A theta function identity and its implications

Author:
Zhi-Guo Liu

Journal:
Trans. Amer. Math. Soc. **357** (2005), 825-835

MSC (2000):
Primary 11F11, 11F12, 11F27, 33E05

DOI:
https://doi.org/10.1090/S0002-9947-04-03572-X

Published electronically:
September 2, 2004

MathSciNet review:
2095632

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we prove a general theta function identity with four parameters by employing the complex variable theory of elliptic functions. This identity plays a central role for the cubic theta function identities. We use this identity to re-derive some important identities of Hirschhorn, Garvan and Borwein about cubic theta functions. We also prove some other cubic theta function identities. A new representation for is given. The proofs are self-contained and elementary.

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Additional Information

**Zhi-Guo Liu**

Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200062, People’s Republic of China

Email:
zgliu@math.ecnu.edu.cn, liuzg18@hotmail.com

DOI:
https://doi.org/10.1090/S0002-9947-04-03572-X

Keywords:
Elliptic functions,
theta function identities,
infinite products

Received by editor(s):
September 18, 2003

Received by editor(s) in revised form:
October 24, 2003

Published electronically:
September 2, 2004

Additional Notes:
The author was supported in part by Shanghai Priority Academic Discipline and the National Science Foundation of China

Article copyright:
© Copyright 2004
American Mathematical Society