Some Theorems on the Rogers–Ramanujan Continued Fraction in Ramanujan’s Lost Notebook

Berndt, Bruce; Huang, Sen-Shan; Sohn, Jaebum; Son, Seung

doi:10.1090/S0002-9947-00-02337-0

Some Theorems on the Rogers–Ramanujan Continued Fraction in Ramanujan’s Lost Notebook
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by Bruce C. Berndt, Sen-Shan Huang, Jaebum Sohn and Seung Hwan Son PDF

Trans. Amer. Math. Soc. 352 (2000), 2157-2177 Request permission

Abstract:

In his first two letters to G. H. Hardy and in his notebooks, Ramanujan recorded many theorems about the Rogers–Ramanujan continued fraction. In his lost notebook, he offered several further assertions. The purpose of this paper is to provide proofs for many of the claims about the Rogers–Ramanujan and generalized Rogers–Ramanujan continued fractions found in the lost notebook. These theorems involve, among other things, modular equations, transformations, zeros, and class invariants.

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