2000 character limit reached
On geometric properties of ratio of two hypergeometric functions (2202.04247v1)
Published 9 Feb 2022 in math.CV
Abstract: R. K\"ustner 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 K\"ustner.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.
