A Remarkable Wronskian with Application to Critical Lengths of Cycloidal Spaces

Rachid Ait-Haddou (1) , Marie-Laurence Mazure (2) , Helmut Ruhland

1 Osaka University [Osaka]
2 CVGI - Calcul des Variations, Géométrie, Image

Recently, Carnicer et al. (Calcolo 54(4):1521–1531, 2017) proved the very elegant and surprising fact that half of the critical length of a cycloidal space coincides with the first positive zero of a spherical Bessel function. Their finding relied in identifying the first positive zero of certain Wronskians. In this paper, we show that these Wronskians admit explicit expressions in terms of spherical Bessel functions. As an application, we recover the above mentioned result.

Domaines: Analyse numérique [math.NA]

Rachid Ait-Haddou, Marie-Laurence Mazure, Helmut Ruhland. A Remarkable Wronskian with Application to Critical Lengths of Cycloidal Spaces. Calcolo, 2019, 56 (4), ⟨10.1007/s10092-019-0343-2⟩. ⟨hal-02305316⟩