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Zbl 0588.65016
Kerimov, M.K.; Skorokhodov, S.L.
Evaluation of complex zeros of Bessel function of second kind and its derivatives. (Russian)
[J] Zh. Vychisl. Mat. Mat. Fiz. 25, No.10, 1457-1473 (1985). ISSN 0044-4669

The authors compute the complex zeros of the function $Y\sb{\nu}(z)$ with real positive $\nu$. First they study the location of complex zeros, using asymptotic formulas for the equations such as $J\sb{\nu}(z)=H\sb{\nu}\sp{(1)}(z)$. They they use Newton's iteration, and give tables of five complex zeros of $Y\sb{\nu}(z)$ $(\nu =0,1,...,5)$ and $Y'\sb{\nu}(z)$ $(\nu =1,...,5)$, which have largest real parts.
[S.Hitotumatu]

MSC 2000:: *65D20 Computation of special functions
33C10 Cylinder functions, etc.

Keywords: Bessel function of second kind; complex zeros; asymptotic formulas; Newton's iteration

Cited in: Zbl 0598.65007

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