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Zeros of some special entire functions

Authors: Árpád Baricz and Sanjeev Singh
Journal: Proc. Amer. Math. Soc. 146 (2018), 2207-2216
MSC (2010): Primary 30D15, 30A08, 33C10, 33C20
Published electronically: January 12, 2018
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Abstract: The real and complex zeros of some special entire functions such as Wright, hyper-Bessel, and a special case of generalized hypergeometric functions are studied by using some classical results of Laguerre, Obreschkhoff, Pólya, and Runckel. The obtained results extend the known theorem of Hurwitz on the exact number of nonreal zeros of Bessel functions of the first kind. Moreover, results on zeros of derivatives of Bessel functions and the cross-product of Bessel functions are also given, which are related to some recent open problems.

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Additional Information

Árpád Baricz
Affiliation: Department of Economics, Babeş-Bolyai University, Cluj-Napoca, Romania; Institute of Applied Mathematics, Óbuda University, Budapest, Hungary

Sanjeev Singh
Affiliation: Indian Statistical Institute, Chennai Centre, Chennai, India
Address at time of publication: Discipline of Mathematics, Indian Institute of Technology Indore, Indore, India

Keywords: Entire function, Laguerre--P\'olya class of entire functions, zeros of entire functions, Bessel, Wright, hyper-Bessel functions, reciprocal gamma function, generalized hypergeometric function.
Received by editor(s): February 14, 2017
Received by editor(s) in revised form: July 31, 2017, and August 15, 2017
Published electronically: January 12, 2018
Additional Notes: The research of Á. Baricz was supported by the STAR-UBB Advanced Fellowship-Intern of the Babeş-Bolyai University of Cluj-Napoca.
Communicated by: Yuan Xu
Article copyright: © Copyright 2018 American Mathematical Society

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