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ISSN 1088-6850(e) ISSN 0002-9947(p)

Some Theorems on the Rogers-Ramanujan Continued Fraction in Ramanujan's Lost Notebook

Author(s): Bruce C. Berndt; Sen-Shan Huang; Jaebum Sohn; Seung Hwan Son
Journal: Trans. Amer. Math. Soc. 352 (2000), 2157-2177.
MSC (2000): Primary 35Dxx; Secondary 11B65, 11A55, 30B70
Posted: February 8, 2000
MathSciNet review: 1615939
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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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