Category: Relation and Functions

Question Number 95465 by mathmax by abdo last updated on 25/May/20 $$\mathrm{solve}{\mathrm{y}}^{{}^{″}}-{\mathrm{y}}^{{}^{\prime }}+2={\mathrm{x}}^2{\mathrm{e}}^{-\mathrm{x}}\mathrm{with}\mathrm{y}\left(0\right)=1\mathrm{and}{\mathrm{y}}^{{}^{\prime }}\left(0\right)=-1$$ Answered by mathmax by abdo last…

Question Number 29844 by abdo imad last updated on 12/Feb/18 $$letgive{f}_{\alpha }\left(t\right)=cos\left(\alpha t\right)2\pi periodicwitht\in [-\pi ,\pi ]and$$$$\alpha \in R-Z$$$$1)developp{f}_{\alpha }atfourierserieandprovethat$$$$cotan\left(\alpha \pi \right)=\frac{1}{\alpha \pi }+\sum _{n=1}^{\mathrm{\infty }}\frac{2\alpha }{\pi ({\alpha }^2-n^2)}$$$$\left.\mathrm{2}\left.\right)\left.{let}\:{x}\in\right]\mathrm{0},\pi\left[\:{ant}\:{g}\left({t}\right)={cotant}\:−\frac{\mathrm{1}}{{t}}\:\:{if}\:{t}\in\right]\mathrm{0},{x}\right]{andg}\left(\mathrm{0}\right)=\mathrm{0}…

Question Number 29841 by abdo imad last updated on 12/Feb/18 $$provethat\mathrm{\forall }x\in ]0,1[\mathrm{\Gamma }\left(x\right).\mathrm{\Gamma }(1-x)=\frac{\pi }{sin\left(\pi x\right)}$$$$\left(complimentsformula\right).$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 29839 by abdo imad last updated on 12/Feb/18 $$find\prod _{n=1}^{\mathrm{\infty }}(1-\frac{x^2}{n^2{\pi }^2}).$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 29831 by abdo imad last updated on 12/Feb/18 $$letgivef\left(x\right)=\frac{1}{1+x^2}1)provethatprovethat$$$$f^{\left(n\right)}\left(x\right)=\frac{p_n\left(x\right)}{{(1+x^2)}^{n+1}}with{p}_{n}isapolynomial$$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:{p}_{{n}+\mathrm{1}} \left({x}\right)=\left(\mathrm{1}+{x}^{\mathrm{2}} \right){p}_{{n}} ^{'} \left({x}\right)\:−\mathrm{2}\left({n}+\mathrm{1}\right){p}_{{n}}…