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On the quintuple product identity |
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| Authors: | Hershel M Farkas Irwin Kra |
| Institution: | Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel ; Department of Mathematics, State University of New York at Stony Brook, Stony Brook, New York 11794 |
| Abstract: | In this note we present a new proof of the quintuple product identity which is based on our study of  order theta functions with characteristics and the identities they satisfy. In this context the quintuple product identity is another example of an identity which when phrased in terms of theta functions, rather than infinite products and sums, has a simpler form and is much less mysterious. |
| Keywords: | $q$-series $k^{th}$ order theta functions with characteristics partitions of integers Jacobi triple product Euler pentagonal number theorem |
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