含Bessel函数导数的函数的几何性质
Geometric Properties of Functions Containing Derivatives of Bessel Functions
摘要：
本文的目的是求出函数$N_ν(z)=az^2J_ν^{\prime\prime}(z)+bzJ_ν^{\prime}(z)+cJ_ν(z),$的三种不同的正规化的$γ$-$α$阶的类螺旋和凸$γ$ -$α$阶的类螺旋的半径，其中$J_ν(z)$是第一类$ν.$阶的Bessel函数。此外，还研究了这些正规化函数的$\mathcal{S}^*\left(φ\right)-$半径和$\mathcal{C}\left(φ\right)-$半径。创建表格，并通过对所得结果中的实数$a,$、$b$和$c$赋予特殊值，用图形进行目视验证。
英文摘要：
In this paper our aim is to find the radii of $γ$-Spirallike of order $α$ and convex $γ$-Spirallike of order $α$ for three different kinds of normalizations of the function $N_ν(z)=az^2J_ν^{\prime\prime}(z)+bzJ_ν^{\prime}(z)+cJ_ν(z),$ where $J_ν(z)$ is the Bessel function of the first kind of order $ν.$ Moreover, the $\mathcal{S}^*\left(φ\right)-$radii and $\mathcal{C}\left(φ\right)-$radii of these normalized functions are investigated. The tables are created and visual verification with graphs are made by giving special values to the real numbers $a,$ $b$ and $c$ in the obtained results.
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