EVIDENCE THAT BEARS ON THE LEFT HALF PLANE ASYMPTOTIC BEHAVIOR OF THE SEM EXPANSION OF SURFACE CURRENTS

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Abstract
The issues which have persisted in connection with the so-called “entire function contribution” and in connection with alternative coupling coefficient form interrelate closely with the larges asymptotic behavior in the left half plane in SEM representations. To date, no generally applicable rigorous information has been gleaned about this asymptotic behavior. On the other hand, the specific scattering geometries of the sphere and the wire loop yield analytic solutions which can be analyzed asymptotically. Further information can be discerned on a numerical basis or through a procedure based on the discretization of an integral equation. All of this evidence form a mutually-consistent picture of the asymptotic behavior in question. The principal conclusion which results is that the observed behavior taken with the Mittag-Leffler-type expansion theory for complex functions leads to SEM representations which are free from entire function constituents.

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