Question Number 2930 by Filup last updated on 30/Nov/15 $$\mathrm{Prove}\:\mathrm{that}\:\Gamma\left({i}\right)=−{i}\left({i}\right)! \\ $$$$\mathrm{where}\:{i}=\sqrt{−\mathrm{1}} \\ $$ Commented by 123456 last updated on 02/Dec/15 $$\Gamma\left({z}\right)\Gamma\left(\mathrm{1}−{z}\right)=\frac{\pi}{\mathrm{sin}\:\pi{z}} \\ $$$$\Gamma\left({z}\right)\Gamma\left(−{z}\right)=−\frac{\pi}{{z}\:\mathrm{sin}\:\pi{z}} \\…
Question Number 133989 by Mamifere last updated on 26/Feb/21 $$\frac{{x}}{{x}\mathrm{2}+\mathrm{1}}<{arctan}\left({x}\right)<{x} \\ $$$$ \\ $$ Answered by Ñï= last updated on 26/Feb/21 $${Let}\:{f}\left({x}\right)={tan}^{−\mathrm{1}} {x} \\ $$$${we}\:{have}\:{f}\left({x}\right)−{f}\left(\mathrm{0}\right)={f}\left(\xi\right)'\left({x}−\mathrm{0}\right)…
Question Number 133916 by shaker last updated on 25/Feb/21 Answered by TheSupreme last updated on 25/Feb/21 $${S}_{{n}} =\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\frac{{e}^{{kx}} +{e}^{−{kx}} }{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{2}}\left\{\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\left({e}^{{x}} \right)^{{k}}…
Question Number 68349 by peter frank last updated on 09/Sep/19 Answered by mr W last updated on 09/Sep/19 $${w}_{{new}} =\mathrm{1}.\mathrm{03}{w}\:\:\:\left(\mathrm{3\%}\:{more}={factor}\:\mathrm{1}.\mathrm{03}\right) \\ $$$${d}_{{new}} =\mathrm{0}.\mathrm{975}{d}\:\:\:\left(\mathrm{2}.\mathrm{5\%}\:{less}={factor}\:\mathrm{0}.\mathrm{975}\right) \\ $$$${t}_{{new}}…
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Question Number 2791 by Filup last updated on 27/Nov/15 $$\mathrm{Knowing}\:\mathrm{that}\:{e}=\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{i}!}, \\ $$$$\mathrm{Show}\:\mathrm{that}\:{e}\:\mathrm{is}\:\mathrm{finite}. \\ $$$$ \\ $$$$\mathrm{That}\:\mathrm{is},\:\mathrm{show}\:\mathrm{the}\:\mathrm{following}\:\mathrm{is}\:\mathrm{true}: \\ $$$${S}=\left\{\exists{x}\in\mathbb{R}:\mid{x}\mid<\infty,\:{e}={x}\right\} \\ $$$$\mathrm{Where}\:{S}\:\mathrm{is}\:\mathrm{the}\:\mathrm{solution} \\ $$ Commented…
Question Number 2777 by Filup last updated on 27/Nov/15 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\zeta\left(−\mathrm{2}{n}\right)=\mathrm{0} \\ $$ Answered by prakash jain last updated on 27/Nov/15 $$\mathrm{Functional}\:\mathrm{Equation}\:\mathrm{for}\:\zeta\left({s}\right) \\ $$$$\zeta\left({s}\right)=\mathrm{2}^{{s}}…
Question Number 68294 by peter frank last updated on 08/Sep/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 68272 by peter frank last updated on 08/Sep/19 Answered by Kunal12588 last updated on 08/Sep/19 $${H}_{{max}} ={maximum}\:{height} \\ $$$${R}={horizontal}\:{range} \\ $$$${H}_{{max}} ={h}=\frac{{u}_{{y}} ^{\mathrm{2}}…
Question Number 2702 by Filup last updated on 25/Nov/15 $$\zeta\left({s}\right)=\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}{i}^{−{s}} =\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}^{{s}} }+\frac{\mathrm{1}}{\mathrm{3}^{{s}} }+… \\ $$$$ \\ $$$$\mathrm{Is}\:\zeta\left({s}\right)>\mathrm{0}\forall{s}\in\mathbb{R}? \\ $$$$\mathrm{1}.\:\mathrm{Can}\:\mathrm{you}\:\mathrm{prove},\:\mathrm{or}\:\mathrm{prove}\:\mathrm{otherwise}? \\ $$$$\mathrm{2}.\:\mathrm{If}\:\zeta\left({s}\right)>{n},\:{s}\in\mathbb{R},\:\mathrm{what}\:\mathrm{are}\:\mathrm{the}\:\mathrm{bounds} \\ $$$$\mathrm{of}\:{s}?\:\mathrm{i}.\mathrm{e}.\:\:{a}\leqslant{s}\leqslant{b}\::\:\zeta\left({s}\right)>{n}…