The Distribution Composition Ž x r . S

Let F be a distribution and let f be a locally summable function. The distribution FŽ f . is defined as the neutrix limit of the sequence FnŽ f .4, where FnŽ x. FŽ x. nŽ x. and nŽ x.4 is a certain sequence of infinitely differentiable functions converging to the Dirac delta function Ž x.. The distribution Ž x r . s is evaluated for r, s 1, 2, . . . Further results are deduced.