Baricz, Á., Kokologiannaki, C. & Pogány, T. (2018) Proceedings of the American Mathematical Society [Matematică, Q2]

Publicat: 24 Noiembrie 2020

Baricz, Á., Kokologiannaki, C. & Pogány, T. (2018) Zeros of Bessel function derivatives. Proceedings of the American Mathematical Society, 146(1), 209-222.

DOI: https://doi.org/10.1090/proc/13725

✓ Publisher: American Mathematical Society
✓ Web of Science Core Collection: Science Citation Index Expanded
✓ Categories: Mathematics, Applied; Mathematics
✓ Article Influence Score (AIS): 0.830 (2018) / Q2 in all categories

Abstract: We prove that for nu > n - 1 all zeros of the nth derivative of the Bessel function of the first kind J(nu) are real. Moreover, we show that the positive zeros of the nth and (n + 1) th derivative of the Bessel function of the first kind J(nu) are interlacing when nu >= n and n is a natural number or zero. Our methods include the Weierstrassian representation of the nth derivative, properties of the Laguerre-Polya 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 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.

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