Contribution to the theory of the complex Kummer function

A numerical investigation of the zeros κ_z,n^(c) in the imaginary part k of the complex first parameter a = c / 2 - jk, ( c - positive integer) of the complex Kummer confluent hypergeometric function Φ(a, c; x) of positive purely imaginary variable x = jz, assumed as a discrete parameter, is performed for the first time. The results are presented both in a tabular and graphical form. A juxtaposition of the values of κ_z,n^(c) is made with the ones of the positive purely imaginary zeros ξ_k,n^(c) of Φ(a, c; x) in z, accepting k as parameter. An ingenious method for computation of the phase characteristics of the circular ferrite waveguide with azimuthal magnetization, propagating normal TE_0n modes is developed, employing the zeros found out. The study constitutes an original contribution to the general theory of the complex Kummer function, as well as to the theory of anisotropic waveguides.