On zeros of the modified Bessel function of the second kind

Zeros of the modified Bessel function of the second kind (Macdonald function) ${{K}_{\nu }}\left(z\right)$ considered as a function of the index $\nu$ are studied. It is proved that, for fixed $z, z >0$, the function ${{K}_{\nu }}\left(z\right)$ has a countable number of simple purely imaginary zeros ${\nu }_{n}$. The asymptotics of the zeros ${{\nu }_{n}}$ as $n \to+\infty$ is found.