کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4615970 1339333 2014 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The t-coefficient method II: A new series expansion formula of theta function products and its implications
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
The t-coefficient method II: A new series expansion formula of theta function products and its implications
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 411, Issue 2, 15 March 2014, Pages 902–915
نویسندگان
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