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Jan 4, 2017 at 2:50 comment added Noam D. Elkies No need for Euler-MacL.: the integrand increases to and decreases from $k=0$, so the difference between integral and sum is bounded by the central contribution, which is about $n^{-1/2}$ times the integral. (In fact by Poisson the difference is much smaller, but Stirling incurs an approximation error too.)
Jan 4, 2017 at 2:43 history answered Brendan McKay CC BY-SA 3.0