Opuscula Math. 39, no. 3 (2019), 361-382
https://doi.org/10.7494/OpMath.2019.39.3.361
Opuscula Mathematica
On the zeros of the Macdonald functions
Yuji Hamana
Hiroyuki Matsumoto
Tomoyuki Shirai
Abstract. We are concerned with the zeros of the Macdonald functions or the modified Bessel functions of the second kind with real index. By using the explicit expressions for the algebraic equations satisfied by the zeros, we describe the behavior of the zeros when the index moves. Results by numerical computations are also presented.
Keywords: zeros, Macdonald functions, Bessel functions.
Mathematics Subject Classification: 33C10, 30C15, 32A60, 33F05.
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- Yuji Hamana
https://orcid.org/0000-0002-9997-3114- Kumamoto University, Department of Mathematics, Kurokami 2-39-1, Kumamoto 860-8555, Japan
- Hiroyuki Matsumoto
- Aoyama Gakuin University, Department of Physics and Mathematics, Fuchinobe 5-10-1, Sagamihara 252-5258, Japan
- Tomoyuki Shirai
- https://orcid.org/0000-0001-6269-5387
- Kyushu University, Institute of Mathematics for Industry, Motooka 744, Fukuoka 819-0395, Japan
- Communicated by P.A. Cojuhari.
- Received: 2018-08-30.
- Revised: 2018-10-02.
- Accepted: 2018-10-04.
- Published online: 2019-02-23.
