Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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On the computation of Infeld's function used in evaluating the admittance of prolate spheroidal dipole antennas


Authors: T. Do-Nhat and R. H. MacPhie
Journal: Quart. Appl. Math. 54 (1996), 721-725
MSC: Primary 78A50; Secondary 33C90
DOI: https://doi.org/10.1090/qam/1417235
MathSciNet review: MR1417235
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Abstract: The Infeld function expressed in terms of the outgoing prolate spheroidal radial wave function and its derivative, and employed in the expression of the input self-admittance of prolate spheroidal antennas, has accurately been calculated by using a newly developed asymptotic expression for large degree $ n$. This asymptotic power series has been derived by using a perturbation method with a perturbation parameter $ \epsilon = 1/\left( {\lambda _{1n}} - {h^2} \right)$, where $ {\lambda _{1n}}$ is the spheroid's eigenvalue for the given parameter $ h$ of the spheroidal wave function.


References [Enhancements On Off] (What's this?)

  • [1] L. Infeld, The influence of the width of the gap upon the theory of antennas, Quart. Appl. Math. 5, 113-132 (1947)
  • [2] J. D. Kotulski, Transient radiation from antennas: Early time response of the spherical antenna and the late time response of the prolate spheroidal impedance antenna, Univ. of Illinois at Chicago, Illinois, Ph. D. Dissertation, 1983
  • [3] T. Do-Nhat and R. H. MacPhie, The input admittance of thin prolate spheroidal dipole antennas with finite gap widths, IEEE Trans. AP-43, 1995, pp. 1243-1252
  • [4] C. Flammer, Spheroidal Wave Functions, Stanford University Press, Stanford, Calif., 1957
  • [5] B. P. Sinha and R. H. MacPhie, On the computation of the prolate spheroidal radial functions of the second kind, J. Math. Phys. 16, 2378-2381 (1975)
  • [6] T. Do-Nhat and R. H. MacPhie, On the accurate computation of the prolate spheroidal radial functions of the second kind, Quart. Appl. Math. 54, 677-685 (1996)
  • [7] J. Kevorkian and J. D. Cole, Perturbation Methods in Applied Mathematics, Springer-Verlag, New York, 1980

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Additional Information

DOI: https://doi.org/10.1090/qam/1417235
Article copyright: © Copyright 1996 American Mathematical Society


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