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Infinite sum of n^2 Exp[-n^2]

• To: mathgroup at smc.vnet.net
• Subject: [mg26477] Infinite sum of n^2 Exp[-n^2]
• From: "A. E. Siegman" <siegman at stanford.edu>
• Date: Fri, 22 Dec 2000 22:46:14 -0500 (EST)
• Organization: Stanford University
• Sender: owner-wri-mathgroup at wolfram.com

Mathematica can do the infinite sums (-Infinity to Infinity) of

   Exp[-n^2] 

and also 

   Exp[- a n^2] 

in closed form, but not

   n^2 Exp[-n^2]

or better

   n^2 Exp[- a n^2]

Are there known closed analytical forms for these?

Thanks     siegman@@stanford.edu