using integration by parts to hate myselfpic.twitter.com/mLwr37sHfU
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Basically the reason this works (and I think I’m recalling this correctly) is because you‘re secretly deriving the taylor polynomial. In your case, the expansion terminates because the function was a polynomial to begin with.
the taylor polynomial of x^n is x^n though? there's no expansion here
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Right, you did the first step and you got back the function you started with
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If you set f=\int f’ dx and IBP the RHS repeatedly in a silly way, you start churning out a taylor polynomial + remainder—I could be wrong, but I remember something like this happening
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