Expansion of the Green’s function in a cylindrical coordinate system
Wan-xian Wang
Source abstract
The expansions of the Green’s function e i k | r − r ′ | / | r − r ′ | {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 {J_{ - 1/2}} and J 1 / 2 {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.
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