An application of the complex Tricomi function

The logarithmic form of complex Tricomi function Psi (a, c; x), holding for c - a positive integer, is used in case a = c/2 - jk - complex, k - real, - infin < k < + infin, x = jz, z -real, positive, to develop a special iterative technique for exact computation of the differential phase shift provided by the circular waveguide with coaxially positioned dielectric cylinder and azimuthally magnetized latching ferrite toroid that sustains normal TE_0n modes. An original form of the structure´s characteristic equation, constructed by the function mentioned and its complex conjugate, and real Bessel functions, valid for equal values of the relative permittivities of the media, is harnessed for the purpose. A highlight of the method makes up the numerical study of Psi(a, c; x), the results of which are illustrated graphically. The effect of parameters of configuration on the differential phase shift for the TE₀₁ mode is explored, too.