Addendum

Since the writing of this article we have become aware of some additional references on the subject of the quintuple product identity (QPI). Indeed, the generalization of the identity, Theorem 2 of our paper has been discovered previously. The current paper places the identity in a general context and, as such, should make it accessible and interesting to a larger audience. We list three more references for the benefit of the reader. We are grateful to S. Cooper for calling our attention to a number of papers on the subject and to M.D. Hirschhorn for supplying us with reprints and preprints. His manuscript [10] contains a nice history of the QPI and his preprint [11] contains another proof of this identity.

10. M.D. Hirschhorn, A generalization of the quintuple product identity, J. Austral. Math Soc. (A) 44 (1988), 42-45.

11. M.D. Hirschhorn, On the expansion of Ramanujan’s continued fraction, to appear.

12. I.G. Macdonald, Affine root systems and Dedekind’s η-function, Invent. Math. 15 (1972), 91-143.