New characterizations for the eigenvalues of the prolate spheroidal wave equation

Françoise Richard-Jung (1) , Jean-Pierre Ramis (2, 3) , Jean Thomann (4) , Frédéric Fauvet (4)

1 CASYS - Calculs Algébriques et Systèmes Dynamiques
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 Académie des sciences [Paris, France]
4 IRMA - Institut de Recherche Mathématique Avancée

In this paper, we give new characterizations for the eigenvalues of the prolate wave equation as limits of the zeros of some families of polynomials: the coefficients of the formal power series appearing in the solutions near 0, 1 or ∞ (in the variables x, x − 1 or 1/x respectively). The result, which seems to be true for all values of the parameter τ , according to our numerical experiments, is here proved for small values of the parameter τ .

Domaines: Mathématiques [math]

Françoise Richard-Jung, Jean-Pierre Ramis, Jean Thomann, Frédéric Fauvet. New characterizations for the eigenvalues of the prolate spheroidal wave equation. Studies in Applied Mathematics, 2017, 138 (1), pp.3-42. ⟨10.1111/sapm.12134⟩. ⟨hal-01151663⟩