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Zbl 0568.65011
Kerimov, M.K.; Skorokhodov, S.L.
Evaluation of complex zeros of the modified Bessel function of the second kind and its derivatives. (Russian)
[J] Zh. Vychisl. Mat. Mat. Fiz. 24, No.8, 1150-1163 (1984). ISSN 0044-4669

The authors consider the problem of computing the zeros of the modified Bessel function of the second kind $K\sb{\nu}(z)$ and its derivatives (with respect to $z$), for real and complex values of $\nu$ and complex values of $z$. A new algorithm based on Newton's iterative method is proposed. A program realization of the algorithm is considered and the results of its application are discussed. Tables of zeros of the functions $K\sb{\nu}(z)$ and $K'\sb{\nu}(z)$ are given, too.
[Vasil A. Popov (Sofia)]

MSC 2000:: *65D20 Computation of special functions
65A05 Tables
33-04 Machine computation, programs (special functions)
33C10 Cylinder functions, etc.

Keywords: Newton's method; complex zeros; zeros of the modified Bessel function of the second kind

Cited in: Zbl 0582.65011

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