Wright函数的星形半径与凸性
Radii of starlikeness and convexity of Wright functions
摘要：
本文的目的是找到三种不同规格化的Wright函数的星形半径和凸性半径。证明主要结果的关键工具是Wright函数的Mittag-Leffler展开式和Wright函数及其导数的实零点的性质。此外，利用Euler-Rayleigh不等式，我们得到了归一化Wright函数的零阶星形半径和凸性半径的一些紧的上下界上界.本文的主要结果是经典第一类Bessel函数的某些已知结果的自然扩张。还提出了一些开放的问题，这可能是感兴趣的进一步研究。
英文摘要：
In this paper our aim is to find the radii of starlikeness and convexity of the normalized Wright functions for three different kind of normalization. The key tools in the proof of our main results are the Mittag-Leffler expansion for Wright function and properties of real zeros of Wright function and its derivative. In addition, by using the Euler-Rayleigh inequalities we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero for the normalized Wright functions. The main results of the paper are natural extensions of some known results on classical Bessel functions of the first kind. Some open problems are also proposed, which may be of interest for further research.
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