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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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Publication:457012
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DOI10.1007/s11139-013-9491-1zbMath1298.33024OpenAlexW2089011800MaRDI QIDQ457012

Li-Chien Shen

Publication date: 26 September 2014

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-013-9491-1


zbMATH Keywords

Eisenstein serieshypergeometric functionWeierstrass elliptic functionLegendre function


Mathematics Subject Classification ID

Elliptic integrals as hypergeometric functions (33C75)


Related Items (4)

On Hecke groups, Schwarzian triangle functions and a class of hyper-elliptic functions ⋮ JACOBIAN ELLIPTIC FUNCTIONS IN SIGNATURE FOUR ⋮ On the approximation of some special functions in Ramanujan's generalized modular equation with signature \(3^{\ast}\) ⋮ Quantum geometry of resurgent perturbative/nonperturbative relations



Cites Work

  • Inversion formulas for elliptic functions
  • Ramanujan's Theories of Elliptic Functions to Alternative Bases
  • Unnamed Item
  • Unnamed Item


This page was built for publication: 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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