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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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] John David Jackson, Classical electrodynamics, 2nd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1975. MR 0436782
  • [2] T. S. M. Maclean, Principles of Antennas: Wire and Aperture, Cambridge University Press, 1986
  • [3] Carson Flammer, Spheroidal wave functions, Stanford University Press, Stanford, California, 1957. MR 0089520
  • [4] G. N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR 1349110

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 34B27

Retrieve articles in all journals with MSC: 34B27


Additional Information

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


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website