Zeros of some special entire functions

Baricz, Árpád; Singh, Sanjeev

doi:10.1090/proc/13927

Zeros of some special entire functions
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by Árpád Baricz and Sanjeev Singh

Proc. Amer. Math. Soc. 146 (2018), 2207-2216

DOI: https://doi.org/10.1090/proc/13927

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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