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MathGroup Archive 2003

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two different results for Sum[Log[n]/n...

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44288] two different results for Sum[Log[n]/n...
  • From: Tom Garcia <tgarcia-ng at NhOiSvPeAmMiTnHdX.org>
  • Date: Tue, 4 Nov 2003 03:24:10 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

I have Mathematica 4.0.1 (oldish I know). Could someone please explain the
behaviour below --- different outputs to same input just because of some
other input in between. If it's a bug, is it fixed in more recent version?
Thanks.

$ math
Mathematica 4.0 for Students: Linux Version
Copyright 1988-1999 Wolfram Research, Inc.
 -- Motif graphics initialized --

In[1]:= Sum[Log[n]/(n),{n,1,Infinity}]

Sum::div: Sum does not converge.

            Log[n]
Out[1]= Sum[------, {n, 1, Infinity}]
              n

In[2]:= Sum[Log[n]/(n^2),{n,1,Infinity}]

Out[2]= -Zeta'[2]

In[3]:= Sum[Log[n]/(n),{n,1,Infinity}]

Out[3]= -StieltjesGamma[1]

-- 
Tom Garcia
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Ceci n'est pas email.


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