rather than interpolating off the grid onto the cylinder, we have also verified that the error due to interpolation onto the cylinder is comparable to that produced by nu- merical integration[4]. Finally, all these small errors can be further reduced with the aid of a finer grid [3, 4]. – 10 – 5 5 10 z – 0.30 – 0.25 – 0.20 – 0.15 – 0.10 – 0.05 C (z) 1,s [0] - 10 - 5 0 5 10 z 0.0001 0.0002 0.0003 0.0004 0.0005 C$_{7,}$$_{s}$ @ 0 D  4.5e-05 z Error in numerical results for C (z) 1,s [0] 5.3 x 10 -5 5.4 x 10 -5 $_{ 5.5 }$x 10 -5 5.6 x 10 -5 $_{ 5.2 }$x 10 -5 $_{ 5.1 }$x 10 -5 $_{ 5.0 }$x 10 -5 $_{ 4.9 }$x 10 -5 $_{ 4.8 }$x 10 -5 4.7 x 10 -5 4.6 x 10 -5 -10 -5 0 5 1 4.5 x 10 -5 – 4 – 2 2 4 z – 1.0 – 0.5 0.5 1.0 1.5 2.0 C (z) 1,s [6] FIG. 14: Difference between exact and numerical results for C [0] 1 $_{,s}$( z ). FIG. 12: Exact and numerical results for C [6] 1 $_{,s}$( z ). Exact results are shown as a solid line, and numerical results are shown as dots. FIG. 11: Exact and numerical results for C [0] 1 $_{,s}$( z ). Exact results are shown as a solid line, and numerical results are shown as dots. FIG. 13: Exact and numerical results for C [0] 7 $_{,s}$( z ). Exact results are shown as a solid line, and numerical results are shown as dots. 12 C. Elliptical Cylinder Results angular points for each of the 4801 selected values of z . The sums in (55) are truncated beyond r = r$_{max}$ , where r$_{max}$ varies from 11 to 29 as necessary to achieve a toler- ance of 1 part in 10 $^{4}$. We evaluate the Fourier transform at 401 values of k in the range [ − K$_{c}$,K$_{c}$ ] with K$_{c}$ = 20, using a spline-based Fourier transform algorithm. We use these same points in k space to evaluate the inverse Fourier transform, providing a set of numerically deter- mined functions C [ n ] $_{m,α}$( z ). Results for the functions C [ n ] $_{m,α}$( z ) are similar to those found in the circular cylinder case [3, 4], and have com- parable accuracy. In the following section, however, we illustrate that functions obtained using an elliptical cylin- der are significantly more robust against numerical noise in the original grid values. The procedure discussed in Section III B has been benchmarked using grid values identitical to those de- scribed in the previous section. Consider an elliptical cylinder of semiminor axis of y$_{max}$ = 2 cm and semima- jor axis x$_{max}$ = 4 cm. In this case, we evaluate the an- gular integrals (49) using a Riemann sum with N = 120. (This is necessary to ensure sufficient convergence of the angular integrals to within 10 − $^{4}$.) Doing so requires in- terpolation off the grid onto the elliptical cylinder at 120