Integral representations and zeros of the Lommel function and the hypergeometric $_1F_2$ function
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911782525730816 |
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| author | Zullo, Federico |
| author_facet | Zullo, Federico |
| contents | We give different integral representations of the Lommel function $s_{μ,ν}(z)$ involving trigonometric and hypergeometric $_2F_1$ functions. By using classical results of Polya, we give the distribution of the zeros of $s_{μ,ν}(z)$ for certain regions in the plane $(μ,ν)$. Further, thanks to a well known relation between the functions $s_{μ,ν}(z)$ and the hypergeometric $ _1F_2$ function, we describe the distribution of the zeros of $_1F_2$ for specific values of its parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00426 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Integral representations and zeros of the Lommel function and the hypergeometric $_1F_2$ function Zullo, Federico Classical Analysis and ODEs We give different integral representations of the Lommel function $s_{μ,ν}(z)$ involving trigonometric and hypergeometric $_2F_1$ functions. By using classical results of Polya, we give the distribution of the zeros of $s_{μ,ν}(z)$ for certain regions in the plane $(μ,ν)$. Further, thanks to a well known relation between the functions $s_{μ,ν}(z)$ and the hypergeometric $ _1F_2$ function, we describe the distribution of the zeros of $_1F_2$ for specific values of its parameters. |
| title | Integral representations and zeros of the Lommel function and the hypergeometric $_1F_2$ function |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2312.00426 |