Radii of Starlikeness and Convexity of the Derivatives of Bessel Function

Abstract

We find the radii of starlikeness and convexity of the derivatives of Bessel function for three different kinds of normalization. The key tools in the proof of our main results are the Mittag-Leffler expansion for the nth derivative of the Bessel function and the properties of its real zeros. 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 nth derivative of the Bessel function. As the main results of our investigations, we can mention natural extensions of some known results for the classical Bessel functions of the first kind.