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JACOBIAN ELLIPTIC FUNCTIONS IN SIGNATURE FOUR
Published online by Cambridge University Press: 13 June 2023
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].
MSC classification
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- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 109 , Issue 1 , February 2024 , pp. 110 - 124
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.