The operator introduced in my previous post has many properties. The most notable ones are:
(1) is a constant
We will add to this list an additonal property:
To derive (6), let us consider
It follows that
The order finite difference of function is defined by
From this definition, we have
as well as
The function shown below generates (see Fig. 1).
delta_(g, n) := block(
for i : 2 thru n do (
Compare to the result of expanding (see Fig. 2)
It seems that
Lets prove it!
We have already shown that (1) is true for .
Assuming (1) is true when :