Uniform enclosures for the phase and zeros of Bessel functions and their derivatives
<|reference_start|>Uniform enclosures for the phase and zeros of Bessel functions and their derivatives: 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.<|reference_end|>
@article{filonov2024uniform,
    title={Uniform enclosures for the phase and zeros of Bessel functions and their
  derivatives},
    author={Nikolay Filonov, Michael Levitin, Iosif Polterovich, David A. Sher},
    journal={arXiv preprint arXiv:2402.06956},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.06956},
    primaryClass={math.CA cs.NA math.NA math.SP}
}