In a previous post on using the Feynman’s trick for Discrete calculus, I used a very strange operator ( ). And whose function is the following :

What is this operator? Well, to be quite frank I am not sure of the name, but I used it as an analogy to Integration. i.e

What are the properties of this operator ? Let’s use the known fact that

And applying the operator twice yields:

We can clearly see a pattern emerging from this already, applying the operator once more :

Or in general, the operator that has the characteristic prescribed in the previous post is the following:

If you guys are aware of the name of this operator, do ping me !