#### 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