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Category: Integration

let-give-A-p-0-pi-t-p-cos-nx-with-nand-p-from-N-1-find-a-relation-between-A-p-and-A-p-2-2-find-arelation-between-A-2p-and-A-2p-2-3-find-a-relation-betweer-A-2p-1-and-A-2p

Question Number 28071 by abdo imad last updated on 20/Jan/18 $${let}\:{give}\:\:{A}_{{p}} =\:\int_{\mathrm{0}} ^{\pi} \:{t}^{{p}} \:{cos}\left({nx}\right)\:\:{with}\:{nand}\:{p}\:{from}\:{N} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{relation}\:{between}\:\:{A}_{{p}} \:{and}\:{A}_{{p}−\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{arelation}\:{between}\:\:{A}_{\mathrm{2}{p}} \:\:{and}\:{A}_{\mathrm{2}{p}−\mathrm{2}} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{a}\:{relation}?{betweer}\:{A}_{\mathrm{2}{p}+\mathrm{1}} \:{and}\:\:{A}_{\mathrm{2}{p}−\mathrm{1}} \\…

let-give-the-function-f-x-x-4-2pi-periodic-and-even-developp-f-atfourier-series-

Question Number 28072 by abdo imad last updated on 20/Jan/18 $${let}\:{give}\:{the}\:{function}\:\:{f}\left({x}\right)={x}^{\mathrm{4}} \:\:\:\mathrm{2}\pi\:{periodic}\:{and}\:{even} \\ $$$${developp}\:\:\:{f}\:{atfourier}\:{series}. \\ $$ Commented by abdo imad last updated on 26/Jan/18 $${f}\left(−{x}\right)={f}\left({x}\right)\:{and}\:{f}\:\mathrm{2}\pi\:{periodic}\:{so}…

Question-159143

Question Number 159143 by mnjuly1970 last updated on 13/Nov/21 Answered by qaz last updated on 14/Nov/21 $$\mathrm{S}=\frac{\mathrm{1}}{\Gamma\left(\mathrm{4}\right)}\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\Gamma\left(\mathrm{4n}+\mathrm{1}\right)\Gamma\left(\mathrm{4}\right)}{\Gamma\left(\mathrm{4n}+\mathrm{5}\right)} \\ $$$$=\frac{\mathrm{1}}{\mathrm{6}}\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{x}^{\mathrm{4n}}…

let-give-I-a-0-t-a-1-1-t-dt-by-using-Residus-theorem-find-the-value-of-I-a-with-0-lt-a-lt-1-

Question Number 28068 by abdo imad last updated on 19/Jan/18 $${let}\:{give}\:\:\:{I}_{{a}} \:\:=\:\:\int_{\mathrm{0}} ^{+\propto} \:\:\:\:\frac{{t}^{{a}−\mathrm{1}} }{\mathrm{1}+{t}}{dt}\:\:\:{by}\:{using}\:{Residus}\:{theorem} \\ $$$${find}\:{the}\:{value}\:{of}\:\:{I}_{{a}} \:\:\:\:\:{with}\:\:\mathrm{0}<{a}<\mathrm{1}\:\:\:. \\ $$ Terms of Service Privacy Policy…