On a generalization of Jacobi's elegantissima
Classical Analysis and ODEs
2023-09-07 v2
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.
Cite
@article{arxiv.2305.06717,
title = {On a generalization of Jacobi's elegantissima},
author = {Luc Haine},
journal= {arXiv preprint arXiv:2305.06717},
year = {2023}
}
Comments
typos corrected, references added, accepted for publication Physica D