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0-J-s-e-s-s-2-R-2-ds-R-R-R-0-

Question Number 219637 by SdC355 last updated on 30/Apr/25 $$\int_{\mathrm{0}} ^{\:\infty} \:\:\frac{{J}_{\nu} \left({s}\right){e}^{−\mu{s}} }{\:\sqrt{{s}^{\mathrm{2}} +{R}^{\mathrm{2}} }}\mathrm{d}{s}\:,\:\left(\nu,\mu\in\mathbb{R}^{+} \:,\:\mathrm{R}\in\mathbb{R}^{+} \backslash\left\{\mathrm{0}\right\}\right) \\ $$ Terms of Service Privacy Policy…

0-sin-z-z-z-2-4-dz-1-4-0-sin-z-z-sin-z-2z-4i-sin-z-2z-4i-dz-and-next-2pii-j-1-M-Res-h-a-j-f-h-

Question Number 219574 by SdC355 last updated on 29/Apr/25 $$\int_{\mathrm{0}} ^{\:\infty} \:\:\frac{\mathrm{sin}\left({z}\right)}{{z}\left({z}^{\mathrm{2}} +\mathrm{4}\right)}\:\mathrm{d}{z}=\frac{\mathrm{1}}{\mathrm{4}}\int_{\mathrm{0}} ^{\:\infty} \:\:\left(\frac{\mathrm{sin}\left({z}\right)}{{z}}−\frac{\mathrm{sin}\left({z}\right)}{\mathrm{2}{z}+\mathrm{4}\boldsymbol{{i}}}−\frac{\mathrm{sin}\left({z}\right)}{\mathrm{2}{z}−\mathrm{4}\boldsymbol{{i}}}\right)\:\mathrm{d}{z} \\ $$$$\mathrm{and}\:\mathrm{next}….??? \\ $$$$\mathrm{2}\pi\boldsymbol{{i}}\underset{{j}=\mathrm{1}} {\overset{{M}} {\sum}}\:\:\mathrm{Res}_{{h}={a}_{{j}} } \left\{{f}\left({h}\right)\right\}…. \\ $$…

pls-Help-prove-S-g-dS-0-div-g-0-

Question Number 219571 by SdC355 last updated on 29/Apr/25 $$\mathrm{pls}\:\mathrm{Help}…..! \\ $$$$\mathrm{prove} \\ $$$$\int\int_{\:\boldsymbol{\mathcal{S}}} \:\overset{\rightarrow} {\boldsymbol{\mathrm{g}}}\centerdot\mathrm{d}\overset{\rightarrow} {\boldsymbol{\mathcal{S}}}=\mathrm{0}\:\leftrightarrows\:\mathrm{div}\:\overset{\rightarrow} {\boldsymbol{\mathrm{g}}}=\mathrm{0} \\ $$ Answered by aleks041103 last updated…