The radius of starlikeness of normalized Bessel functions of the first kind
\'Arp\'ad Baricz, P\'al A. Kup\'an, R\'obert Sz\'asz
TL;DR
This paper determines the radius of starlikeness for normalized Bessel functions of the first kind using Mittag-Leffler expansion and properties of Dini functions' zeros.
Contribution
It provides new results on the radius of starlikeness for three types of normalized Bessel functions, employing advanced analytical tools.
Findings
Calculated the radius of starlikeness for different normalizations
Utilized Mittag-Leffler expansion in the analysis
Established bounds based on zeros of Dini functions
Abstract
In this note our aim is to determine the radius of starlikeness of the normalized Bessel functions of the first kind for three different kinds of normalization. The key tool in the proof of our main result is the Mittag-Leffler expansion for Bessel functions of the first kind and the fact that, according to Ismail and Muldoon [IM2], the smallest positive zeros of some Dini functions are less than the first positive zero of the Bessel function of the first kind.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Mathematical functions and polynomials