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Bug in Mathematica 6 - Sum - 1 - (Log, Exp, invalid value)

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Vladimir Bondarenko

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Jul 5, 2007, 1:44:54 PM7/5/07
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Hello again from the VM machine...

N[Sum[Log[n]^2 Exp[-n], {n, 1, Infinity}]]
NSum[Log[n]^2 Exp[-n], {n, 1, Infinity}]

-3.42385 10^-13
0.191621

Best wishes,

Vladimir Bondarenko

VM and GEMM architect
Co-founder, CEO, Mathematical Director

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dimitris

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Jul 6, 2007, 11:21:29 AM7/6/07
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Vladimir Bondarenko :

The same holds true in version 5.2

In[190]:=
NSum[Log[n]^2*Exp[-n], {n, 1, Infinity}]

Out[190]=
0.19162119250353019

but

In[198]:=
Simplify[Sum[Log[n]^2*Exp[-n], {n, 1, Infinity}]]

Out[198]=
Derivative[2, 0][PolyLog][0, 1/E] - Derivative[0, 2, 0][LerchPhi][1/E,
0, 1]/E

which is incorrect

In[200]:=
N[%]

Out[200]=
-5.713485240477212*^-13

Note that, very interestingly,

In[202]:=
List @@ (Derivative[2, 0][PolyLog][0, 1/E] - Derivative[0, 2, 0]
[LerchPhi][1/E, 0, 1]/E)
N[%]

Out[202]=
{Derivative[2, 0][PolyLog][0, 1/E], -(Derivative[0, 2, 0][LerchPhi][1/
E, 0, 1]/E)}

Out[203]=
{0.19162119250292617, -0.19162119250349752}

Dimitris

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