Double integrals and transformation formulas for Appell--Lauricella hypergeometric functions $F_D$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918321587224576 |
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| author | Wang, Shihao Yu, Chenglong Zheng, Zhiwei |
| author_facet | Wang, Shihao Yu, Chenglong Zheng, Zhiwei |
| contents | The monodromy of hypergeometric functions can govern the properties of the functions themselves. Previously, the second and third authors studied the commensurability relations among monodromy groups of the Appell--Lauricella hypergeometric functions using Deligne--Mostow theory and the geometric correspondence between curves and surfaces. In this paper, we apply the same construction to obtain transformation formulas among these hypergeometric functions. This also provides an alternative approach to some of Goursat's quadratic transformations via double integrals and Fubini's theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03601 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Double integrals and transformation formulas for Appell--Lauricella hypergeometric functions $F_D$ Wang, Shihao Yu, Chenglong Zheng, Zhiwei Classical Analysis and ODEs Algebraic Geometry 33C65 The monodromy of hypergeometric functions can govern the properties of the functions themselves. Previously, the second and third authors studied the commensurability relations among monodromy groups of the Appell--Lauricella hypergeometric functions using Deligne--Mostow theory and the geometric correspondence between curves and surfaces. In this paper, we apply the same construction to obtain transformation formulas among these hypergeometric functions. This also provides an alternative approach to some of Goursat's quadratic transformations via double integrals and Fubini's theorem. |
| title | Double integrals and transformation formulas for Appell--Lauricella hypergeometric functions $F_D$ |
| topic | Classical Analysis and ODEs Algebraic Geometry 33C65 |
| url | https://arxiv.org/abs/2602.03601 |