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{\bf Wenchang Chu and Qinglun Yan}
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{\bf Unification of the Quintuple and Septuple Product Identities}
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By combining the functional equation method with Jacobi's triple
product identity, we establish a general equation with five free
parameters on the modified Jacobi theta function, which can be
considered as the common generalization of the quintuple, sextuple
and septuple product identities. Several known theta function
formulae and new identities are consequently proved.
\bye