Complex integration problem


hi,

any hint how to (formally) prove that

\sum_{k = -n^2, k \neq 0}^{n^2} (e^{i * (k/n) * t} - 1)/(n *
ABS(k/n)^{1+a})

converges to

\int_{-\infty}^{\infty} (e^{i*t*s} - 1)/s^{1+a} ds

when n goes to infinity?

Variable t is REAL number, a is real, 0 < a < 1, i is complex unity. As
far as I understand the problem, the variable s is also real and
therefore we don't need to have integration path specified.

Thanks,
Sunil

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