### Abstract

On page 45 in his lost notebook, Ramanujan asserts that a certain q-continued fraction has three limit points. More precisely, if A_{n}/B_{n} denotes its nth partial quotient, and n tends to ∞ in each of three residue classes modulo 3, then each of the three limits of A_{n}/B_{n} exists and is explicitly given by Ramanujan. Ramanujan's assertion is proved in this paper. Moreover, general classes of continued fractions with three limit points are established.

Original language | English (US) |
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Pages (from-to) | 231-258 |

Number of pages | 28 |

Journal | Advances in Mathematics |

Volume | 192 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2005 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Andrews, G. E., Berndt, B. C., Sohn, J., Yee, A. J., & Zaharescu, A. (2005). Continued fractions with three limit points.

*Advances in Mathematics*,*192*(2), 231-258. https://doi.org/10.1016/j.aim.2004.04.004