### 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 - Jan 1 2003 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

^{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

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^{2};q

^{3})

_{ ∞}(q; q

^{3})

_{∞}',

*Transactions of the American Mathematical Society*, vol. 355, no. 6, pp. 2397-2411. https://doi.org/10.1090/S0002-9947-02-03155-0

**On Ramanujan's continued fraction for (q ^{2};q^{3})_{ ∞}(q; q^{3})_{∞}.** / Andrews, George E.; Berndt, Bruce C.; Sohn, Jaebum; Yee, Ae Ja; Zaharescu, Alexandru.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On Ramanujan's continued fraction for (q2;q3) ∞(q; q3)∞

AU - Andrews, George E.

AU - Berndt, Bruce C.

AU - Sohn, Jaebum

AU - Yee, Ae Ja

AU - Zaharescu, Alexandru

PY - 2003/1/1

Y1 - 2003/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0037693039&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037693039&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-02-03155-0

DO - 10.1090/S0002-9947-02-03155-0

M3 - Article

VL - 355

SP - 2397

EP - 2411

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 6

ER -

^{2};q

^{3})

_{ ∞}(q; q

^{3})

_{∞}. Transactions of the American Mathematical Society. 2003 Jan 1;355(6):2397-2411. https://doi.org/10.1090/S0002-9947-02-03155-0