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MathGroup Archive 2005

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Moments of gaussian sums?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg63436] Moments of gaussian sums?
  • From: AES <siegman at stanford.edu>
  • Date: Sat, 31 Dec 2005 06:40:34 -0500 (EST)
  • Organization: Stanford University
  • Sender: owner-wri-mathgroup at wolfram.com

Pardon me if this is mathematics and not Mathematica -- but is there a 
closed form for

   Sum[n^2 Exp[ -a n^2], {n, -Infinity, Infinity}]

or

   Sum[n^2 k(n^2), {n, -Infinity, Infinity}]

like the EllipticTheta result with the n^2 left out?

(And just out of curiosity, how does Sum know to step over the integers 
in sums like these?  Is Infinity an Integer?)


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