Zeros of the Macdonald function of complex order

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