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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the theory of elliptic functions based on ${}_{2}F_{1}(\frac{1}{3},\frac{2}{3};\frac{1}{2};z)$


Author: Li-Chien Shen
Journal: Trans. Amer. Math. Soc. 357 (2005), 2043-2058
MSC (2000): Primary 11L05
Published electronically: November 4, 2004
MathSciNet review: 2115090
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Abstract: Based on properties of the hypergeometric series ${}_{2}F_{1}(\frac{1}{3},\frac{2}{3};\frac{1}{2};z)$, we develop a theory of elliptic functions that shares many striking similarities with the classical Jacobian elliptic functions.


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Additional Information

Li-Chien Shen
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611-2082
Email: shen@math.ufl.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03600-1
PII: S 0002-9947(04)03600-1
Keywords: Jacobian elliptic functions, theta functions, Weierstrass $\wp $ function
Received by editor(s): December 20, 2002
Received by editor(s) in revised form: December 15, 2003
Published electronically: November 4, 2004
Article copyright: © Copyright 2004 American Mathematical Society