Inclusion of Bessel functions in a subclass of spiral functions

In this article, we derived conditions on the order $ \nu $ of the classical Bessel functions $ J_{\nu} $ that guarantee the inclusion of three distinct normalized forms of $ J_{\nu} $ in a subclass of $ \alpha $-spirallike functions. The primary goal was to determine the subintervals within $ (-\frac{\pi}{2}, \frac{\pi}{2}) $ where these inclusion conditions are satisfied. A key component in establishing our results was the upper bound of the ratio $ J_{\nu+1}(1)/J_{\nu}(1) $. The theoretical findings were validated through numerical experiments and accompanying graphical demonstrations.