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

Bruce C. Berndt, Song Heng Chan, Boon Pin Yeap, Ae Ja Yee

Research output: Contribution to journalArticle

17 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)27-37
Number of pages11
JournalRamanujan Journal
Volume13
Issue number1-3
DOIs
StatePublished - Jun 1 2007

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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