The comments on this question point to a paper which demonstrates that the Gaussians $$E_b(x)=e^{-bx^2}$$ are dense in the even functions in $\mathcal{S}(\mathbb{R})$. I'm wondering if there's a nice analytic way to generate an infinite series of Gaussians centered at zero that converges to a given such function?
This is different from much of the radial basis function discussion I found online because I have an explicit formula for my function, so I don't want the loss of accuracy that comes from sampling it at points.
