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

✍ Scribed by Sen-Shan Huang

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 516 KB
• Volume: 68
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.1997.2205

✦ Synopsis

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 Go llnitz Gordon functions which are analogous to Ramanujan's forty identities. Furthermore, we extract interesting partition results from some of the modular relations.