Question Number 221513 by MrGaster last updated on 07/Jun/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 221470 by wewji12 last updated on 06/Jun/25 Answered by MathematicalUser2357 last updated on 06/Jun/25 $$\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 221481 by MrGaster last updated on 06/Jun/25 $$\mathrm{prove}:\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\frac{{k}!\left({n}−{k}\right)!}{{n}!}=−\frac{{i}\mathrm{2}^{{n}−\mathrm{1}} \Gamma\left({n}+\mathrm{2}\right)\left(\pi−{iB}_{\mathrm{2}} \left({n}+\mathrm{2},\mathrm{0}\right)\right)}{{n}!} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 221473 by wewji12 last updated on 06/Jun/25 Answered by MathematicalUser2357 last updated on 06/Jun/25 $$\mathrm{279}\pi \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 221435 by wewji12 last updated on 05/Jun/25 $$\mathrm{g};\mathbb{R}\rightarrow\mathbb{R}\:,\:\mathrm{g}\in\mathcal{C}^{\omega} \:\mathrm{at}\:\mathbb{R}\:\mathrm{space} \\ $$$$\:\mathrm{evauate}\: \\ $$$$−\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \:{y}\centerdot\mathrm{g}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)\mathrm{d}{x}\mathrm{d}{y} \\ $$$$\mathrm{when}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{z}^{\mathrm{2}}…
Question Number 221447 by Nicholas666 last updated on 05/Jun/25 $$ \\ $$$$\:\:\:\:\mathrm{if}\:\:\:\:\:\:\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\prod}}\:\left({x}\:+\:{r}_{{i}} \right)\:\equiv\:\underset{{j}=\mathrm{0}} {\overset{{n}} {\sum}}\:{a}_{{j}} {x}^{{n}−{i}} \: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{show}\:\mathrm{that}\:; \\ $$$$\:\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\:\mathrm{tan}^{−\mathrm{1}}…
Question Number 221416 by wewji12 last updated on 04/Jun/25 $$\mathrm{ex3}. \\ $$$$\mathrm{prove} \\ $$$${f}^{\left({n}\right)} \left(\alpha\right)=\frac{{n}!}{\mathrm{2}\pi\boldsymbol{{i}}}\:\oint_{\:\partial{S}} \:\frac{{f}\left({z}\right)}{\left({z}−\alpha\right)^{{n}+\mathrm{1}} }\:\mathrm{d}{z} \\ $$$$\mathrm{ex4}. \\ $$$$\mathrm{Let}\:{z}_{\mathrm{0}} \:\mathrm{be}\:\mathrm{any}\:\mathrm{point}\:\mathrm{interior}\:\mathrm{to}\:\mathrm{a}\:\mathrm{positively} \\ $$$$\mathrm{oriented}\:\mathrm{simple}\:\mathrm{closed}\:\mathrm{contour}\:\mathcal{C} \\…
Question Number 221415 by wewji12 last updated on 04/Jun/25 $$\int\:\:\mathrm{d}{z}\:\left[−\frac{\mathrm{1}}{\pi}\left(\frac{\mathrm{2}}{{z}}\right)^{\nu} \centerdot\underset{{k}=\mathrm{0}} {\overset{\nu−\mathrm{1}} {\sum}}\:\frac{\Gamma\left(\nu−{k}\right)}{{k}!}\left(\frac{{z}}{\mathrm{2}}\right)^{\mathrm{2}{k}} +\frac{\mathrm{2}}{\pi}\mathrm{ln}\left(\frac{\mathrm{1}}{\mathrm{2}}{z}\right){J}_{\nu} \left({z}\right)−\frac{\mathrm{1}}{\pi}\left(\frac{{z}}{\mathrm{2}}\right)^{\nu} \underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{k}} \left(\psi^{\left(\mathrm{0}\right)} \left({k}+\nu+\mathrm{1}\right)+\psi^{\left(\mathrm{0}\right)} \left({k}+\mathrm{1}\right)\right)}{{k}!\left({k}+\nu\right)!}\left(\frac{{z}}{\mathrm{2}}\right)^{\mathrm{2}{k}} \right] \\ $$ Answered…
Question Number 221391 by SdC355 last updated on 02/Jun/25 $$\int_{\mathrm{0}} ^{\:\infty} {J}_{\nu} ^{\left(\mathrm{1}\right)} \left({t}\right){Y}_{\nu} \left({t}\right)\mathrm{sin}\left({t}\right)\mathrm{d}{t}−\int_{\mathrm{0}} ^{\:\infty} {J}_{\nu} \left({t}\right){Y}_{\nu} ^{\left(\mathrm{1}\right)} \left({t}\right)\mathrm{sin}\left({t}\right)\mathrm{d}{t}=?? \\ $$$${J}_{\nu} \left({t}\right)\:\mathrm{is}\:\nu\:\mathrm{th}\:\mathrm{Bessel}\:\mathrm{function}\:\mathrm{first}\:\mathrm{Kind} \\ $$$${Y}_{\nu}…
Question Number 221387 by Nicholas666 last updated on 02/Jun/25 $$ \\ $$$$\:\:\:\:\:\:\:\underset{{k}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\left(\mathrm{2}\underset{{n}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} \:+\:{kn}}\right)^{\mathrm{2}} \:=\:? \\ $$$$ \\ $$ Answered by MrGaster…