A system of hypergeometric differential equations in $m$ variables of rank $p^m$
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| author | Kaneko, Jyoichi Matsumoto, Keiji Ohara, Katsuyoshi Terasoma, Tomohide |
| author_facet | Kaneko, Jyoichi Matsumoto, Keiji Ohara, Katsuyoshi Terasoma, Tomohide |
| contents | We define a hypergeometric series in $m$ variables with $p+(p-1)m$ parameters, which reduces to the generalized hypergeometric series $_pF_{p-1}$ when $m=1$, and to Lauricella's hypergeometric series $F_C$ in $m$ variables when $p=2$. We give a system of hypergeometric differential equations annihilating the series. Under some non-integral conditions on parameters, we give an Euler type integral representation of the series, and linearly independent $p^m$ solutions to this system around a point near to the origin. We show that this system is of rank $p^m$, and determine its singular locus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00295 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A system of hypergeometric differential equations in $m$ variables of rank $p^m$ Kaneko, Jyoichi Matsumoto, Keiji Ohara, Katsuyoshi Terasoma, Tomohide Classical Analysis and ODEs Algebraic Geometry 33C70, 32S40 We define a hypergeometric series in $m$ variables with $p+(p-1)m$ parameters, which reduces to the generalized hypergeometric series $_pF_{p-1}$ when $m=1$, and to Lauricella's hypergeometric series $F_C$ in $m$ variables when $p=2$. We give a system of hypergeometric differential equations annihilating the series. Under some non-integral conditions on parameters, we give an Euler type integral representation of the series, and linearly independent $p^m$ solutions to this system around a point near to the origin. We show that this system is of rank $p^m$, and determine its singular locus. |
| title | A system of hypergeometric differential equations in $m$ variables of rank $p^m$ |
| topic | Classical Analysis and ODEs Algebraic Geometry 33C70, 32S40 |
| url | https://arxiv.org/abs/2404.00295 |