TELECOMMUNICATIONS AND RADIO ENGINEERING - 2012 Vol. 71,
No 3 		 

 

 

 

ON THE CONFLUENT HYPERGEOMETRIC FUNCTIONS AND THEIR APPLICATION: BASIC ELEMENTS OF THE TRICOMI THEORY. CASE OF WAVEGUIDE PROPAGATION



G.N. Georgiev1 & M.N. Georgieva–Grosse2
1 Faculty of Mathematics and Informatics,
University of Veliko Tirnovo “St. St. Cyril and Methodius”,
BG–5000 Veliko Tirnovo, Bulgaria,
2 2, Tcherny vrikh Str., BG–5138 Polikraishte, Bulgaria
Address all correspondence to G.N. Georgiev E-mail: afis@ire.kharkov.ua

Abstract
The distinguishing features of the Tricomi theory of confluent hypergeometric functions (the theory of the Kummer and Tricomi ones) are specified. A numerical study of the latter is performed in the complex plane for selected values of their parameters. The results are depicted in a graphical form. The computation of the differential phase shift, provided by the circular waveguide, containing an azimuthally magnetized remanent ferrite toroid and a dielectric cylinder for the normal TE01 mode, is presented as an example of the employment of the functions in question.
KEY WORDS: boundary value problems, circular waveguides, confluent hypergeometric functions, nonreciprocal wave propagation, numerical analysis

References

  1. Whittaker, E.T. and Watson, G.N., (1965), A Course of Modern Analysis, Cambridge, UK: Cambridge Univ. Press.
  2. Buchholz, H., (1953) Die Konfluente Hypergeometrische Funktion mit Besonderer Berucksichtigung Ihrer Anwendungen, Berlin, Gottingen, Heidelberg, Germany: Springer-Verlag.
  3. Erdelyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F.G., (1953) Higher Transcendental Functions, Bateman project. Vol. I, New York, Toronto, London: McGraw-Hill.
  4. Tricomi, F.G., (1954), Funzioni Ipergeometriche Confluenti, Rome, Italy, Edizioni Cremonese.
  5. Tricomi, F.G., (1960), Fonctions Hypergeometriques Confluentes, Paris, France: Gauthier-Villars.
  6. Georgiev, G.N. and Georgieva-Grosse, M.N., (2003), A new property of the complex Kummer function and its application to waveguide propagation, IEEE Antennas Wireless Propagat. Lett., 2:306-309.
  7. Georgiev, G.N. and Georgieva-Grosse, M.N., (2009), An application of the complex Tricomi function, Proc. Eleventh Int. Conf. Electromagn. Adv. Applicat. ICEAA’09, Turin, Italy, pp. 819-822, in CDROM.
  8. Georgiev, G.N. and Georgieva-Grosse, M.N., (2009), Effect of the dielectric filling on the phase behaviour of the circular waveguide with azimuthally magnetized ferrite toroid and dielectric cylinder, Proc. Asia-Pacific Microwave Conf. APMC-2009, Singapore, pp. 870-873, in CDROM.
  9. Georgiev, G.N. and Georgieva-Grosse, M.N., (2010), Iterative method for differential phase shift computation in the azimuthally magnetized circular ferrite waveguide, Proc. 27th Progr. in Electromagn. Res. Symp. PIERS 2010,Xi’an, China, p. 186, pp. 274-278; (2010) PIERS Online, 6(4):365-369.
  10. Georgieva-Grosse, M.N and Georgiev, G.N., (2010), Advanced studies of the differential phase shift in the azimuthally magnetized circular ferrite waveguide, Proc. 28th Progr. in Electromagn. Res. Symp. PIERS 2010, Cambridge, MA, USA, p. 505, in Abstracts, pp. 841-845.
  11. Georgiev, G.N. and Georgieva-Grosse, M.N., (2010), Analysis of the differential phase shift in the circular ferrite-dielectric waveguide with azimuthal magnetization, Proc. 2010 IEEE Int. Symp. Antennas Propagat. & CNC-USNC/URSI Radio Science Meeting AP-S 2010, Toronto, ON, Canada,
    p. 330.9, in CDROM.
  12. Georgiev, G.N. and Georgieva-Grosse, M.N., (2010), The Tricomi theory of confluent hypergeometric functions and its application to waveguide propagation, Proc. Radar Methods and Systems Worksh. RMSW-2010, Kiev, Ukraine, pp. 250-254.
  13. Georgieva-Grosse, M.N and Georgiev, G.N., (2011), Area of phase shifter operation of the azimuthally magnetized coaxial ferrite waveguide, Proc. 29th Progr. In Electromagn. Res. Symp. PIERS 2010, Marrakesh, Morocco, p. 830, in Abstracts, pp. 1318-1322.
  14. Georgiev, G.N. and Georgieva-Grosse, M.N., (2011), Numerical study of the differential phase shift in a circular ferrite-dielectric waveguide, Proc. 5th Europ. Conf. Antennas Propagat. EuCAP 2011, Rome, Italy, pp. 1666-1670.
  15. Georgieva-Grosse, M.N and Georgiev, G.N., (2011), On the class of  numbers: Definition, numerical modeling, domain of existence and application, Proc. XXX URSI General Assembly, Istanbul, Turkey, article ID BP1.47, 4 pages, in CDROM.
  16. Georgieva-Grosse, M.N and Georgiev, G.N., (2011), Transmission properties of the circular waveguide completely or partially filled with azimuthally magnetized ferrite: Review of recent results, Proc. 1st IEEE-APS Topical Conf. Antennas Propagat. Wireless Commun. IEEE APWC’11, Turin, Italy, pp. 865-868.


pages 209-216

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