2017/01/26 by Jean-Christophe Feauveau, Feauveau, Jean-Christophe
Mathematics · #11G16 #11J89 #33E05 #Complex Variables (math.CV) #FOS: Mathematics #History and Theory of Mathematics #Mathematical functions and polynomials #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.1701.07890
openalex publication_date 2017/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Elliptic functions are largely studied and standardized mathematical objects. The two usual approaches are due to Jacobi and Weierstrass. From a contour integral which allowed us to unify many summation formulae (Euler-MacLaurin, Poisson, Voronoï or Circle formulae), we will find the entirety of the elliptic functions, proposed either in the shape of Jacobi or Weierstrass. But with one translation which appears in their natural form. What could seem a defect will lead us to a renormalisation of the elliptic functions making it possible to determine, in a rather simple way, a Fourier series representation and a factorization of these functions.