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.
- Bessel functions of the first kind
- close-to-convex functions
- infinite product
- starlike functions
- transcendental entire functions
- zeros of Bessel functions
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