I wanted to confirm that a certain infinite sum agrees with a certain number to thousands of digits of accuracy. I know this is true from a fascinating formula at the top of page 2 of the paper referenced here: http://arxiv.org/abs/math.GM/0409014/
The following one liner outputs the error in the sum.... sage: n(100*sqrt(pi/log(10.0))-sum(10^(-k^2/10000.0) for k in range(-10000,10000))) -1.27897692436818e-13 My finite sum should approximate the infinite sum more accurately as I change the 10000 to 20000 but it does not.... sage: n(100*sqrt(pi/log(10.0))-sum(10^(-k^2/10000.0) for k in range(-20000,20000))) -1.27897692436818e-13 Why isn't the error improving as I increase the number of terms that are summed? Am I doing something wrong in Sage? (Yes it is possible that this infinite sum converges unimaginably slowly so I wanted to check first I wasn't doing something dumb.) Thanks, Chris -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
