Bounds for radii of starlikeness of some $q$-Bessel functions

Abstract

In this paper the radii of starlikeness of the Jackson and Hahn-Exton $q$-Bessel functions are considered and for each of them three different normalization are applied. By applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre-Pólya class of real entire functions plays an important role in this study. In particular, we obtain some new bounds for the first positive zero of the derivative of the classical Bessel function of the first kind.

10 pages

References in corpus (7)

• The radius of convexity of normalized Bessel functions of the first kind
• Radii of starlikeness of some special functions
• Radii of starlikeness and convexity of some $q$-Bessel functions
• Radii of convexity of some Lommel and Struve functions
• Close-to-convexity of some special functions and their derivatives
• Zeros of Bessel function derivatives
• Radii of starlikeness and convexity of regular Coulomb wave functions

Cited by in corpus (4)

• Bounds for radii of convexity of some $q$-Bessel functions
• Radii of Starlikeness and Convexity of Bessel Functions
• Asymptotic expansions for the radii of starlikeness of normalised Bessel functions
• Geometric and monotonic properties of hyper-Bessel functions