2020/09/29 by Limei Wang, Wang, Li-Mei
Mathematics · Materials Science · #Analytic and geometric function theory #Polymer Synthesis and Characterization #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2009.13728
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 \citePonVuor:2001