On the hypergeometric function and families of holomorphic functions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914824559001600 |
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| author | Elin, Mark Jacobzon, Fiana |
| author_facet | Elin, Mark Jacobzon, Fiana |
| contents | In this work, we examine one two-parameter family of sets consisting of functions holomorphic in the unit disk, previously investigated by several mathematicians. We focus on the set-theoretic properties of this family, identify the general form of filtrations within it, and discover that it is not a lattice. This insight motivates us to introduce a refined concept of quasi-infima and quasi-suprema, and to establish their complete description.
Unexpectedly, some new properties of the Gauß hypergeometric function play a crucial role in our investigation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02747 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the hypergeometric function and families of holomorphic functions Elin, Mark Jacobzon, Fiana Complex Variables In this work, we examine one two-parameter family of sets consisting of functions holomorphic in the unit disk, previously investigated by several mathematicians. We focus on the set-theoretic properties of this family, identify the general form of filtrations within it, and discover that it is not a lattice. This insight motivates us to introduce a refined concept of quasi-infima and quasi-suprema, and to establish their complete description. Unexpectedly, some new properties of the Gauß hypergeometric function play a crucial role in our investigation. |
| title | On the hypergeometric function and families of holomorphic functions |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2406.02747 |