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On the computation of complex zeros of the modified Bessel function of the second kind. (English) Zbl 0594.34014
The author develops a high accuracy algorithm for computing the complex zeros of the modified Bessel function of the second kind K ν (z) and its derivatives with respect to z in the case of real or complex values of ν. He states that the implementation of the algorithm has proved its high efficiency. It is shown that all he first zeros of the function K ν+2p (z), p=0,1,···, as p, lie on a straight line parallel to the real axis, and the distance between two adjacent zeros tends to a constant. All the second, third,... zeros have the same asymptotic property. The author constructs a table of all the complex zeros with nine significant figures of the function K ν (z) for ν=2(1)20, and of the function K ν ' (z) for 1/2ν20. To determine the distribution of zeros of the derivatives of higher order, the loci of the zeros were constructed.
Reviewer: M.Shahin
MSC:
34A40Differential inequalities (ODE)
65D20Computation of special functions, construction of tables