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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• Hiroyuki Matsumoto
• Aoyama Gakuin University, Department of Physics and Mathematics, Fuchinobe 5-10-1, Sagamihara 252-5258, Japan
• Communicated by P.A. Cojuhari.
• Revised: 2018-10-02.
• Accepted: 2018-10-04.
• Published online: 2019-02-23.