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?)