On the generalized interlacing property for the zeros of Bessel functions
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917786890010624 |
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| author | Chung, Seok-Young Lee, Sujin Park, Young Woong |
| author_facet | Chung, Seok-Young Lee, Sujin Park, Young Woong |
| contents | This paper investigates a generalized interlacing property between Bessel functions, particularly $J_ν$ and $J_μ$, where the difference $|ν-μ|$ exceeds $2$. This interlacing phenomenon is marked by a compensatory interaction with the zeros of Lommel polynomials, extending our understanding beyond the traditional $|ν-μ| \le 2$ regime. The paper extends the generalized interlacing property to cylinder functions and derivative of Bessel functions, as an application. It is also discussed that Siegel's extension of Bourget hypothesis to rational numbers of $ν$ cannot be further improved to arbitrary real numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_13542 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the generalized interlacing property for the zeros of Bessel functions Chung, Seok-Young Lee, Sujin Park, Young Woong Classical Analysis and ODEs 33C10, 33C45, 26D15 This paper investigates a generalized interlacing property between Bessel functions, particularly $J_ν$ and $J_μ$, where the difference $|ν-μ|$ exceeds $2$. This interlacing phenomenon is marked by a compensatory interaction with the zeros of Lommel polynomials, extending our understanding beyond the traditional $|ν-μ| \le 2$ regime. The paper extends the generalized interlacing property to cylinder functions and derivative of Bessel functions, as an application. It is also discussed that Siegel's extension of Bourget hypothesis to rational numbers of $ν$ cannot be further improved to arbitrary real numbers. |
| title | On the generalized interlacing property for the zeros of Bessel functions |
| topic | Classical Analysis and ODEs 33C10, 33C45, 26D15 |
| url | https://arxiv.org/abs/2310.13542 |