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 $x{J}_{\nu +1}∕{J}_{\nu }\left(x\right)$, where ${J}_{\nu }$ are Bessel functions of the first kind and $\nu >-1$. These bounds are asymptotically correct close to the zeros of ${J}_{\nu }$, allowing us to derive sharp estimates for the zeros of the function $x{J}_{\nu +1}\left(x\right)-\beta {J}_{\nu }\left(x\right)$, 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
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