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 ${e^{ik\left | {r - r’} \right |}}/\left | {r - r’} \right |$ 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.
- John David Jackson, Classical electrodynamics, 2nd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1975. MR 0436782
T. S. M. Maclean, Principles of Antennas: Wire and Aperture, Cambridge University Press, 1986
- Carson Flammer, Spheroidal wave functions, Stanford University Press, Stanford, California, 1957. MR 0089520
- 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
J. D. Jackson, Classical Electrodynamics, John Wiley and Sons, New York, 1962
T. S. M. Maclean, Principles of Antennas: Wire and Aperture, Cambridge University Press, 1986
C. Flammer, Spheroidal Wave Functions, Stanford University Press, 1957
G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, 1962
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Article copyright:
© Copyright 1990
American Mathematical Society
