Hypergeometric transforms of functions with derivative in a half plane. (English) Zbl 0934.30006

The author proves inequalities for the Taylor coefficients of the Gaussian hypergeometric function and of the confluent hypergeometric function. These inequalities enable him to get certain geometric properties of the images of the unit disk under such transformations. These geometric properties are used to prove invariance properties of operators defined by convolution with hypergeometric functions.


30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
33C15 Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\)
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