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Question about yet another bug in Sum
*To*: mathgroup at smc.vnet.net
*Subject*: [mg35204] Question about yet another bug in Sum
*From*: Vladimir Bondarenko <vvb at mail.strace.net>
*Date*: Tue, 2 Jul 2002 02:11:59 -0400 (EDT)
*Reply-to*: Vladimir Bondarenko <vvb at mail.strace.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Hello.
Mathematica is a great environment. I observe that every time before it
becomes stronger, Mathematica expeciences a collapse ;-)
Now we at this leg of its majestic trajectory...
Here is another bug in Sum.
$Version
"4.2 for Microsoft Windows (February 28, 2002)"
Sum[Exp[-I Pi n] n /(1 + n^2), {n, 0, Infinity}]
ACTUAL: Sum::"div": "Sum does not converge."
EXPECTED: -1/2*HypergeometricPFQ[{2, 1 + I, 1 - I}, {2 - I, 2 + I}, -1]
CHECK-UP: N[%, 20]//Chop
-0.26961050270800898180
NSum[Exp[-I Pi n] n/(1 + n^2), {n, 0, Infinity}, WorkingPrecision->20]//Chop
-0.269610502708010
This bug is present in 4.1, 4.0, 3.0. Version 2.2 leaves the sum unevaluated.
Can anyone explain the origin of the bug?
Best,
Vladimir Bondarenko
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