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arXiv · 2402.06956

Uniform enclosures for the phase and zeros of Bessel functions and their derivatives

Nikolay Filonov·Michael Levitin·Iosif Polterovich·David A. Sher
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Abstract

We prove explicit uniform two-sided bounds for the phase functions of Bessel functions and of their derivatives. As a consequence, we obtain new enclosures for the zeros of Bessel functions and their derivatives in terms of inverse values of some elementary functions. These bounds are valid, with a few exceptions, for all zeros and all Bessel functions with non-negative indices. We provide numerical evidence showing that our bounds either improve or closely match the best previously known ones.

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Nikolay Filonov, Michael Levitin, Iosif Polterovich, David A. Sher. 2024-02-10. Uniform enclosures for the phase and zeros of Bessel functions and their derivatives. https://arxiv.org/abs/2402.06956

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