### 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 language | English |
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Pages (from-to) | 2157-2177 |

Number of pages | 21 |

Journal | Transactions of the American Mathematical Society |

Volume | 352 |

Issue number | 5 |

Publication status | Published - 2000 Dec 1 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*352*(5), 2157-2177.

}

*Transactions of the American Mathematical Society*, vol. 352, no. 5, pp. 2157-2177.

**Some theorems on the ro gers-ramanujan continued fraction in Ramanujan's lost notebook.** / Berndt, Bruce C.; Huang, Sen Shan; Sohn, Jaebum; Son, Seung Hwan.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Some theorems on the ro gers-ramanujan continued fraction in Ramanujan's lost notebook

AU - Berndt, Bruce C.

AU - Huang, Sen Shan

AU - Sohn, Jaebum

AU - Son, Seung Hwan

PY - 2000/12/1

Y1 - 2000/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=23044520241&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23044520241&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:23044520241

VL - 352

SP - 2157

EP - 2177

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 5

ER -