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Sep 8, 2014 at 22:01 vote accept Michael
Sep 8, 2014 at 21:30 comment added Michael Renardy Then the answer is different and approximation is possible. For instance, you can set $\exp(-x^2)=u$ and $f(x)=g(u)$. Now use the Weierstrass approximation theorem to approximate g by a polynomial on the interval [0,1].
Sep 8, 2014 at 20:23 comment added Michael Thanks! $w_n$ don't have to be nonnegative though, as long as the sum remains nonnegative.
Sep 8, 2014 at 19:17 history answered Michael Renardy CC BY-SA 3.0