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
Full-text PDF Free Access
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