### Abstract

The continued fraction in the title is perhaps the deepest of Ramanujan's q-continued fractions. We give a new proof of this continued fraction, more elementary and shorter than the only known proof by Andrews, Berndt, Jacobsen, and Lamphere. On page 45 in his lost notebook, Ramanujan states an asymptotic formula for a continued fraction generalizing that in the title. The second main goal of this paper is to prove this asymptotic formula.

Original language | English (US) |
---|---|

Pages (from-to) | 2397-2411 |

Number of pages | 15 |

Journal | Transactions of the American Mathematical Society |

Volume | 355 |

Issue number | 6 |

DOIs | |

State | Published - Jun 2003 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

## Fingerprint Dive into the research topics of 'On Ramanujan's continued fraction for (q<sup>2</sup>;q<sup>3</sup>)<sub> ∞</sub>(q; q<sup>3</sup>)<sub>∞</sub>'. Together they form a unique fingerprint.

## Cite this

Andrews, G. E., Berndt, B. C., Sohn, J., Yee, A. J., & Zaharescu, A. (2003). On Ramanujan's continued fraction for (q

^{2};q^{3})_{ ∞}(q; q^{3})_{∞}.*Transactions of the American Mathematical Society*,*355*(6), 2397-2411. https://doi.org/10.1090/S0002-9947-02-03155-0