Hello everyone:
So, I was just messing around with the assume command, and did:
var('i')
assume(abs(x) < 1)
f(x) = sum(x^i, i, 0, oo )
This is just 1/(1-x). I wanted to see what would happen when I tried using
x > 1, and it still evaluates properly, even though the sum should be
divergent for x > 1. How does this happen behind the scenes exactly? Is
Sage/Maxima substituting 1/(1-x) for my sum? Further, I took the integral
from 0 to 2:
integrate(f(x),x,0,2)
which returned -I*pi. How does this work? What exactly is it doing here?
I'm assuming it's using an analytic continuation somehow, but how does it
find it and where is it substituted in exactly? What I mean is, what
exactly is the function f(x) equal to if it can be integrated like that?
Thank you!
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