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


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


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