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


Authors: Árpád Baricz, Pál Aurel Kupán and Róbert Szász
Journal: Proc. Amer. Math. Soc. 142 (2014), 2019-2025
MSC (2010): Primary 30C45, 33C10
DOI: https://doi.org/10.1090/S0002-9939-2014-11902-2
Published electronically: February 17, 2014
MathSciNet review: 3182021
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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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Additional Information

Árpád Baricz
Address at time of publication: Department of Economics, Babeş-Bolyai University, Cluj-Napoca 400591, Romania
Email: bariczocsi@yahoo.com

Pál Aurel Kupán
Affiliation: Department of Mathematics and Informatics, Sapientia Hungarian University of Transylvania, Târgu Mureş 540485, Romania
Email: kupanp@ms.sapientia.ro

Róbert Szász
Affiliation: Department of Mathematics and Informatics, Sapientia Hungarian University of Transylvania, Târgu Mureş 540485, Romania
Email: rszasz@ms.sapientia.ro

DOI: https://doi.org/10.1090/S0002-9939-2014-11902-2
Keywords: Bessel and modified Bessel functions of the first kind, univalent, starlike and convex functions, radius of starlikeness
Received by editor(s): February 6, 2012
Received by editor(s) in revised form: June 18, 2012
Published electronically: February 17, 2014
Communicated by: Sergei K. Suslov
Article copyright: © Copyright 2014 American Mathematical Society

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