Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Expansion of the Green's function in a cylindrical coordinate system


Author: Wan-xian Wang
Journal: Quart. Appl. Math. 48 (1990), 499-501
MSC: Primary 34B27
DOI: https://doi.org/10.1090/qam/1074964
MathSciNet review: MR1074964
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Abstract: The expansions of the Green's function $ {e^{ik\left\vert {r - r'} \right\vert}}/\left\vert {r - r'} \right\vert$ in spherical and spheroidal coordinate systems were studied by some researchers; however, because of its complexity this kind of expansion has not been performed in a cylindrical coordinate system. With the aid of the expressions of the Bessel functions $ {J_{ - 1/2}}$ and $ {J_{1/2}}$ and of the transformation from these functions to the spherical Bessel functions, the author has analytically derived the expansion of the Green's function in the cylindrical coordinate system.


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

  • [1] J. D. Jackson, Classical Electrodynamics, John Wiley and Sons, New York, 1962 MR 0436782
  • [2] T. S. M. Maclean, Principles of Antennas: Wire and Aperture, Cambridge University Press, 1986
  • [3] C. Flammer, Spheroidal Wave Functions, Stanford University Press, 1957 MR 0089520
  • [4] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, 1962 MR 1349110

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DOI: https://doi.org/10.1090/qam/1074964
Article copyright: © Copyright 1990 American Mathematical Society

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