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

By 'Arp'ad Baricz, P'al A. Kup'an, R'obert Sz'asz. 2012

104 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/973f809f7e3eb2b8acf7f1b1b086e9635b64b196

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Bounds for radii of starlikeness and convexity of some special functions (2016, background): “But, the smallest positive zero of z 7→ (zg ν(z))′ is actually the radius of starlikeness of z 7→ zg ν(z), according to [7, 8].”
Close-to-Convexity of Some Special Functions and Their Derivatives (2014, background): “Some of these problems have been studied later in the papers [1, 2, 3, 5, 6, 8, 19, 20], however, there are still some open problems in this direction.”
The radius of convexity of normalized Bessel functions (2015, background): “The case α = 0 was proved already in [4].”