Category: Relation and Functions

Question Number 2675 by prakash jain last updated on 24/Nov/15 $$\mathrm{Bases}\mathrm{on}\mathrm{suggestion}\mathrm{from}\mathrm{Filup}\mathrm{and}\mathrm{some}$$$$\mathrm{discussion}\mathrm{on}\mathrm{that}\mathrm{I}\mathrm{am}\mathrm{suggesting}\mathrm{that}\mathrm{we}$$$$\mathrm{sequence},\mathrm{series}\mathrm{and}\mathrm{related}\mathrm{function}\mathrm{as}\mathrm{a}$$$$\mathrm{topic}\mathrm{for}\mathrm{this}\mathrm{month}.$$$$\zeta \left(x\right)=\underset{n=1}{\sum ^{\mathrm{\infty }}}{n}^{-x},x\in \mathbb{R},x>1$$$$\mathrm{Show}\:\mathrm{that} \…

Question Number 2644 by 123456 last updated on 24/Nov/15 $$a_{n+1}=\frac{a_n}{n}+n$$$$a_1=1$$$$a_n=???n\in {\mathbb{N}}^{\ast }$$ Commented by RasheedAhmad last updated…

Question Number 68129 by mathmax by abdo last updated on 05/Sep/19 $$provethat\pi cotan\left(\alpha \pi \right)=\frac{1}{\alpha }+\sum _{n=1}^{\mathrm{\infty }}\frac{2\alpha }{{\alpha }^2-n^2}$$$$with\alpha \in R-Z.$$$$provealsothatfort\ne 0$$$${cotan}\left({t}\right)\:=\frac{\mathrm{1}}{{t}}\:+\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{2}{t}}{{t}^{\mathrm{2}} −{n}^{\mathrm{2}}…

Question Number 68034 by mathmax by abdo last updated on 03/Sep/19 $$letf\left(x\right)=e^{-x},2\pi periodicdeveloppfatfourierserie.$$ Commented by mathmax by abdo last updated on 07/Sep/19 $${f}\left({x}\right)\:=\sum_{{n}=−\infty}…

Question Number 68019 by mathmax by abdo last updated on 03/Sep/19 $$letF\left(x\right)={\int }_x^{x^2+1}{e}^{-2t}sin\left(xt\right)dt$$$$determineF{}^{{}^{\prime }}\left(x\right)andcalculate{lim}_{x\to 0}F\left(x\right).$$$$$$ Commented…