Question Number 67522 by mathmax by abdo last updated on 28/Aug/19 $${let}\:{z}\:{from}\:{C}−{Z}\:\:\:\:\:{prove}\:{that} \\ $$$$\frac{\pi}{{sin}\left(\pi{z}\right)}\:=\frac{\mathrm{1}}{{z}}\:+\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} \mathrm{2}{z}}{{z}^{\mathrm{2}} −{n}^{\mathrm{2}} }\:\:{and} \\ $$$$\frac{\pi{cos}\left(\pi{z}\right)}{{sin}\left(\pi{z}\right)}\:=\frac{\mathrm{1}}{{z}}\:+\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{2}{z}}{{z}^{\mathrm{2}} −{n}^{\mathrm{2}} }…
Question Number 67520 by mathmax by abdo last updated on 28/Aug/19 $${let}\:{f}\left({x},{z}\right)\:=\frac{{z}\:{e}^{{xz}} }{{e}^{{z}} −\mathrm{1}}\:\:\:\:\:\:\left({x}\:{and}\:{z}\:{from}\:{C}\right) \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{f}\left({x},{z}\right)\:=\sum_{{n}=\mathrm{0}} ^{\infty} \:{B}_{{n}} \left({x}\right)\frac{{z}^{{n}} }{{n}!} \\ $$$${with}\:{B}_{{n}} \left({x}\right)\:{is}\:{a}\:{unitaire}\:{polynome}\:{with}\:{degre}\:{n} \\ $$$${determine}\:{B}_{{n}}…
Question Number 67521 by mathmax by abdo last updated on 28/Aug/19 $${calculate}\:\:\:{A}\left({x}\right)\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} \:{cos}\left({nx}\right)}{{n}} \\ $$$${and}\:{B}\left({x}\right)\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} \:{sin}\left({nx}\right)}{{n}} \\ $$ Terms of Service…
Question Number 67518 by mathmax by abdo last updated on 28/Aug/19 $${if}\:{z}\:={x}+{iy}\:\:\:{find}\:\:{lnz}\:\:{interms}\:{of}\:{x}\:{and}\:{y} \\ $$$$ \\ $$ Commented by mathmax by abdo last updated on 30/Aug/19…
Question Number 67519 by mathmax by abdo last updated on 28/Aug/19 $${if}\:\frac{{z}}{{e}^{{z}} −\mathrm{1}}\:=\sum_{{n}=\mathrm{0}} ^{\infty} \:{B}_{{n}} \:\frac{{z}^{{n}} }{{n}!} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{B}_{\mathrm{0}} ,{B}_{\mathrm{1}} ,{B}_{\mathrm{2}} ,{B}_{\mathrm{3}} ,{B}_{\mathrm{4}} \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:{z}\rightarrow\frac{\mathrm{1}}{{e}^{{z}}…
Question Number 1979 by prakash jain last updated on 27/Oct/15 $${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${g}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({x}+{y}\right)={f}\left({x}\right){g}\left({y}\right)+{g}\left({x}\right){f}\left({y}\right) \\ $$$${g}\left({x}+{y}\right)={f}\left({x}\right){f}\left({y}\right)+{g}\left({x}\right){g}\left({y}\right) \\ $$$${f}\left({x}\right)=? \\ $$$${g}\left({x}\right)=? \\ $$ Answered by…
Question Number 1976 by 123456 last updated on 27/Oct/15 $${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${g}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({x}+{y}\right)={f}\left({x}\right){g}\left({x}\right)+{f}\left({y}\right){g}\left({y}\right) \\ $$$${g}\left({x}+{y}\right)={f}\left({x}\right){f}\left({y}\right)+{g}\left({x}\right){g}\left({y}\right) \\ $$$$\left[{f}\left({x}\right)\right]^{\mathrm{2}} +\left[{g}\left({x}\right)\right]^{\mathrm{2}} =? \\ $$$$\left[{f}\left({x}\right)+{g}\left({y}\right)\right]\left[{g}\left({x}\right)+{f}\left({y}\right)\right]=?? \\ $$$${f}\left({x}\right)=??? \\…
Question Number 1963 by 123456 last updated on 26/Oct/15 $${f}:\left[\mathrm{0},+\infty\right)\rightarrow\mathbb{R},{a}:\mathbb{N}\rightarrow\mathbb{R} \\ $$$${a}_{{n}+\mathrm{1}} ={f}\left({a}_{{n}} \right)−{a}_{{n}} \\ $$$${f}\left({x}\right)\geqslant{f}\left({y}\right),\forall{x}\geqslant{y}\geqslant\mathrm{0} \\ $$$$\mathrm{does} \\ $$$${a}_{{n}} \geqslant{a}_{{m}} ,\forall{n}\geqslant{m}\geqslant\mathrm{0}? \\ $$ Answered…
Question Number 1956 by 123456 last updated on 26/Oct/15 $${x}_{{n}+\mathrm{1}} ={y}_{{n}} −\mathrm{1} \\ $$$${y}_{{n}+\mathrm{1}} ={x}_{{n}} +\mathrm{1} \\ $$$${x}_{\mathrm{0}} =\mathrm{1},{y}_{\mathrm{0}} =\mathrm{1} \\ $$$${x}_{\mathrm{10}} +{y}_{\mathrm{10}} =? \\…
Question Number 67461 by mathmax by abdo last updated on 27/Aug/19 $${find}\:{the}\:{value}\:{of}\:\sum_{{p}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{p}} }{\left(\mathrm{2}{p}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com