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edited Jan 7, 2017 at 18:55

asymptotic estimate for log-tan sum

I am finding the following first order estimate.

Question. As $y\rightarrow\infty$, $$\sum_{n=1}^{\infty}\frac{\log n}n\,\arctan\frac{y}n\,\, \sim\,\,\frac{\pi}4\log^2y.$$ Is it true?

asked Jan 7, 2017 at 18:21