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Spirallikeness of shifted hypergeometric functions
In the present paper, we study spirallikenss (including starlikeness) of the
shifted hypergeometric function with complex parameters
where stands for the Gaussian hypergeometric
function. First, we observe the asymptotic behaviour of around
the point to obtain necessary conditions for to be
-spirallike for a given with We
next give sufficient conditions for to be -spirallike. As special
cases, we obtain sufficient conditions of strong starlikeness and examples of
spirallike, but not starlike, shifted hypergeometric functions.Comment: 16 pages, 1 figur
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