Rawlins' method and the diaphanous cone

Approximate expansions are obtained for the field when an electromagnetic w ave is scattered by a dielectric circular cone with refractive index near u nity. They indicate that the field near the tip of the cone contains not on ly powers of the distance but also its logarithm. The analysis entails the singular behaviour of an integral of a product of Hankel functions as a generalized function. Also a uniformly valid asymptot ic formula for the hypergeometric function with parameters outside the usua l range is derived.