Approximate analytic continuation of the Rayleigh series (radar cross-section)

Pade approximants are used to continue approximately the Rayleigh series for the radar cross section (RCS) of the sphere beyond its radius of convergence. Numerical studies show that accurate results for the RCS can be obtained to ka approximately 2.2 if many series terms are available. Since this is rarely, if ever, the case, it is further demonstrated that even with only four nonzero terms available the technique is accurate to ka approximately 1.1. This provides an indication of the number of series coefficients that must be calculated to use the Rayleigh series in the lower part of the resonance regime. An additional point that is demonstrated is the ability of the technique to provide highly accurate estimates of the radius of convergence of the series. A useful byproduct is the generation of an approximation for the scattering of the sphere, valid for all real values of ka, which has a maximum error of less than 3%.<
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