The radius of starlikeness of normalized Bessel functions of the first kind

Baricz, Árpád; Kupán, Pál; Szász, Róbert

doi:10.1090/S0002-9939-2014-11902-2

The radius of starlikeness of normalized Bessel functions of the first kind
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by Árpád Baricz, Pál Aurel Kupán and Róbert Szász PDF

Proc. Amer. Math. Soc. 142 (2014), 2019-2025 Request permission

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, 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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