Recurrence relations for the Maclaurin coefficients of products of elementary functions and Hypergeometric functions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914402082488320 |
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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 the recurrence relations for the Maclaurin coefficients of the products of elementary functions and hypergeometric functions. Specifically, we focus on the confluent hypergeometric function $\mathcal{M}(z) = h(z) M(a,c;z)$ and the Gaussian hypergeometric function $\mathcal{F}(z) = h(z) F(a,b;c;z)$, considering several specific choices for the function $h(z)$. In particular, we explore cases where $h(z)$ is chosen 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_2603_16465 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Recurrence relations for the Maclaurin coefficients of products of elementary functions and Hypergeometric functions Mao, Zhong-Xuan Tian, Jing-Feng Complex Variables 33C15, 33C05 In this paper, we investigate the recurrence relations for the Maclaurin coefficients of the products of elementary functions and hypergeometric functions. Specifically, we focus on the confluent hypergeometric function $\mathcal{M}(z) = h(z) M(a,c;z)$ and the Gaussian hypergeometric function $\mathcal{F}(z) = h(z) F(a,b;c;z)$, considering several specific choices for the function $h(z)$. In particular, we explore cases where $h(z)$ is chosen 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 Hypergeometric functions |
| topic | Complex Variables 33C15, 33C05 |
| url | https://arxiv.org/abs/2603.16465 |