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

The theory of the L numbers - the positive real limits of certain sequences of numbers, constructed through the positive purely imaginary zeros of the complex Kummer or of definite special functions, composed of several complex Kummer and Tricomi confluent hypergeometric and eventually also of some real cylindrical ones of suitably chosen parameters, is formulated. The limits are attained, when the imaginary part of the complex first parameter(s) of the confluent function(s) tends to minus infinity (to minus and plus infinity, if cylindrical functions are involved). The discussion is confined to the subclasses L
₁
(c,n) and L
₂
(c,ρ,n) , (c - arbitrary real, n - natural and ρ - positive real number, less than unity) of the general family of L numbers, linked with the zeros of the Kummer function and of a function, formed as a combination of two Kummer and two Tricomi ones, resp. Definitions of the numbers are given, procedures for their computational modeling are devised and some of their properties are found. The cases c - different from and c - equal to a negative integer or zero (when the Kummer function has no sense), are considered. Tables of values of L
₁
(c,n) and L
₂
(c,ρ,n) are compiled. Graphs illustrate the numerical results. The application of quantities examined in the analysis of the normal TE
_0n
modes propagation in the azimuthally magnetized circular and coaxial ferrite waveguide, is debated.