Several Asymptotic Products of Particular Distributions
C.K. Li *
Department of Mathematics and Computer Science Brandon University, Brandon, Manitoba, Canada R7A 6A9.
*Author to whom correspondence should be addressed.
Abstract
The problem of defining products of distributions is a difficult and not completely understood problem, studied from several points of views since Schwartz established the theory of distributions around 1950. Many fields, such as wave propagation or quantum mechanics, require such multiplications. The product of an infinitely differentiable function (x) and distribution 4(x) inRn is well defined by 
since 
Using an induction, we derive an interesting formula for 
and hence we are able to write out an explicit expression of the product 
In particular, we imply the product 
with a few applications in further simplifying existing distributional products. Furthermore, we obtain an asymptotic expression for 
which isequivalent to the well-known Pizzetti’s formula. Several asymptotic products including 
as wellasthemore generalized 
are calculated and presented as infinitely series.
Keywords: Distribution, product, asymptotic expansion, asymptotic product, neutrix limit and Pizzetti’s formula