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Why won't this sum evaluate?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg120526] Why won't this sum evaluate?
  • From: PAR123 <reiser.paul at gmail.com>
  • Date: Wed, 27 Jul 2011 06:13:57 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

In[120]:= $Version
Out[120]= "7.0 for Mac OS X x86 (32-bit) (January 30, 2009)"

In[122]:= Sum[c^n/(1 + c^(2*n)), {n, 1, Infinity}]
Out[122]= -(1/4) + 1/4 EllipticTheta[3, 0, c]^2

In[123]:= Sum[c^n/(1 + c^(2*n)), {n, 0, Infinity}]
Out[123]= (won't simplify)

The only thing different in the two sums is that the second sum is from 0 to Infinity rather than 1 to Infinity. Clearly, the n=zero term is 1/2. 

I have tried various Regularizations and Methods, (not exhaustively) but none seem to work on either of the sums, much less the last.

A side problem - Is there a way to determine what Regularization and Method were used when none were specified?

Thanks




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