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.
Authors
- Iosif Polterovich
- David A. Sher (ORCID: https://orcid.org/0009-0003-2478-1083)
- N. Filonov (ORCID: https://orcid.org/0000-0002-1586-3031)
- Michael Levitin (ORCID: https://orcid.org/0000-0003-0020-3265)
Institutions
- DePaul University (US)
- St. Petersburg Department of Steklov Institute of Mathematics (RU)
- Université de Montréal (CA)
- University of Reading (GB)
Publication Details
- Journal
- SIAM Journal on Mathematical Analysis
- Published
- 2024-11-25
- DOI
- https://doi.org/10.1137/24m1642032
- Citations
- 3
- Primary Topic
- Mathematical functions and polynomials
- Type
- article
- Field-Weighted Citation Impact
- 2.93
Funders
- University of Reading
- Russian Science Foundation
- Natural Sciences and Engineering Research Council of Canada
- Engineering and Physical Sciences Research Council