In the present paper, we study spirallikenss (including starlikeness) of the shifted hypergeometric function f(z) = z2F1(a, b; c; z) with complex parameters a, b, c, where 2F1(a, b; c; z) stands for the Gaussian hypergeometric function. First, we observe the asymptotic behaviour of 2F1(a, b; c; z) around the point z = 1 to obtain necessary conditions for f to be λ-spirallike for a given λ with -π/2 < λ < π/2. We next give sufficient conditions for f to be λ-spirallike. As special cases, we obtain sufficient conditions of strong starlikeness and examples of spirallike, but not starlike, shifted hypergeometric functions.
|ジャーナル||Annales Academiae Scientiarum Fennicae Mathematica|
|出版ステータス||Published - 2017|
ASJC Scopus subject areas
- 数学 (全般)