How to estimate the correction to the integral approximation of a discrete
sum?
In the following approximation,
$~\epsilon\sum_{n\in Z} F(\epsilon n)=\int_{-\infty}^{+\infty} dx~ F(x) +
$ correction,
how can one estimate the `leading' order correction for small $\epsilon$?
Here the function, $F(x)$, and its all derivatives, $F^{(n)}(x)$, drop off
rapidly at $\pm \infty$ such that the Euler–Maclaurin formula does not
help. For example, $e^{-x^{2}}$.
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