Geometric Properties of Functions Containing Derivatives of Bessel Functions

In this paper our aim is to find the radii of $\gamma$-Spirallike of order $\alpha$ and convex $\gamma$-Spirallike of order $\alpha$ for three different kinds of normalizations of the function $N_{\nu }(z)=a{z}^2{J}_{\nu }^{\mathrm{\prime }\mathrm{\prime }}(z)+bz{J}_{\nu }^{\mathrm{\prime }}(z)+c{J}_{\nu }(z),$ where $J_{\nu }(z)$ is the Bessel function of the first kind of order $\nu \mathrm{.}$ Moreover, the ${\mathcal{S}}^{\ast }\left(\phi \right)-$radii and $\mathcal{C}\left(\phi \right)-$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.