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JACOBIAN ELLIPTIC FUNCTIONS IN SIGNATURE FOUR

Part of: Other special functions

Published online by Cambridge University Press:  13 June 2023

P. L. ROBINSON Open the ORCID record for P. L. ROBINSON [Opens in a new window]
P. L. ROBINSON*
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
*
e-mail: paulr@ufl.edu
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Abstract

The signature four elliptic theory of Ramanujan is provided with a counterpart to the Jacobian modular sine; this counterpart yields natural direct proofs of several hypergeometric identities recorded by Ramanujan, bypassing the signature four transfer principle of Berndt et al. [‘Ramanujan’s theories of elliptic functions to alternative bases’, Trans. Amer. Math. Soc. 347 (1995), 4163–4244].

Keywords

alternative baseselliptic functionshypergeometric transformations

MSC classification

Primary: 33E05: Elliptic functions and integrals
Secondary: 33C75: Elliptic integrals as hypergeometric functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 109 , Issue 1 , February 2024 , pp. 110 - 124
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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References

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