I am trying to find a closed form solution for this problem. Numerically I can show that for all positive a and b values it converges to a fixed value but have no luck to find the expression for it.
\(\displaystyle \lim_{N\to\infty} {1\over N} \sum_{i=1}^{i=N} {exp({-a\times(i-0.5)^2 \over b\times N^2}})\)
Thank you,
\(\displaystyle \lim_{N\to\infty} {1\over N} \sum_{i=1}^{i=N} {exp({-a\times(i-0.5)^2 \over b\times N^2}})\)
Thank you,