Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 963-977

SPIRALLIKENESS OF SHIFTED HYPERGEOMETRIC FUNCTIONS

Toshiyuki Sugawa and Li-Mei Wang

Tohoku University, Graduate School of Information Sciences
Aoba-ku, Sendai 980-8579, Japan; sugawa 'at' math.is.tohoku.ac.jp

University of International Business and Economics, No. 10, School of Statistics
Huixin Dongjie, Chaoyang District, Beijing 100029, P.R. China; wangmabel 'at' 163.com

Abstract. 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.

2010 Mathematics Subject Classification: Primary 30C45; Secondary 33C05.

Key words: Strongly starlike function, spirallike function, cluster set.

Reference to this article: T. Sugawa and L.-M. Wang: Spirallikeness of shifted hypergeometric functions. Ann. Acad. Sci. Fenn. Math. 42 (2017), 963-977.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4257