Mapping properties of the zero-balanced hypergeometric functions
Abstract
In the present paper, the order of convexity of z(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 under some shifted zero-balanced hypergeometric functions z(a,b;a+b;z) are convex and bounded by two horizontal lines which solves the problem raised by Ponnusamy and Vuorinen in PonVuor:2001
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