Zeros of Bessel function derivatives
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- by Árpád Baricz, Chrysi G. Kokologiannaki and Tibor K. Pogány PDF
- Proc. Amer. Math. Soc. 146 (2018), 209-222 Request permission
Abstract:
We prove that for $\nu >n-1$ all zeros of the $n$th derivative of the Bessel function of the first kind $J_{\nu }$ are real. Moreover, we show that the positive zeros of the $n$th and $(n+1)$th derivative of the Bessel function of the first kind $J_{\nu }$ are interlacing when $\nu \geq n$ and $n$ is a natural number or zero. Our methods include the Weierstrassian representation of the $n$th derivative, properties of the Laguerre-Pólya class of entire functions, and the Laguerre inequalities. Some similar results for the zeros of the first and second derivatives of the Struve function of the first kind $\mathbf {H}_{\nu }$ are also proved. The main results obtained in this paper generalize and complement some classical results on the zeros of Bessel and Struve functions of the first kind. Some open problems related to Hurwitz’s theorem on the zeros of Bessel functions are also proposed.References
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Additional Information
- Árpád Baricz
- Affiliation: Department of Economics, Babeş-Bolyai University, 400591 Cluj-Napoca, Romania; Institute of Applied Mathematics, Óbuda University, 1034 Budapest, Hungary
- MR Author ID: 729952
- Email: bariczocsi@yahoo.com
- Chrysi G. Kokologiannaki
- Affiliation: Department of Mathematics, University of Patras, 26500 Patras, Greece
- Email: chrykok@math.upatras.gr
- Tibor K. Pogány
- Affiliation: Faculty of Maritime Studies, University of Rijeka, 51000 Rijeka, Croatia; Institute of Applied Mathematics, Óbuda University, 1034 Budapest, Hungary
- Email: poganj@pfri.hr
- Received by editor(s): December 13, 2016
- Received by editor(s) in revised form: January 31, 2017, and February 16, 2017
- Published electronically: August 1, 2017
- Communicated by: Mourad E. H. Ismail
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 209-222
- MSC (2010): Primary 33C10, 30D15
- DOI: https://doi.org/10.1090/proc/13725
- MathSciNet review: 3723134