On a theory of elliptic functions based on the incomplete integral of the hypergeometric function {_{2}}F_{1}(\frac{1}{4},\frac{3}{4};\frac{1}{2};z) |
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Authors: | Li-Chien Shen |
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Institution: | 1. Department of Mathematics, University of Florida, Gainesville, FL, 32611-8105, USA
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Abstract: | Using the properties of conformal mappings and differential equations, we develop a class of elliptic functions associated with the hypergeometric function ${_{2}}F_{1}(\frac{1}{4},\frac{3}{4};1;z)$ . A detailed comparison is made with the classical Jacobi elliptic functions. Within the frame work of this theory, we provide a proof and new insight into a set of identities of Ramanujan associated with the above hypergeometric function. |
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