integral over a finite sum with unknown upper limit
Subject: integral over a finite sum with unknown upper limit
From: Robert Dodier
Date: Fri, 30 Jun 2006 09:07:03 -0600
Tobias,
2 things here -- (1) it appears you are using Maxima 5.9.1
(or older). If that's the case, I recommend pretty strongly
that you get 5.9.3. There have been many changes,
including changes in the way sum is evaluated.
(2) Let's separate the evaluation of the integral into two steps.
First integrate(f(x), x); then evaluate the result.
Here's what I get (using Maxima 5.9.3).
(%i2) integrate( sum( q[k]*s^k, k, 1, n ), s);
(%o2) 'sum(q[k]*s^(k+1)/(k+1),k,1,n)
(%i3) ev(%, s=2) - ev(%, s=1);
(%o3) 'sum(2^(k+1)*q[k]/(k+1),k,1,n)-'sum(q[k]/(k+1),k,1,n)
(%i4) u[k](s) := s^k;
(%o4) u[k](s):=s^k
(%i5) integrate( sum( q[k]*u[k](s), k, 1, n ), s);
(%o5) 'sum(q[k]*s^(k+1)/(k+1),k,1,n)
(%i6) ev(%, s=1) - ev(%, s=0);
(%o6) 'sum(q[k]/(k+1),k,1,n)
Hope this helps,
Robert Dodier