Unification of the Quintuple and Septuple Product Identities

Wenchang Chu, Qinglun Yan


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.

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