English

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.

Keywords

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