### 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) |
---|---|

Pages (from-to) | 231-258 |

Number of pages | 28 |

Journal | Advances in Mathematics |

Volume | 192 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2005 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Advances in Mathematics*,

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

}

*Advances in Mathematics*, vol. 192, no. 2, pp. 231-258. https://doi.org/10.1016/j.aim.2004.04.004

**Continued fractions with three limit points.** / Andrews, George E.; Berndt, Bruce C.; Sohn, Jaebum; Yee, Ae Ja; Zaharescu, Alexandru.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Continued fractions with three limit points

AU - Andrews, George E.

AU - Berndt, Bruce C.

AU - Sohn, Jaebum

AU - Yee, Ae Ja

AU - Zaharescu, Alexandru

PY - 2005/4/1

Y1 - 2005/4/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=13644279376&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=13644279376&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2004.04.004

DO - 10.1016/j.aim.2004.04.004

M3 - Article

VL - 192

SP - 231

EP - 258

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 2

ER -