Uniform enclosures for the phase and zeros of Bessel functions and their derivatives
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909374856822784 |
|---|---|
| author | Filonov, Nikolay Levitin, Michael Polterovich, Iosif Sher, David A. |
| author_facet | Filonov, Nikolay Levitin, Michael Polterovich, Iosif Sher, David A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06956 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform enclosures for the phase and zeros of Bessel functions and their derivatives Filonov, Nikolay Levitin, Michael Polterovich, Iosif Sher, David A. Classical Analysis and ODEs Numerical Analysis Spectral Theory 33C10 (Primary) 33F05, 34B30, 65D20 (Secondary) 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. |
| title | Uniform enclosures for the phase and zeros of Bessel functions and their derivatives |
| topic | Classical Analysis and ODEs Numerical Analysis Spectral Theory 33C10 (Primary) 33F05, 34B30, 65D20 (Secondary) |
| url | https://arxiv.org/abs/2402.06956 |