ABSTRACT
Useful mathematical identities can be obtained if we solve a physical problem by using different representations for Green’s function. In particular, through the consideration of situations where physical quantities vary only in a single direction, we learn of the properties of the important class of functions called Bessel functions. If all of space is considered, however, we are dealing with a solution of Poisson’s inhomogeneous equation, where the delta function appears as the charge density. The analogous two- and three-dimensional completeness statements are similar consequences of the appropriate delta function constructions.
