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Calculation of modified Bessel functions in the complex domain. (English) Zbl 0568.65010
Algorithms for the computation of the values of the modified Bessel functions of the first and second kind ${I}_{\nu }\left(z\right)$ and ${K}_{\nu }\left(z\right)$ for complex values of $\nu$ and $z$ are given. The algorithm for the computation of the Bessel function ${I}_{\nu }\left(z\right)$ is based on the so-called Miller-Olver algorithm, and the algorithm for the computation of ${K}_{\nu }\left(z\right)$ on the algorithm by N. M. Temme [J. Comput. Phys. 19, 324–337 (1975; Zbl 0334.65013)]. The authors consider also a program realization of the algorithms. The results of numerical experiments are given and discussed.

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