The t-coefficient method II: A new series expansion formula of theta function products and its implications

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:411

Article

Ma, Xinrong

关键词: Jacobi's triple product identity;    Quintuple;    Sextuple;    Septuple;    Octuple;    Bilateral series;    Coefficient functional;    t-Coefficient method;    Laurent series expansion;    Modular equation;    Schroter formula;    Macdonald identity;   

DOI  :  10.1016/j.jmaa.2013.10.030

来源: Elsevier

【 摘 要 】

By means of Jacobi's 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 Schroter formula. As further applications, we also set up a series expansion formula for the product of three theta functions. It not only generalizes Ewell's and Chen-Chen-Huang's 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 A(2) 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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free