Non-variational nature of the functional obtained by testing with a Dirac delta function

Since the Dirac delta function is not a conventional function, it must be approximated by a conventional function h/sub c/, that is large in a small neighborhood of the location of the delta function and is zero elsewhere. Moreover, the integral of h/sub c/, must be unity. It was found that increasing the number of expansion functions will usually increase the accuracy of the moment approximation to any conventional function but not the moment approximation to a delta function because increasing the number of expansion functions shrinks the "effective domain" of the delta function, making the delta function more difficult to approximate. The "effective domain" is the domain outside of which the approximation to the delta function is very small.<>