Mapping properties of the zero-balanced hypergeometric functions
Complex Variables
2020-09-30 v1
Abstract
In the present paper, the order of convexity of z\Gauss(a,b;c;z) is first given under some conditions on the positive real parameters a, b and c. Then we show that the image domains of the unit disc \D under some shifted zero-balanced hypergeometric functions z\Gauss(a,b;a+b;z) are convex and bounded by two horizontal lines which solves the problem raised by Ponnusamy and Vuorinen in \cite{PonVuor:2001
Cite
@article{arxiv.2009.13728,
title = {Mapping properties of the zero-balanced hypergeometric functions},
author = {Li-Mei Wang},
journal= {arXiv preprint arXiv:2009.13728},
year = {2020}
}
Comments
12 pages