Category: Relation and Functions

Question Number 133168 by bemath last updated on 19/Feb/21 Answered by floor(10²Eta[1]) last updated on 19/Feb/21 $$\mathrm{x}\to 1-\frac{1}{\mathrm{x}}$$$$\left(\mathrm{I}\right):\mathrm{f}\left(\frac{\mathrm{x}}{\mathrm{x}-1}\right)+\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)=\frac{\mathrm{x}-1}{\mathrm{x}}$$$$\mathrm{but}\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)=\mathrm{x}-\mathrm{f}(1-\mathrm{x}),\mathrm{so}$$$$\mathrm{f}\left(\frac{\mathrm{x}}{\mathrm{x}-1}\right)+\mathrm{x}-\mathrm{f}(1-\mathrm{x})=\frac{\mathrm{x}-1}{\mathrm{x}}$$$$\left(\mathrm{II}\right):\:\mathrm{f}\left(\frac{\mathrm{x}}{\mathrm{x}−\mathrm{1}}\right)−\mathrm{f}\left(\mathrm{1}−\mathrm{x}\right)=\frac{−\mathrm{x}^{\mathrm{2}}…

Question Number 133122 by abdomsup last updated on 19/Feb/21 $$let{V}_n=\sum _{k=0}^n\frac{1}{\sqrt{n^2+1}}$$$$findaewivalentof{V}_n(n⌣\mathrm{\infty })$$ Terms of Service Privacy Policy Contact:…

Question Number 67540 by mathmax by abdo last updated on 28/Aug/19 $$provethat\mid \mathrm{\Gamma }(\frac{1}{2}+it)\mid =\sqrt{\frac{2\pi }{e^{\pi t}+e^{-\pi t}}}$$$$and\mid \mathrm{\Gamma }(1+it)\mid =\sqrt{\frac{2\pi t}{e^{\pi t}-e^{-\pi t}}}$$ Commented by ~ À ®…

Question Number 67537 by mathmax by abdo last updated on 28/Aug/19 $$provethat\frac{1}{\mathrm{\Gamma }\left(z\right)}=z{e}^{\gamma z}\prod _{n=1}^{\mathrm{\infty }}(1+\frac{z}{n})e^{-\frac{z}{n}}$$ Commented by ~ À ® @ 237 ~…

Question Number 67532 by mathmax by abdo last updated on 28/Aug/19 $$provethat\pi cotan\left(\pi \alpha \right)={lim}_{n\to +\mathrm{\infty }}\sum _{k=-n}^n\frac{1}{\alpha -k}$$ Commented by ~ À ® @ 237 ~…