Theory of the L̿3 numbers: Definition, computational modeling, properties and application

The definition, computational modeling, some properties and an example for the putting into practice (the main points of the theory) of the L_3± (c, ε, ρ, α_±, n) numbers (c, ε, ρ and α_±β - real, c = 3, ε > 1, 0 <; ρ <; 1, -1 <; α_- <; 0, 0 <; α₊ <; 1 and n = 1,2,3...) - the real positive limits of special sequences of real numbers, devised by the positive purely imaginary zeros of a complex transcendental function, composed of two complex Kummer confluent hypergeometric and eight real cylindrical ones of suitably selected parameters and variables, are put up. The existence of numbers (of limits attained when the imaginary part of the complex first parameters of confluent functions tends to plus and minus infinity, resp.) is grounded numerically and illustrated graphically. A table of certain of their values is compiled. The application of quantities L_3± in the study of normal TE_0n modes in the circular waveguide, comprising an azimuthally magnetized ferrite cylinder and a dielectric toroid, in case the permittivity of the second is twice larger than that of the first one, is debated.