Starlikeness of Bessel functions and their derivatives
\'Arp\'ad Baricz, Murat \c{C}a\u{g}lar, Erhan Deniz
TL;DR
This paper establishes necessary and sufficient conditions for the starlikeness of Bessel functions of the first kind and their derivatives, using advanced complex analysis techniques and properties of zeros.
Contribution
It provides new criteria for starlikeness of Bessel functions and their derivatives, extending previous results with novel analytical methods.
Findings
Derived necessary and sufficient conditions for starlikeness
Connected starlikeness to zeros and derivatives of Bessel functions
Extended understanding of geometric properties of Bessel functions
Abstract
In this paper necessary and sufficient conditions are deduced for the starlikeness of Bessel functions of the first kind and their derivatives of the second and third order by using a result of Shah and Trimble about transcendental entire functions with univalent derivatives and some Mittag-Leffler expansions for the derivatives of Bessel functions of the first kind, as well as some results on the zeros of these functions.
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Taxonomy
TopicsAnalytic and geometric function theory · Mathematical functions and polynomials · Meromorphic and Entire Functions