Category: Relation and Functions

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}}…

Question Number 95216 by mathmax by abdo last updated on 24/May/20 $$\mathrm{calculste}\sum _{\mathrm{n}=0}^{\mathrm{\infty }}\frac{\mathrm{n}}{{(2\mathrm{n}+1)}^2(\mathrm{n}+3)}$$ Answered by abdomathmax last updated on 25/May/20 $$\mathrm{let}\:\mathrm{S}_{\mathrm{n}}…

Question Number 95217 by mathmax by abdo last updated on 24/May/20 $$\mathrm{calculate}\sum _{\mathrm{n}=1}^{\mathrm{\infty }}\frac{{(-1)}^{\mathrm{n}}}{{\mathrm{n}}^2{(\mathrm{n}+2)}^3}$$ Answered by mathmax by abdo last…