the Göllnitz–Gordon Functions with Applications to Partitions Original Research Article

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 Ramanujanʹs forty identities. Furthermore, we extract interesting partition results from some of the modular relations.