NDLI: On the zeros of Kummer function: Basic properties and their application in the theory of the azimuthally magnetized circular ferrite waveguide

Content Provider	IEEE Xplore Digital Library
Author	Georgieva-Grosse, M.N. Georgiev, G.N.
Copyright Year	2013
Description	Author affiliation: Fac. of Math. & Inf., Univ. of Veliko Tirnovo St. St. Cyril & Methodius, Veliko Tirnovo, Bulgaria (Georgiev, G.N.)
Abstract	A numerical evaluation of the first several purely imaginary (real) zeros $ζ_{k,n}^{(c)}$ in x, resp. in z $(ζ̂_{k̂,n̂}^{(c)}$ in x̂) of the complex (real) Kummer confluent hypergeometric function Φ(a,c;x), [Φ(â,ĉ;x̂)] is performed, assuming a = c / 2 - jk, c = 1 and c = 3, x = jz, k, z - real, -∞ <; k <; +∞, z > 0 (â = ĉ/2 + k̂, ĉ=1 and ĉ = 3, k̂, x̂ - real, -∞ <; k̂ <; -ĉ / 2, x̂ > 0). The results of analysis are presented in a tabular form, depending on the imaginary part k of parameter a of Φ̂̂(a,c; x) [on the addition k̂ in parameter â of Φ̂(â,ĉ;x̂)]. Momentous characteristics of quantities studied, concerning the number n (n̂) of zeros of the complex (real) function, their specification and their behaviour in case k → -∞ (k̂→-∞), are established. Some related numbers, called $L_{1}(c,n)$ $[L̂_{1}(ĉ,n̂)]$ ones and their features, are also considered. The employment of zeros $ζ_{k,n}^{(c)}$ and $ζ̂_{k̂,n̂}^{(ĉ)},$ and of the derivative of them quantities $L_{1}(c,n)$ and $L̂_{1}(ĉ,n̂)$ in the theory of waveguides, is discussed, as well.
Starting Page	151
Ending Page	160
File Size	256709
Page Count	10
File Format	PDF
ISBN	9789660267657
ISSN	21653585
e-ISBN	9789660267664
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-09-23
Publisher Place	Ukraine
Access Restriction	Subscribed
Rights Holder	Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, NASU
Subject Keyword	Magnetic resonance imaging Ferrites Waveguide theory Three-dimensional displays Magnetic properties Physics Computers
Content Type	Text
Resource Type	Article

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