On geometric properties of ratio of two hypergeometric functions

2022/02/09 by Sugawa, Toshiyuki, Wang, Li-Mei
#Complex Variables (math.CV) #FOS: Mathematics #Primary 30C45 #Secondary 33C05

paper · doi:10.48550/arxiv.2202.04247

Abstract

R. Küstner proved in his 2002 paper that the function w_a,b,c(z)= F(a+1,b;c;z)/F(a,b;c;z) maps the unit disk |z|<1 onto a domain convex in the direction of the imaginary axis under some condition on the real parameters a,b,c. Here F(a,b;c;z) stands for the Gaussian hypergeometric function. In this paper, we study the order of convexity of w_a,b,c. In particular, we partially solve the problem raised by the afore-mentioned paper by Küstner.

Related

• On the order of convexity for the shifted hypergeometric functions
• Mapping properties of the zero-balanced hypergeometric functions
• Close-to-Convexity properties of Clausen's Hypergeometric Function ₃F₂(a,b,c;d,e;z)
• Subordination Involving Gauss Hypergeometric Function
• On quotients and differences of hypergeometric functions