
Calculus of Finite Differences/Finite Calculus [pdf] - mettamage
https://www.cs.purdue.edu/homes/dgleich/publications/Gleich%202005%20-%20finite%20calculus.pdf
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mettamage
I'm studying up on data structures and algorithms via MIT 6.006. At one point,
I got frustrated as to why there is no mechanical way of collapsing finite
sums in their closed forms. Or how I used to say a couple of hours ago "create
a formula out of those sums."

So I looked some things up and this is a nice tutorial that I found on it.
It's a bit crazy if you're not too mathematically inclined (like me, I know
basic calculus), but it allowed me to kind of see that there is a system for
creating closed forms out of certain finite sums.

Two very new things you'll learn:

1\. Falling powers (also called falling factorials).

2\. Stirling numbers (and that they are useful for converting falling powers
to the normal powers we're used to).

edit:

another good resource:
[http://faculty.cs.tamu.edu/klappi/csce411-s15/csce411-setFDC...](http://faculty.cs.tamu.edu/klappi/csce411-s15/csce411-setFDCalculus.pdf)

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mettamage
Another good resource that aided in my understanding:
[http://notes.komputerwiz.net:8000/wiki/Calculus_of_Finite_Di...](http://notes.komputerwiz.net:8000/wiki/Calculus_of_Finite_Differences)

