The Application of a Hankel Transformation to a Class of Circularly Symmetric Coverage Problems

The expected coverage of a target with a circularly symmetric value density function by a circularly symmetric damage function, where the distance between their centers is a stochastic variable, is expressed in terms of Hankel transforms. In problems of this type, the Hankel transformation of order zero plays a role similar to that of the Fourier transformation in the case of ordinary convolution integrals. Several well-known singular results for circularly symmetric coverage problems are unified and generalized.