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MathGroup Archive 2002

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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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