Theory of the L3 numbers: Definition, computational modeling, properties and application

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 real positive limits of certain sequences of real positive numbers, devised through the positive purely imaginary zeros of a definite complex special function, composed of two complex Kummer confluent hypergeometric and eight real cylindrical ones of suitably chosen parameters and variables, is advanced. The same are attained, when the imaginary part of the complex first parameters of the confluent functions tends to plus and minus infinity, resp. The limiting process is illustrated both numerically and graphically. The definition of the numbers is given, the procedure for their computational modeling is worked out, a table of their values is compiled and some of their main characteristics are found out. The application of quantities examined in the analysis of the normal TE_0n modes propagation in the circular ferrite waveguide, loaded with an azimuthally magnetized ferrite cylinder and a dielectric toroid, provided the permittivities of the two media are identical, is debated.