Corpus ID: 237581284

Modular transformations and the elliptic functions of Shen

@inproceedings{Robinson2021ModularTA,
  title={Modular transformations and the elliptic functions of Shen},
  author={P. L. Robinson},
  year={2021}
}
  • P. L. Robinson
  • Published 14 September 2021
  • Mathematics
We employ Weierstrassian modular transformations to compute fundamental periods for the elliptic functions dn2 and dn3 of Shen. 

References

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1 Theta Functions.- 2 Jacobi's Elliptic Functions.- 3 Elliptic Integrals.- 4 Geometrical Applications.- 5 Physical Applications.- 6 Weierstrass's Elliptic Function.- 7 Applications of the WeierstrassExpand
ON THE THEORY OF ELLIPTIC FUNCTIONS
Based on properties of the hypergeometric series 2F1( 1 3 , 2 3 ; 1 2 ; z), we develop a theory of elliptic functions that shares many striking similarities with the classical Jacobian ellipticExpand
On a theory of elliptic functions based on the incomplete integral of the hypergeometric function ${_{2}}F_{1}(\frac{1}{4},\frac{3}{4};\frac{1}{2};z)$
Using the properties of conformal mappings and differential equations, we develop a class of elliptic functions associated with the hypergeometric function ${_{2}}F_{1}(\frac{1}{4},\frac{3}{4};1;z)$.Expand