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Evaluation of complex zeros of the modified Bessel function of the second kind and its derivatives. (Russian) Zbl 0568.65011
The authors consider the problem of computing the zeros of the modified Bessel function of the second kind ${K}_{\nu }\left(z\right)$ 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 ${K}_{\nu }\left(z\right)$ and ${K}_{\nu }^{\text{'}}\left(z\right)$ are given, too.

##### MSC:
 65D20 Computation of special functions, construction of tables 65A05 Tables (numerical analysis) 33-04 Machine computation, programs (special functions) 33C10 Bessel and Airy functions, cylinder functions, ${}_{0}{F}_{1}$