论文标题
函数的几何属性$ az^{2}
Geometric Properties of function $az^{2}J_{ν}^{\prime \prime }(z)+bzJ_{ν}^{\prime}(z)+cJ_{ν}(z)$
论文作者
论文摘要
在本文中，我们的目的是找到三种不同类型的标准化的$n_ν（z）= az^{2} j_ {v}^{c {\ prime \ prime}（z）+bzj_+bzj_ {ν}^{n p prime}^（z）+cj _ q j qj_ qj_ = n n qj___）的三种不同类型的标准化的半径。我们主要结果证明的第一种订单$ν的贝塞尔功能是$n_ν（z）$函数的Mittag-Leffler扩展和实际零的属性。此外，通过使用Euler-rayleigh的不等式，我们为归一化的$N_ν（Z）$函数获得了一些紧张的下限和上限。最后，我们评估了$n_ν（z）$函数的某些零多总和。
In this paper our aim is to find the radii of starlikeness and convexity for three different kind of normalization of the $N_ν(z)=az^{2}J_{ν}^{\prime \prime }(z)+bzJ_{ν}^{\prime}(z)+cJ_{ν}(z)$ function, where $J_ν(z)$ is called the Bessel function of the first kind of order $ν.$ The key tools in the proof of our main results are the Mittag-Leffler expansion for $N_ν(z)$ function and properties of real zeros of it. 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 $N_ν(z)$ function. Finally, we evaluate certain multiple sums of the zeros for $N_ν(z)$ function.
