Complex zeros of Bessel function derivatives and associated orthogonal polynomials
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911918074101760 |
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| author | Chung, Seok-Young Lee, Sujin Park, Young Woong |
| author_facet | Chung, Seok-Young Lee, Sujin Park, Young Woong |
| contents | We introduce a sequence of orthogonal polynomials whose associated moments are the Rayleigh-type sums, involving the zeros of the Bessel derivative $J_ν'$ of order $ν$. We also discuss the fundamental properties of those polynomials such as recurrence, orthogonality, etc. Consequently, we obtain a formula for the Hankel determinant, elements of which are chosen as the aforementioned Rayleigh-type sums. As an application, we complete the Hurwitz-type theorem for $J_ν'$, which deals with the number of complex zeros of $J_ν'$ depending on the range of $ν$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09746 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Complex zeros of Bessel function derivatives and associated orthogonal polynomials Chung, Seok-Young Lee, Sujin Park, Young Woong Classical Analysis and ODEs Complex Variables 30C15, 30B70, 33C10, 33C47 We introduce a sequence of orthogonal polynomials whose associated moments are the Rayleigh-type sums, involving the zeros of the Bessel derivative $J_ν'$ of order $ν$. We also discuss the fundamental properties of those polynomials such as recurrence, orthogonality, etc. Consequently, we obtain a formula for the Hankel determinant, elements of which are chosen as the aforementioned Rayleigh-type sums. As an application, we complete the Hurwitz-type theorem for $J_ν'$, which deals with the number of complex zeros of $J_ν'$ depending on the range of $ν$. |
| title | Complex zeros of Bessel function derivatives and associated orthogonal polynomials |
| topic | Classical Analysis and ODEs Complex Variables 30C15, 30B70, 33C10, 33C47 |
| url | https://arxiv.org/abs/2406.09746 |