Zhu Cao

Affiliation: University of Illinois

Email: zhucao@uiuc.edu

Title Of Talk: Product Identities in Theta Functions

Abstract: Firstly we derive a general method for establishing $q$-series identities. Products of theta-functions can be written as linear combinations of other products of theta-functions using this method. Many known identities can be shown as special cases of this general formula. Several entries in Ramanujan's notebooks as well as new identities are proved as applications. Next we give several generalized forms of Schr\"{o}ter's formula. A general identity by W. Chu and Q.Yan and the Blecksmith-Brillhart-Gerst theorem and are both special cases of our generalized Schr\"{o}ter formula.


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