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Zbl 1187.30017
Hästö, Peter; Ponnusamy, S.; Vuorinen, M.
Starlikeness of the Gaussian hypergeometric functions. (English)
[J] Complex Var. Elliptic Equ. 55, No. 1-3, 173-184 (2010). ISSN 1747-6933; ISSN 1747-6941/e

The authors derive conditions on the parameters $a$, $b$, $c$ so that the function $zF(a,b;c;z)$ is starlike in $\mathbb{D}$, where $zF(a,b;c;z)$ denotes the classical hypergeometric function. They give some consequences of their results including some mapping properties of convolution operators. The authors propose some interesting problems. All results are correct and can open new research in this field.
[Daniel Breaz (Alba Iulia)]

MSC 2000:: *30C45 Special classes of univalent and multivalent functions
33C45 Orthogonal polynomials and functions of hypergeometric type

Keywords: Gaussian hypergeometric functions; univalence; starlikeness; convexity; Carlson-Shaffer convolution operator

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