#8582: sum(1/(1+k^2), k, -oo, oo) returns 0
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Reporter: mvngu | Owner: burcin
Type: defect | Status: new
Priority: major | Milestone: sage-4.6
Component: symbolics | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by kcrisman):
This seems to be fixed in Maxima 5.21.1 or so:
{{{
(%i2) load(simplify_sum);
(%o2) /Users/.../maxima/share/contrib/solve_rec/simplif\
y_sum.mac
(%i5) display2d:false;
(%o5) false
(%i6) simplify_sum(sum(1/(1+k^2),k,-inf,inf));
(%o6) -%i*(psi[0](%i+1)+%gamma)/2-%i*(psi[0](%i)+%gamma)/2
+%i*(psi[0](-%i)+%gamma)/2
+%i*(psi[0](1-%i)+%gamma)/2
}}}
Which uses the digamma function quite a bit. We don't get the (perhaps)
simpler answer `pi coth(pi)`.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8582#comment:1>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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