**by Wei Xi Fan**

R: What is

L:

R: What is the quantum analogue of

L: I have no clue.

R: Let’s try This is the sequence

L: OK. . I can’t get anywhere from here that would make it look remotely close to .

R: What do we do?

L: We call upon the fire of inspiration itself, Ignis.

IGNIS: The truth ye seek is but a cascading staircase, but one that ends.

L: What do you think that means?

R: Instead of trying , let’s try

there are terms in total just like , but here, each term is one less than the previous.

L: Like a factorial that suddenly ends. All right, so

Oh! The factors line up. The subtraction yields

This is exactly what we are looking for.

R: Great! So we have the identity

corresponding to

in the real calculus.

L: OK. What about when or when ?

R: Well… what do we do to get from to

L: Well, we divide by its last term, which is , to get to , because the only difference between them is that is missing the term.

R: What do we get when we go from to

L: Well, , and so we divide this by to get to , so I guess we should define

R: What about

L: Well, we would divide this by so I guess it is

R: So what’s the general formula?

L:

Are you sure the identity (*) still holds for these new definitions?

R: For these situations, we should call upon the minion of non-illuminating bashing, Grunt.

GRUNT: ‘Tis done.

R: There, this fact has been verified.

L: I shall call these Pochhammer symbols.

R: WTF?

L: Or we can call them falling factorials. Or falling powers.

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## About mlbaker

just another guy trying to make the diagrams commute.

I practically died laughing @ IGNIS and GRUNT.