Journal Article

Elliptic Functions and the Appell Theta Functions

Zhi-Guo Liu

in International Mathematics Research Notices

Volume 2010, issue 11, pages 2064-2093
Published in print January 2010 | ISSN: 1073-7928
Published online December 2009 | e-ISSN: 1687-0247 | DOI: http://dx.doi.org/10.1093/imrn/rnp212
Elliptic Functions and the Appell Theta Functions

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In this paper, we prove a general theta function identity, which contains the quintuple product identity and Winquist’s identity and many other important results of elliptic theta functions as special cases. This identity can also be used to derive some important identities for the Appell theta functions. A new representation for the generating function for sums of three squares is given.

Journal Article.  5113 words.  Illustrated.

Subjects: Mathematics

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