Question Number 219076 by MrGaster last updated on 19/Apr/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 219077 by zetamaths last updated on 19/Apr/25 $$\int_{\mathrm{0}} ^{+\infty} \left(\frac{{sin}\left({n}\right)}{{n}}\right)^{{m}} {dn}=\pi\centerdot\frac{{m}}{\mathrm{2}^{{m}} }\centerdot\underset{\phi=\mathrm{0}} {\overset{{m}/\mathrm{2}} {\sum}}\left(−\mathrm{1}\right)^{\emptyset} \centerdot\frac{\left({n}−\mathrm{2}\phi\right)^{{m}−\mathrm{1}} }{\left({m}−\phi\right)!\centerdot\phi!}\:\:\:\:\:\:\:\:\:\:\:\:\:\:{Proof}\:{this}\:{formula} \\ $$ Terms of Service Privacy Policy…
Question Number 219078 by zetamaths last updated on 19/Apr/25 $$\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}{m}}\right).\underset{{k}=\mathrm{1}} {\overset{{m}} {\sum}}\left(−\mathrm{1}\right)^{{k}−\mathrm{1}} \centerdot{k}\centerdot\frac{\left({m}!\right)^{\mathrm{2}} }{\left({m}−{k}\right)!\left({m}+{k}\right)!}=\frac{\mathrm{1}}{\mathrm{4}}\:\:\:\:\:\:{Proof}\:{this}\:{formula} \\ $$ Answered by MrGaster last updated on 19/Apr/25 $$\mathrm{Let}\:{S}\left({m}\right)\underset{{k}=\mathrm{1}} {\overset{{m}}…
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Question Number 219025 by universe last updated on 18/Apr/25 Answered by vnm last updated on 19/Apr/25 $${the}\:{generating}\:{function}\:{of}\: \\ $$$${this}\:{sequence}\:{is} \\ $$$${f}\left({x}\right)=\frac{{x}−\mathrm{2ln}\left(\mathrm{1}−{x}\right)+\frac{\mathrm{1}}{\mathrm{1}−{x}}−\mathrm{1}}{\left(\mathrm{2}−{x}\right)^{\mathrm{2}} } \\ $$ Commented…
Question Number 219017 by Nicholas666 last updated on 18/Apr/25 Commented by Nicholas666 last updated on 18/Apr/25 https://www.quora.com/How-do-You-solve-f-x-1-frac-3-x-frac-7-x-2-frac-17-x-3-frac-41-x-4-frac-99-x-5-frac-239-x-6-dots-f-left-frac-3-sqrt-13-2-right/answer/Bekicot-5?ch=10&oid=1477743855612858&share=66e3ed2c&srid=5Xg5SU&target_type=answer Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 219003 by hardmath last updated on 17/Apr/25 Answered by maths2 last updated on 18/Apr/25 $${S}_{{p}} =\Sigma\Sigma\underset{{k}=\mathrm{0}} {\sum}\frac{{k}^{\mathrm{2}} }{\left({n}−{k}\right)^{\mathrm{2}} +{k}^{\mathrm{2}} }=\Sigma\Sigma\underset{{k}=\mathrm{0}} {\sum}\frac{\left({n}−{k}\right)^{\mathrm{2}} }{\left({n}−{k}\right)^{\mathrm{2}} +{k}^{\mathrm{2}}…
Question Number 218997 by hardmath last updated on 17/Apr/25 Answered by MrGaster last updated on 19/Apr/25 $$\mathrm{4}!\underset{\alpha+\beta+\gamma+\delta=\mathrm{4}} {\sum}\frac{\left[{x}\right]^{\alpha} \left[{x}/\mathrm{2}\right]^{\beta} \left[{x}/\mathrm{4}\right]^{\gamma} \left[{x}/\mathrm{8}\right]^{\delta} }{\alpha!\beta!\gamma!\delta!}=\left(\left[{x}\right]+\left[\frac{{x}}{\mathrm{2}}\right]+\left[\frac{{x}}{\mathrm{4}}\right]+\left[\frac{{x}}{\mathrm{8}}\right]\right)^{\mathrm{4}} \\ $$$$\Rightarrow\left(\left[{x}\right]+\left[\frac{{x}}{\mathrm{2}}\right]+\left[\frac{{x}}{\mathrm{4}}\right]\left[\frac{{x}}{\mathrm{8}}\right]\right)^{\mathrm{4}} \equiv\mathrm{1}\:\left(\mathrm{mod}\:\mathrm{5}\right)\:\left(^{\ast}…
Question Number 218914 by SdC355 last updated on 17/Apr/25 $$\mathrm{prove} \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:{J}_{\nu} \left(\alpha{t}\right){J}_{\nu} \left(\beta{t}\right)\mathrm{d}{t}=\frac{\mathrm{2}}{\pi}\centerdot\frac{\mathrm{sin}\left(\frac{\pi}{\mathrm{2}}\left(\alpha−\beta\right)\right)}{\alpha^{\mathrm{2}} −\beta^{\mathrm{2}} } \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:{t}\centerdot{J}_{\nu} \left(\alpha{t}\right){J}_{\nu} \left(\beta{t}\right)\mathrm{d}{t}=\frac{\mathrm{1}}{\alpha}\centerdot\delta\left(\alpha−\beta\right) \\…
Question Number 218975 by SdC355 last updated on 18/Apr/25 $$\mathrm{In}\:\mathrm{physics}\:,\:\mathrm{Flux}\:\mathrm{integral}\:\oint_{\:\partial\boldsymbol{\mathcal{S}}} \:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\centerdot\:\mathrm{d}\overset{\rightarrow} {\boldsymbol{\mathrm{S}}}\:\mathrm{is}\:\mathrm{a}\: \\ $$$$\mathrm{concept}\:\mathrm{that}\:\mathrm{widely}\:\mathrm{used}\:\mathrm{in}\:\mathrm{eletric}\:\mathrm{equation}\:\mathrm{or} \\ $$$$\mathrm{Heat}\:\mathrm{Eqaution} \\ $$$$\mathrm{for}\:\mathrm{example}…..\: \\ $$$$\oint_{\:{A}} \:\overset{\rightarrow} {\boldsymbol{\mathrm{D}}}\centerdot\mathrm{d}\overset{\rightarrow} {\boldsymbol{\mathrm{A}}}={Q}_{\mathrm{0}} \:\left(\mathrm{Gauss}\:\mathrm{law}\right)\:\overset{\rightarrow}…