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The L(c, n) numbers and their application in the theory of waveguides

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2 Author(s)
Georgiev, G.N. ; Fac. of Math. & Inf., Univ. of Veliko Tirnovo St. St. Cyril & Methodius, Veliko Tirnovo, Bulgaria ; Georgieva-Grosse, M.N.

The theorem for existence and for the basic properties of the L(c, n) numbers (positive real numbers, coherent with the positive purely imaginary zeros zetak, n (c) in x of the complex Kummer confluent hypergeometric function Phi(a, c; x) with a = c/2 - jk - complex, c - real, (c ne l, l = 0, -1, -2, -3,...), k - real, x = jz, z - real, positive and n = 1, 2, 3,...), is formulated and proved numerically. It is composed of three lemmas. Lemmas 1 and 2 demonstrate the existence of quantities and determine them in case c ne l and c = l (in which Phi(a, c; x) is not defined) as the common limits of the couples of infinite sequences of positive real numbers {K_(c, n, k)_)} and {M_(c, n, k_)}, (K_(c, n, k_) = |k_|zetak_, n (c), M_(c, n, k_) = |a_|zetak_, n (c) for k_ rarr -infin, and {L(l - epsiv, n)} and {L(l + epsiv, n + 1)}, (epsiv - infinitesimal positive real number) for epsiv rarr 0, resp. (The subscript ldquo-rdquo indicates quantities, corresponding to negative k.) Lemma 3 reveals the main features of the numbers (recurrence relation, formula for symmetry and bond of some of them with the Ludolphian number). Tables and graphs illustrate the influence of parameters c and n on L(c, n). The benefit of numbers is manifested in the theory of azimuthally magnetized circular ferrite waveguides, propagating normal TE0n modes.

Published in:

Days on Diffraction, 2008. DD '08. Proceedings of the International Conference

Date of Conference:

3-6 June 2008

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