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Zbl 1132.33309
Ferreira, Erasmo M.; Sesma, Javier
Zeros of the Macdonald function of complex order. (English)
[J] J. Comput. Appl. Math. 211, No. 2, 223-231 (2008). ISSN 0377-0427

Summary: The $z$-zeros of the modified Bessel function of the third kind $K_{\nu }(z)$, also known as modified Hankel function or Macdonald function, are considered for arbitrary complex values of the order $\nu $. Approximate expressions for the zeros, applicable in the cases of very small or very large $|\nu |$, are given. The behaviour of the zeros for varying $|\nu |$ or arg$\nu $, obtained numerically, is illustrated by means of some graphics.

MSC 2000:: *33C10 Cylinder functions, etc.

Keywords: Macdonald function; modified Bessel function of the third kind; Hankel function; zeros

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