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 . This asymptotic power series has been derived by using a perturbation method with a perturbation parameter , where is the spheroid's eigenvalue for the given parameter of the spheroidal wave function.

**[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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DOI:
https://doi.org/10.1090/qam/1417235

Article copyright:
© Copyright 1996
American Mathematical Society