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Abstract
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We obtain sharp bounds for the quotient
, where
are Bessel functions
of the first kind and
.
These bounds are asymptotically correct close to the zeros of
,
allowing us to derive sharp estimates for the zeros of the function
, with
applications to eigenvalue problems associated with the Laplace and Dirac
operators.
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Keywords
Bessel functions, eigenvalues, Mittag–Leffler expansion
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Mathematical Subject Classification
Primary: 33C10, 34B30
Secondary: 35P15
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Milestones
Received: 4 September 2020
Accepted: 11 October 2021
Published: 13 December 2021
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