Please use this identifier to cite or link to this item: https://doi.org/10.1007/s11139-006-0241-5
Title: A reciprocity theorem for certain q-series found in Ramanujan's lost notebook
Authors: Berndt, B.C.
Chan, S.H. 
Yeap, B.P.
Yee, A.J.
Keywords: Combinatorial bijection
q-series
Quintuple product identity
Ramanujan's 1ψ1 summation theorem
Reciprocity theorem
Sums of three squares
Issue Date: Jun-2007
Citation: Berndt, B.C., Chan, S.H., Yeap, B.P., Yee, A.J. (2007-06). A reciprocity theorem for certain q-series found in Ramanujan's lost notebook. Ramanujan Journal 13 (1-3) : 27-37. ScholarBank@NUS Repository. https://doi.org/10.1007/s11139-006-0241-5
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 1ψ1 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. © 2006 Springer Science + Business Media, LLC.
Source Title: Ramanujan Journal
URI: http://scholarbank.nus.edu.sg/handle/10635/104521
ISSN: 13824090
DOI: 10.1007/s11139-006-0241-5
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