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 language | English (US) |
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Pages (from-to) | 27-37 |
Number of pages | 11 |
Journal | Ramanujan Journal |
Volume | 13 |
Issue number | 1-3 |
DOIs | |
State | Published - Jun 2007 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory