On the theory of elliptic functions based on ${}_{2}F_{1}(\frac {1}{3},\frac {2}{3};\frac {1}{2};z)$
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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.References
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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
- Received by editor(s): December 20, 2002
- Received by editor(s) in revised form: December 15, 2003
- Published electronically: November 4, 2004
- © Copyright 2004 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 357 (2005), 2043-2058
- MSC (2000): Primary 11L05
- DOI: https://doi.org/10.1090/S0002-9947-04-03600-1
- MathSciNet review: 2115090