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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 5, Pages 837–840 (Mi zvmmf11078)  

This article is cited in 1 scientific paper (total in 1 paper)

On zeros of the modified Bessel function of the second kind

S. M. Bagirovaa, A. Kh. Khanmamedovbc

a Ganja State University, AZ 2000 Ganja, Azerbaijan
b Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku
c Azerbaijan University, AZ 1007 Baku, Azerbaijan

Abstract: Zeros of the modified Bessel function of the second kind (Macdonald function) ${{K}_{\nu }}(z)$ considered as a function of the index $\nu$ are studied. It is proved that, for fixed $z, z >0$, the function ${{K}_{\nu }}(z)$ has a countable number of simple purely imaginary zeros ${\nu }_{n}$. The asymptotics of the zeros ${{\nu }_{n}}$ as $n \to+\infty$ is found.

Key words: Bessel functions, zeros of Bessel functions, Schrödinger equation, eigenvalues.

DOI: https://doi.org/10.31857/S004446692005004X


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:5, 817–820

Bibliographic databases:

UDC: 519.65
Received: 30.09.2019
Revised: 19.12.2019
Accepted:14.01.2020

Citation: S. M. Bagirova, A. Kh. Khanmamedov, “On zeros of the modified Bessel function of the second kind”, Zh. Vychisl. Mat. Mat. Fiz., 60:5 (2020), 837–840; Comput. Math. Math. Phys., 60:5 (2020), 817–820

Citation in format AMSBIB
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\paper On zeros of the modified Bessel function of the second kind
\jour Zh. Vychisl. Mat. Mat. Fiz.
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\vol 60
\issue 5
\pages 837--840
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\crossref{https://doi.org/10.31857/S004446692005004X}
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\jour Comput. Math. Math. Phys.
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\vol 60
\issue 5
\pages 817--820
\crossref{https://doi.org/10.1134/S0965542520050048}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yuri Krynytskyi, Andrij Rovenchak, “Asymptotic Estimation for Eigenvalues in the Exponential Potential and for Zeros of $K_{i\nu}(z)$ with Respect to Order”, SIGMA, 17 (2021), 057, 7 pp.  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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