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RE: Question about yet another bug in Sum

• To: mathgroup at smc.vnet.net
• Subject: [mg35224] RE: [mg35204] Question about yet another bug in Sum
• From: "DrBob" <majort at cox-internet.com>
• Date: Wed, 3 Jul 2002 05:13:23 -0400 (EDT)
• Reply-to: <drbob at bigfoot.com>
• Sender: owner-wri-mathgroup at wolfram.com

>>I observe that every time before it becomes stronger, Mathematica
expeciences a collapse ;-)

This isn't a new behavior in Version 4.2.  It does the same thing in
4.1.

Bobby Treat

-----Original Message-----
From: Vladimir Bondarenko [mailto:vvb at mail.strace.net] 
To: mathgroup at smc.vnet.net
Subject: [mg35224] [mg35204] Question about yet another bug in Sum

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