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