The Rogers--Ramanujan continued fraction

Abstract

The primary purpose of this paper is to provide a survey of properties, values, identities, and generalizations of the Rogers--Ramanujan continued fraction, which is closely related to the Rogers--Ramanujan identities. Many of these results are found in Ramanujan's first two letters to Hardy, Ramanujan's notebooks, and his lost notebook. Short historical accounts are provided for both the notebooks and lost notebook.