### Abstract

Three proofs are given for a reciprocity theorem for a certain q-series found in Ramanujan's lost notebook. The first proof uses Ramanujan's
_{1}
ψ
_{1}
summation theorem, the second employs an identity of N. J. Fine, and the third is combinatorial. Next, we show that the reciprocity theorem leads to a two variable generalization of the quintuple product identity. The paper concludes with an application to sums of three squares.

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

Pages (from-to) | 27-37 |

Number of pages | 11 |

Journal | Ramanujan Journal |

Volume | 13 |

Issue number | 1-3 |

DOIs | |

State | Published - Jun 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

*Ramanujan Journal*,

*13*(1-3), 27-37. https://doi.org/10.1007/s11139-006-0241-5

}

*Ramanujan Journal*, vol. 13, no. 1-3, pp. 27-37. https://doi.org/10.1007/s11139-006-0241-5

**A reciprocity theorem for certain q-series found in Ramanujan's lost notebook.** / Berndt, Bruce C.; Chan, Song Heng; Yeap, Boon Pin; Yee, Ae Ja.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A reciprocity theorem for certain q-series found in Ramanujan's lost notebook

AU - Berndt, Bruce C.

AU - Chan, Song Heng

AU - Yeap, Boon Pin

AU - Yee, Ae Ja

PY - 2007/6/1

Y1 - 2007/6/1

N2 - Three proofs are given for a reciprocity theorem for a certain q-series found in Ramanujan's lost notebook. The first proof uses Ramanujan's 1 ψ 1 summation theorem, the second employs an identity of N. J. Fine, and the third is combinatorial. Next, we show that the reciprocity theorem leads to a two variable generalization of the quintuple product identity. The paper concludes with an application to sums of three squares.

AB - Three proofs are given for a reciprocity theorem for a certain q-series found in Ramanujan's lost notebook. The first proof uses Ramanujan's 1 ψ 1 summation theorem, the second employs an identity of N. J. Fine, and the third is combinatorial. Next, we show that the reciprocity theorem leads to a two variable generalization of the quintuple product identity. The paper concludes with an application to sums of three squares.

UR - http://www.scopus.com/inward/record.url?scp=33845770686&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33845770686&partnerID=8YFLogxK

U2 - 10.1007/s11139-006-0241-5

DO - 10.1007/s11139-006-0241-5

M3 - Article

VL - 13

SP - 27

EP - 37

JO - Ramanujan Journal

JF - Ramanujan Journal

SN - 1382-4090

IS - 1-3

ER -