### Abstract

On page 26 in his lost notebook, Ramanujan states an asymptotic formula for the generalized Rogers-Ramanujan continued fraction. This formula is proved and made slightly more precise. A second primary goal is to prove another continued fraction representation for the Rogers-Ramanujan continued fraction conjectured by R. Blecksmith and J. Brillhart. Two further entries in the lost notebook are examined. One of them is an identity bearing a superficial resemblance to the generating function for the generalized Roger-Ramanujan continued fraction. Thus, our third main goal is to establish, with the help of an idea of F. Franklin, a partition bijection to prove this identity.

Original language | English (US) |
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Pages (from-to) | 321-331 |

Number of pages | 11 |

Journal | Ramanujan Journal |

Volume | 7 |

Issue number | 1-3 |

DOIs | |

State | Published - Mar 1 2003 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

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## Cite this

*Ramanujan Journal*,

*7*(1-3), 321-331. https://doi.org/10.1023/A:1026215700375