A note on zeros of derivatives of ultraspherical Bessel functions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916912155328512 |
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| author | Jiang, Tao |
| author_facet | Jiang, Tao |
| contents | For any fixed $ν\ge 0, δ\in \mathbb R$ and $x>0$, we investigate the positive zeros of the derivatives $j'_{ν,δ}(x)$ and $y'_{ν,δ}(x)$, where \begin{equation*} j_{ν,δ}(x)=x^{-δ}J_ν(x)\quad\text{and} \quad y_{ν,δ}(x)=x^{-δ}Y_ν(x). \end{equation*} We derive asymptotic expansions for their $k$-th positive zeros as $k\rightarrow \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16426 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on zeros of derivatives of ultraspherical Bessel functions Jiang, Tao Classical Analysis and ODEs For any fixed $ν\ge 0, δ\in \mathbb R$ and $x>0$, we investigate the positive zeros of the derivatives $j'_{ν,δ}(x)$ and $y'_{ν,δ}(x)$, where \begin{equation*} j_{ν,δ}(x)=x^{-δ}J_ν(x)\quad\text{and} \quad y_{ν,δ}(x)=x^{-δ}Y_ν(x). \end{equation*} We derive asymptotic expansions for their $k$-th positive zeros as $k\rightarrow \infty$. |
| title | A note on zeros of derivatives of ultraspherical Bessel functions |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2508.16426 |