Maxima 5.28.0 http://maxima.sourceforge.net
using Lisp SBCL 1.0.55.0-abb03f9
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) load(simplify_sum);
(%o1) /Applications/MathApps/Maxima.app/Contents/Resources/maxima/share/maxima\
/5.28.0/share/solve_rec/simplify_sum.mac
(%i2) simplify_sum(sum(1/((2*n-1)^2*(2*n+1)^2*(2*n+3)^2), n, 0, inf));
2
%pi
2 ---- - 4
%pi 2
(%o2) ---- + --------
128 128
But this is not right. The extra -1/32 is spurious.
(%i4) float(simplify_sum(sum(1/((2*n-1)^2*(2*n+1)^2*(2*n+3)^2), n, 0, 100)));
(%o4) .1156594265749686
(%i5) float (simplify_sum(sum(1/((2*n-1)^2*(2*n+1)^2*(2*n+3)^2), n, 0, inf)));
(%o5) .08440942657526591
(%i6) float(1/32);
(%o6) 0.03125
This was first reported at http://trac.sagemath.org/sage_trac/ticket/13712 and http://ask.sagemath.org/question/1985/unexpected-result-for-the-sum-of-a-series
Andrej Vodopivec
2013-02-08
Andrej Vodopivec
2013-02-08
Fixed in git:
(%i3) simplify_sum(sum(1/((2n-1)^2(2n+1)^2(2n+3)^2), n, 0, inf)), ratsimp;
(%o3) 3%pi^2/256