An Introduction to Neutrix Composition of Distributions and Delta Function

The composition of the distribution σ(s) (x) and an infinitely differentiable function f(x) having a simple zero at the point x = x0 is defined by gel’fand shilov by the equation σ(s)(f(x))=1/ vert f'(x0) vert [1/f'(x)* 1/d(x)]x σ(x-x0) it is shown how this definition can be extended to functions f(x) which are not necessarily infinitely differentiable or not having simple zeros at the point x=x0 , by defining σ(s) (f(x)) as the limit or neutrix limit of the sequence {σ(s)n (f(x))} , where {σn(x)} is a certain sequence of infinitely differentiable functions converging to the dirac delta-function σ (x). anumber of examples are given