Close-to-convexity of normalized Dini functions
\'Arpad Baricz, Erhan Deniz, Nihat Yagmur
TL;DR
This paper establishes necessary and sufficient conditions for the close-to-convexity of certain combinations of Bessel functions and their derivatives, using advanced complex analysis techniques and new Mittag-Leffler expansions.
Contribution
It introduces new criteria for close-to-convexity of Bessel function combinations, expanding understanding of their geometric properties in complex analysis.
Findings
Derived conditions for close-to-convexity of Bessel function combinations
Utilized a result of Shah and Trimble on transcendental entire functions
Discovered new Mittag-Leffler expansions for Bessel functions
Abstract
In this paper necessary and sufficient conditions are deduced for the close-to-convexity of some special combinations of Bessel functions of the first kind and their derivatives by using a result of Shah and Trimble about transcendental entire functions with univalent derivatives and some newly discovered Mittag-Leffler expansions for Bessel functions of the first kind.
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