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

Filonov, N., Levitin, M. ORCID: https://orcid.org/0000-0003-0020-3265, Polterovich, I. and Sher, D. A. (2024) Uniform enclosures for the phase and zeros of Bessel functions and their derivatives. SIAM Journal on Mathematical Analysis (SIMA), 56 (6). pp. 7644-7682. ISSN 1095-7154 doi: 10.1137/24M1642032

Abstract/Summary

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.

Additional Information	The accompanying Mathematica script and its printout are available for download at https://michaellevitin.net/bessels.html
Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/117826
Identification Number/DOI	10.1137/24M1642032
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Uncontrolled Keywords	Bessel functions, Bessel zeros, phase function, Sturm oscillation theorem, one-dimensional Schrödinger equation
Additional Information	The accompanying Mathematica script and its printout are available for download at https://michaellevitin.net/bessels.html
Publisher	Society for Industrial and Applied Mathematics
Download/View statistics	View download statistics for this item