$$I_{k,m}(n)=\int_{0}^{1}u^k\cot{\frac{\pi(1-u)}{m}}\sin{\frac{2\pi n(1-u)}{m}}\,du$$
Conjecture: $\lim_{n\rightarrow\infty} I_{k,m}(n)=m/2$, for $m\geq 1$ and any $k\in\{1,2,3,\ldots\}$.
Carlo Beenakker
- 188.3k
- 18
- 448
- 651