On the hypergeometric function and families of holomorphic functions

Mark Elin; Fiana Jacobzon

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arXiv · 2406.02747

On the hypergeometric function and families of holomorphic functions

Mark Elin·Fiana Jacobzon

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Abstract

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 Gau\ss\ hypergeometric function play a crucial role in our investigation.

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Mark Elin, Fiana Jacobzon. 2024-06-04. On the hypergeometric function and families of holomorphic functions. https://arxiv.org/abs/2406.02747

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