Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

Question Number 73774 by mind is power last updated on 15/Nov/19

$$\mathrm{hello},\mathrm{show}\mathrm{that}$$$$\sum _{\mathrm{n}⩾1}\frac{{(-1)}^{\mathrm{n}}\mathrm{nsin}\left(\mathrm{n}\right)}{1+{\mathrm{n}}^2}=\frac{\pi {\mathrm{e}}^1-\pi {\mathrm{e}}^{-1}}{-{2\mathrm{e}}^{\pi }+{2\mathrm{e}}^{-\pi }}$$$$\mathrm{indication},\mathrm{Residus}\mathrm{Theorem}\mathrm{let}$$$$\mathrm{f}\left(\mathrm{z}\right)=\frac{\mathrm{zsin}\left(\mathrm{z}\right)}{(1+{\mathrm{z}}^2)\sin \left(\pi \mathrm{z}\right)}$$$$\mathrm{have}\mathrm{a}\mathrm{very}\mathrm{nice}\mathrm{day}!$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com