On the L̅3 numbers and their application in the theory of waveguides

An extension of the theory of the L̅_3±(c,ε̅,ρ,α_±,n) numbers (c = 3, ε̅ = 1, ρ and α_± - real, 0<;ρ<;1, -1<;α_-<;0, 0<;α₊<;1 and n = 1,2,3...) - the attained under definite conditions real positive limits of certain sequences of real positive numbers, pieced together through the positive purely imaginary zeros of a given complex special function, composed of two complex Kummer confluent hypergeometric and eight real cylindrical ones of suitably chosen parameters and variables, is presented. Based on the recently developed procedure for the computational modeling of quantities considered, detailed tables of their values are compiled for ρ = 0.1, 0.2 and 0.3, n = 1 and |α| = 0.01 (0.01) 0.99. In addition, the dependence of L̅_3±(c,ε̅,ρ,α_±,n) on |a| for ρ = 0.1 (0.1) 0.5 and n = 1 is depicted in a graphical form. The influence of parameters on the numbers in question is examined. The application of the same in the analysis of the normal TE_0n modes propagation in the circular ferrite waveguide, containing an azimuthally magnetized ferrite cylinder and a dielectric toroid, on the understanding that the permittivities of the two media are identical, is discussed.