Question Number 213877 by issac last updated on 20/Nov/24 $$\mathrm{evaluate}. \\ $$$$\int_{−\pi} ^{\:+\pi} \:\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{3cos}^{\mathrm{2}} \left({z}\right)}\:\mathrm{d}{z} \\ $$$$\mathrm{real}\:\mathrm{analysis}\:\mathrm{method}: \\ $$$$\mathrm{complex}\:\mathrm{analysis}\:\mathrm{method}: \\ $$ Terms of Service Privacy…
Question Number 213871 by 073 last updated on 19/Nov/24 Commented by Frix last updated on 20/Nov/24 $$\mathrm{Elliptic}\:\mathrm{Integral}: \\ $$$$\mathrm{4}\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\sqrt{{a}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} \:{x}\:+{b}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \:{x}}\:{dx}\:=\mathrm{4}{a}\mathrm{E}\:\frac{{a}^{\mathrm{2}}…
Question Number 213862 by issac last updated on 19/Nov/24 $$\mathrm{Help}\:\mathrm{me}…..!!!\:\::\left(\:\:\right. \\ $$$$\mathrm{complex}\:\mathrm{anaylsis}\:\mathrm{problem}.. \\ $$$${f}\left({z}\right)\:\mathrm{is}\:\mathrm{entire}\:\mathrm{in}\:\mathrm{path}\:{C}\: \\ $$$$\mathrm{entire}:\:\mathrm{Differantiable}\:\mathrm{complex}\:\mathrm{function} \\ $$$$\mathrm{mean}\:{f}\left({z}\right)\:\mathrm{satisfy}\:{f}\left({z}\right)={u}\left({x},{y}\right)+\boldsymbol{{i}}\centerdot{v}\left({x},{y}\right)\:\: \\ $$$$\frac{\partial{u}}{\partial{x}}=−\frac{\partial{v}}{\partial{y}}\:\mathrm{or}\:\:\frac{\partial{u}}{\partial{y}}=−\frac{\partial{v}}{\partial{x}}\:\left(\mathrm{couchy}-\mathrm{riemann}\right) \\ $$$$\mathrm{show}\:\mathrm{that}\:\int_{\:{C}} \:\frac{{f}\left({z}\right)}{{f}'\left({z}\right)}\:\mathrm{d}{z}=\mathrm{2}\pi\boldsymbol{{i}}\underset{{h}=\mathrm{1}} {\overset{{M}} {\sum}}\:{P}_{{h}}…
Question Number 213846 by issac last updated on 18/Nov/24 $$\mathrm{path}\:\mathscr{C}\:\mathrm{is}\:\mathrm{closed} \\ $$$${f}\:\mathrm{is}\:\mathrm{regular}\:\mathrm{function}\:\mathrm{in}\:\mathrm{Path}\:\mathscr{C} \\ $$$${f}\:\mathrm{is}\:\mathrm{have}\:\mathrm{zero}\:\mathrm{point}\:\mathrm{and}\:\mathrm{poles}\:\mathrm{in}\:\mathscr{C} \\ $$$$\mathrm{show}\:\mathrm{that}\: \\ $$$$\oint_{\:\mathscr{C}} \:\frac{{f}\left({z}\right)}{{f}'\left({z}\right)}\:\mathrm{d}{z}=\mathrm{2}\pi\boldsymbol{{i}}\left({Z}−{P}\right) \\ $$$$\mathrm{and}\:\mathrm{if}\:\mathrm{poles}\:\mathrm{are}\:\mathrm{not}\:\mathrm{exist} \\ $$$$\mathrm{show}\:\mathrm{that} \\ $$$$\oint_{\:\mathscr{C}\:}…
Question Number 213790 by issac last updated on 16/Nov/24 $$\mathrm{So}\:\mathrm{Weird}…… \\ $$$$\int_{\mathrm{0}} ^{\:\infty} {J}_{\nu} \left({t}\right){e}^{−{st}} \mathrm{d}{t}=\frac{\left({s}+\sqrt{{s}^{\mathrm{2}} +\mathrm{1}}\right)^{−\nu} }{\:\sqrt{{s}^{\mathrm{2}} +\mathrm{1}}}\: \\ $$$${J}_{−\nu} \left({t}\right)=\left(−\mathrm{1}\right)^{\nu} {J}_{\nu} \left({t}\right)\:\: \\…
Question Number 213764 by Hanuda354 last updated on 16/Nov/24 Answered by mr W last updated on 16/Nov/24 $$\left(\mathrm{1}\right)\:\mathrm{4}−\mathrm{1}−\mathrm{3}−\mathrm{2} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{4}−\mathrm{3}−\mathrm{1}−\mathrm{2} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{1}−\mathrm{4}−\mathrm{3}−\mathrm{2} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{1}−\mathrm{4}−\mathrm{2}−\mathrm{3} \\…
Question Number 213725 by zakirullah last updated on 14/Nov/24 $${please}\:{prove}\:\frac{\mathrm{1}}{{x}}\:=\:{x}^{−\mathrm{1}} \\ $$ Answered by Rasheed.Sindhi last updated on 14/Nov/24 $$\:\:\:\:\:\frac{\mathrm{1}}{{x}}=\frac{{x}^{\mathrm{0}} }{{x}^{\mathrm{1}} }={x}^{\mathrm{0}−\mathrm{1}} ={x}^{−\mathrm{1}} \\ $$…
Question Number 213713 by issac last updated on 14/Nov/24 $$\mathrm{Does}\:\mathrm{Volume}\:\mathrm{integral}\: \\ $$$${V}=\pi\centerdot\int_{\mathrm{0}} ^{\:\infty} {J}_{\nu} ^{\:\mathrm{2}} \left({z}\right)\mathrm{d}{z}\:\mathrm{is}\:\mathrm{divergence}…?? \\ $$$${J}_{\nu} \left({z}\right)\:\mathrm{is}\:\nu\left(\mathrm{nu}\right)'\mathrm{th}\:\mathrm{Bessel}\:\mathrm{function} \\ $$ Terms of Service Privacy…
Question Number 213680 by issac last updated on 13/Nov/24 Commented by Frix last updated on 13/Nov/24 $$\mathrm{WolframAlpha} \\ $$$$\mathrm{It}'\mathrm{s}\:\mathrm{worthless}\:\mathrm{if}\:\mathrm{you}\:\mathrm{don}'\mathrm{t}\:\mathrm{understand}\:\mathrm{how} \\ $$$$\mathrm{to}\:\mathrm{get}\:\mathrm{there}. \\ $$ Commented by…
Question Number 213679 by issac last updated on 13/Nov/24 $${Q}\mathrm{213662} \\ $$$$…… \\ $$$$\mathrm{Not}\:\mathrm{easy}……. \\ $$$$\:\:_{{p}} \boldsymbol{\mathrm{F}}_{{q}} \left({z};\cancel{\underbrace{ }}\:\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\right)\:\mathrm{is}\:\mathrm{hypergeometric}\:\mathrm{function} \\ $$$$\mathrm{Li}_{\nu} \left({z}\right)\:\mathrm{is}\:\mathrm{Dilogarithm}\:\mathrm{function}. \\ $$ Terms…