Geometric and monotonic properties of hyper-Bessel functions

Abstract

Some geometric properties of a normalized hyper-Bessel functions are investigated. Especially we focus on the radii of starlikeness, convexity, and uniform convexity of hyper-Bessel functions and we show that the obtained radii satisfy some transcendental equations. In addition, we give some bounds for the first positive zero of normalized hyper-Bessel functions, Redheffer-type inequalities, and bounds for this function. In this study we take advantage of Euler-Rayleigh inequalities and Laguerre-Pólya class of real entire functions, intensively.

arXiv comment12 pages

References in corpus (7)

• The radius of convexity of normalized Bessel functions of the first kind
• Radii of starlikeness of some special functions
• Bounds for radii of starlikeness of some $q$-Bessel functions
• The radius of uniform convexity of Bessel functions
• Zeros of some special entire functions
• Bounds for radii of convexity of some $q$-Bessel functions
• Redheffer type bounds for Bessel and modified Bessel functions of the first kind