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arXiv · 2305.06717

On a generalization of Jacobi's elegantissima

Luc Haine
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Abstract

We establish a generalization of Jacobi's elegantissima, which solves the pendulum equation. This amazing formula appears in lectures by the famous cosmologist Georges Lema\^itre, during the academic years 1955-1956 and 1956-1957. Our approach uses the full power of Jacobi's elliptic functions, in particular imaginary time is crucial for obtaining the result.

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Luc Haine. 2023-05-11. On a generalization of Jacobi's elegantissima. https://doi.org/10.1016/j.physd.2023.133894

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