On the hypergeometric function and families of holomorphic functions
Complex Variables
2024-06-06 v1
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.
Cite
@article{arxiv.2406.02747,
title = {On the hypergeometric function and families of holomorphic functions},
author = {Mark Elin and Fiana Jacobzon},
journal= {arXiv preprint arXiv:2406.02747},
year = {2024}
}