Article ID Journal Published Year Pages File Type
4615970 Journal of Mathematical Analysis and Applications 2014 14 Pages PDF
Abstract

By means of Jacobiʼs triple product identity and the t  -coefficient method, we establish a general series expansion formula with five free parameters for the product of arbitrary two Jacobi theta functions. It embodies the triple, quintuple, sextuple and septuple theta function product identities and the generalized Schröter formula. As further applications, we also set up a series expansion formula for the product of three theta functions. It not only generalizes Ewellʼs and Chen–Chen–Huangʼs octuple product identities, but also contains three cubic theta function identities due to Farkas–Kra and Ramanujan respectively and the Macdonald identity for the root system A2A2 as special cases. In the meantime, many other new identities including a new short expression of the triple theta series of Andrews are also presented.

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Physical Sciences and Engineering Mathematics Analysis
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