Theory of the L numbers and its application to electromagnetism

Under definite conditions some infinite sequences of real positive numbers, constructed by means of the positive purely imaginary (real) roots of certain transcendental equations, involving complex (real) confluent hypergeometric functions of specially selected parameters and variable, and possibly real cylindrical ones, tend to finite real positive limits, termed as L numbers. The latter are object of a new field of knowledge - the theory of L numbers. The equations referred to in the complex (real) case describe the propagation of normal (slow) TE0n modes in the azimuthally magnetized circular ferrite or ferrite-dielectric waveguides. For the first set of fields the structures in question exhibit properties of microwave digital phase shifters (G. N. Georgiev and M. N. Georgieva-Grosse, Proc. AP-S URSI, Toronto, Canada, 2010, article ID 330.9; M. N. Georgieva-Grosse and G. N. Georgiev, Proc. ICEAA′12, Cape Town, South Africa, 2012, pp. 1129–1132; M. N. Georgieva-Grosse and G. N. Georgiev, Proc. EMTS, Hiroshima, Japan, 2013, pp. 763–766; G. N. Georgiev and M. N. Georgieva-Grosse, PIERS Proc., Stockholm, Sweden, 2013, pp. 940–945; G. N. Georgiev and M. N. Georgieva-Grosse, Proc. ICEAA′14, Palm Beach, Aruba, 2014, pp. 383–386; G. N. Georgiev and M. N. Georgieva-Grosse, Proc. XXXI URSI GASS, Beijing, China, 2014, paper ID B14.4).