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

*To*: mathgroup at smc.vnet.net*Subject*: [mg26483] Re: Infinite sum of n^2 Exp[-n^2]*From*: "Kevin J. McCann" <KevinMcCann at home.com>*Date*: Thu, 28 Dec 2000 02:52:22 -0500 (EST)*References*: <9217t2$com@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Sort of. Try f[a_]=Sum[Exp[-a n^2],{n,1,Infinity}] then your summation is just the derivative with a->1 f'[a]==-Sum[n^2 Exp[-a n^2],{n,1,Infinity}] Evaluate the derivative WRT a with a=1 -f'[1] or =-f'[1]//N The first is given in terms of the EllipticTheta function, which is closed form, but maybe not what you would like. BTW, you can't go {n,-Infinity,Infinity} - blows up. Kevin The wise words of A. E. Siegman on 22 Dec 2000 22:58:26 -0500: > 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 >