TELECOMMUNICATIONS AND RADIO ENGINEERING - 2012 Vol. 71,
No 2 		 

 

 

 

SOME FURTHER RESULTS FOR COMPUTATION OF THE UNIFORM FOCK FUNCTIONS



S.-E. Sandstrom
Department of Computer Science, Physics and Mathematics,
Linnaeus University, S-351 95, V?axj?o, Sweden
E-mail: sven-erik.sandstrom@lnu.se

Abstract
The Fock functions are used in diffraction theory to describe the surface current on perfectly conducting convex scatterers. They are fairly accurate near the shadow boundary. A uniform counterpart to these functions can be obtained for cylindrical geometry. This communication presents some additional results for efficient numerical evaluation of these functions in the lit zone.
KEY WORDS: the Fock function, integral representation, asymptotic expansion, interpolation

References

  1. Bowman, J.J., Senior, T.B.A., and Uslenghi, P.L.E., (1987), Electromagnetic and Acoustic Scattering by Simple Shapes.  New York: Hemisphere Publishing.
  2. Fock, V.A., (1946), The distribution of currents induced by a plane wave on the surface of a conductor, J. Phys. (USSR), 10:130–136.
  3. Vyunnik V.I. and Zvyagintsev, A.A., (2009), Asymptotic methods on the solution of diffraction problems on the convex impedance cylinders, International conference on antenna theory and techniques, 6-9 October, Lviv, Ukraine, pp. 74–75.
  4. Sandstrom, S.-E., (2012), An extension of the Fock current distribution functions, Int. J. Electron. Commun. (AEU?), in press.
  5. Olver, F.W.J., (1997), Asymptotics and Special Functions. Natick: A.K. Peters.
  6. Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P., (1992), Numerical recipes in Fortran. Cambridge: Cambridge University Press.
  7. Goriainov, A.S., (1958), An asymptotic solution of the problem of diffraction of a plane electromagnetic wave by a conducting cylinder, Radio Eng. Electron. (USSR), 3:23–39.
  8. Sandstrom, S.-E., (2008), A remark on the computation of Fock functions for negative arguments, Int. J. Electron. Commun. (AEU?), 62:324–326.
  9. Pearson, L.W., (1987), A scheme for automatic computation of Fock-type integrals, IEEE AP, 35:1111–1118.
  10. Sandstrom, S.-E. and Ackr?en, C., (2007), Note on the complex zeros of ,
     J. Comput. Appl. Math., 201:3–7.
  11. Landau, L.J., (2000), Bessel functions: monotonicity and bounds, J. London Math. Soc., 61:197–215.
  12. Apelblat, A. and Kravitsky, N., (1985), Integral representation of derivatives and integrals with respect to the order of the Bessel functions , the Anger function  and the integral Bessel funtcion , IMA J. Appl. Math., 34:187–210.
  13. Brychkov Yu.A. and Geddes, K.O., (2005), On the derivatives of the Bessel and Struve functions with respect to order, INTEGR TRANSF SPEC F, 16:187–198.
  14. Ancarani L.U. and Gasaneo, G., (2008), Derivatives of any order of the confluent hypergeometric function  with respect to the parameter a or b, J. Math. Phys., 49:063508.
  15. Melrose R.B. and Taylor, M.E., (1985), Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle, Adv. Math., 55:242–315.


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