Hypothesis for the Identity of the L_2(c,ρ,n) and (L)_2((c), (ρ), (n)) Numbers and Its Application in the Theory of Waveguides

摘要

A guess is made that if for the limited arbitrary real numbers c and c, for the less than unity real positive ones ρ and ρ, and for the natural n and the positive integer n it holds: c = c, ρ = ρ and n = n, then the real positive numbers L_2(c,p, n) and L_2(c, ρ, n), connected with the positive purely imaginary, resp. real zeros in x, resp. in x of a special function, devised by two complex Φ(a, c; x) and Φ(a, c; ρx), resp. real Φ(a, c; x) and Φ(a, c; ρx) Kummer, and two complex Ψ(a,c;x) and Ψ(a,c;ρx), resp. real Ψ(a,c;x) and Ψ(a,c;ρx) Tricomi confluent hypergeometric ones of suitably selected complex a and real c, resp. real a and c parameters and a positive purely imaginary x or ρx, resp. real x or ρx variable, coincide. This assumption, called Hypothesis for the identity of the L_2(c, ρ, n) and L_2(c, ρ, n) numbers, is substantiated numerically with a higher or lower accuracy, depending on the value of c (c). The curve of equation, written through any of the quantities L_2(c, ρ, n) or L_2(c, ρ, n) which separates the domains of propagation of the normal T E_(0n) and of the one of the two possible slow (TE_(0n)) modes - the (TE_(0n)~(1) wave (n = n) in the coaxial waveguide with ferrite, magnetized azimuthally in negative (clockwise) direction, is interpreted as a physical image of the result obtained in case c = c = 3, postulating ρ (ρ) as a relative thickness of the central conductor of the structure and n (n) as an order of the mode.