Bessel quotients and Robin eigenvalues

We obtain sharp bounds for the quotient $x J_{ν + 1} ∕ J_{ν} (x)$ , where $J_{ν}$ are Bessel functions of the first kind and $ν > - 1$ . These bounds are asymptotically correct close to the zeros of $J_{ν}$ , allowing us to derive sharp estimates for the zeros of the function $x J_{ν + 1} (x) - β J_{ν} (x)$ , with applications to eigenvalue problems associated with the Laplace and Dirac operators.

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Keywords

Bessel functions, eigenvalues, Mittag–Leffler expansion

Mathematical Subject Classification

Primary: 33C10, 34B30

Secondary: 35P15

Milestones

Received: 4 September 2020

Accepted: 11 October 2021

Published: 13 December 2021

Authors

Pedro Freitas
Departamento de Matemática Instituto Superior Técnico Universidade de Lisboa Lisboa Portugal	Grupo de Física Matemática Faculdade de Ciências Universidade de Lisboa Lisboa Portugal

Vol. 315, No. 1, 2021

Pedro Freitas

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors