Some theorems on the ro gers-ramanujan continued fraction in Ramanujan's lost notebook

Bruce C. Berndt, Sen Shan Huang, Jaebum Sohn, Seung Hwan Son

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18 Citations (Scopus)

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 RogersRamanujan and generalized Rogers-Ramanujan continued fractions found in the lost notebook. These theorems involve, among other things, modular equations, transformations, zeros, and class invariants.

Original languageEnglish
Pages (from-to)2157-2177
Number of pages21
JournalTransactions of the American Mathematical Society
Volume352
Issue number5
Publication statusPublished - 2000 Dec 1

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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