/sci/ - Science & Math

I find a bunch of formulas in my notes, mostly because it relates to the Dyson formula
https://ncatlab.org/nlab/show/Dyson+formula
In that context, it's one dimensional with time, but for field theories in RxR^3 such integrals might pop up.

Could is be that you're off by one, leading to a canceling boundary term via
[math] \int_0^1 F(x) dx = \sum_{i=0}^{n-1} G(i) = \sum_{i=1}^n G(i) - (G(n) - G(0)) [/math]

It's interesting, can you try a simple monomial or rational function and take the limit on wolframalpha or so?

>>11526413
>>11526415
I find a bunch of formulas like this, mostly because in one dimension it relates to the Dyson formula (there the one dimension is time)
https://ncatlab.org/nlab/show/Dyson+formula
I imagine this thing pops up if you deal with field theories and you got some x's to integrate over.

Could it be that you're off by one an you get a boundary term via
[math]\int_0^1 F(x) dx = \sum_{i=0}^{n-1} G(i) = \sum_{i=1}^n G(i) + G(0) - G(n) [/math]
?