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
http://www.cybertester.com/ Cyber Tester, LLC
http://maple.bug-list.org/ Maple Bugs Encyclopaedia
http://www.CAS-testing.org/ CAS Testing
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