Vol. 315, No. 1, 2021

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Bessel quotients and Robin eigenvalues

Pedro Freitas

Vol. 315 (2021), No. 1, 75–87
Abstract

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

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