Recurrence Relations for the Maclaurin Coefficients of Products of Elementary Functions and the Bessel Functions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911399333068800 |
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| author | Mao, Zhong-Xuan Tian, Jing-Feng |
| author_facet | Mao, Zhong-Xuan Tian, Jing-Feng |
| contents | In this paper, we investigate recurrence relations for the Maclaurin coefficients of the products of a elementary function and the Bessel function of the first kind $\mathcal{J}(z) = h(z) J_ν(z)$ and the modified Bessel function of the first kind $\mathcal{I}(z) = h(z) I_ν(z)$ in the complex plane corresponding to several specific choices of $h(z)$. In particular, we specialize $h(z)$ as $e^{pz}$, $(1-θz)^p$, $e^{-p \arctan z}$, $\sin(pz)$, $\cos(pz)$, $\sinh(pz)$, $\cosh(pz)$, $\arcsin(pz)$ and $\arccos(pz)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18332 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Recurrence Relations for the Maclaurin Coefficients of Products of Elementary Functions and the Bessel Functions Mao, Zhong-Xuan Tian, Jing-Feng Complex Variables 33C10, 11B37 In this paper, we investigate recurrence relations for the Maclaurin coefficients of the products of a elementary function and the Bessel function of the first kind $\mathcal{J}(z) = h(z) J_ν(z)$ and the modified Bessel function of the first kind $\mathcal{I}(z) = h(z) I_ν(z)$ in the complex plane corresponding to several specific choices of $h(z)$. In particular, we specialize $h(z)$ as $e^{pz}$, $(1-θz)^p$, $e^{-p \arctan z}$, $\sin(pz)$, $\cos(pz)$, $\sinh(pz)$, $\cosh(pz)$, $\arcsin(pz)$ and $\arccos(pz)$. |
| title | Recurrence Relations for the Maclaurin Coefficients of Products of Elementary Functions and the Bessel Functions |
| topic | Complex Variables 33C10, 11B37 |
| url | https://arxiv.org/abs/2601.18332 |