paper 150304075406

Abstract

The theorem for existence of the G1 (c, n) numbers (finite real positive numbers, (c) coherent with the zeros κz, n in the imaginary part κ of the complex first parameter a of the complex Kummer confluent hypergeometric function Φ(a, c; x) with a = c/2 + jκ — complex, c = 2Rea — restricted positive integer (c = 1, 2, 3, . . .), κ — real (positive, negative or zero, −∞ < κ < +∞), x = jz — positive purely imaginary, z — real, positive and n = 1, 2, 3, . . .) is formulated and proved numerically. It serves as a definition of quantities in question and determines them as the limit of the infinite sequence of real numbers {D1 (c, n, z)} (D1 (c, n, z) = (c) κz, n z) for z → 0. Supposedly this assumption holds, the theorem states that the sequence of (c) the zeros {κz, n } is divergent and its terms become infinitely large positive. Moreover, if z → +∞ (c) both {κz, n } and {D1 (c, n, z)} are divergent and tend to −∞. Tables and graphs illustrate the influence of parameters c and n on G1 (c, n). The benefit of numbers is manifested in the theory of azimuthally magnetized circular ferrite waveguides, propagating normal TE 0n modes.

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