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Given $z_0inmathbb Csetminus{-1}$, define the sequence $$z_{n+1}=frac{2sqrt{z_n}}{1+z_n}$$ where the square root is the one with positive real part (or, if that's not possible, non-negative imaginary part). This is...
Asked on 11/02/2021 by mr_e_man
3 answerBy $S+S$, I mean ${x+y,$ with $x,y in S}$. By equidistributed, I mean equidistributed in residue classes, as defined here (the definition is very intuitive, and...
Asked on 11/02/2021 by Vincent Granville
1 answerI am wondering how to evaluate the indefinite integral $$int frac{dx}{sin(ln(x))} quad (1)$$Attempt 1 I tried using Weierstrass substitution.The Weierstrass substitution, (named after K.Weierstrass (1815)), is a substitution used...
Asked on 11/02/2021
6 answerIs there any difference between answers of $[1]$ and $[2]$?$$Bigglfloorfrac12+frac1{2^2}+frac1{2^3}+cdotsBiggrfloor tag*{$space.....[1]$}$$$$lim _{n rightarrow infty} Bigglfloorfrac{1}{2}+frac{1}{2^{2}}+frac{1}{2^{3}}+cdots+frac{1}{2^{n}}Biggrfloor tag*{$ space.....[2] $}$$ If yes then please do...
Asked on 11/02/2021 by dRIFT sPEED
2 answerFrom a uniform disk of radius $R$ a circular disk of radius $frac{R}{2}$ is being cut out. The center...
Asked on 11/02/2021
6 answerLet $f,g:mathbb{R}^ntomathbb{R}$ be such that $nabla f=nabla g$. I believe this implies that $f$ and $g$ only differ by a constant, like in the one-dimensional...
Asked on 11/02/2021
4 answerWhat loops are possible when doing this function to the rationals? Let's define this function on a simplified fraction $frac{a}{b}$. $$fleft(frac{a}{b}right)=frac{a+b}{b+1}$$ I started this with $f(frac{2}{3})=frac{5}{4}$ then...
Asked on 11/02/2021 by user808945
2 answerAs part of my answer to another question, I needed the following fact: if $S = {1, ldots, n}$ and $k leq n/2$, then there is a...
Asked on 11/01/2021 by Gregory J. Puleo
2 answerHow can determine the radius $r$ of 4 identical circles inside equilateral triangle $ABC$ of side $a$ ? ...
Asked on 11/01/2021 by user766881
5 answerLet the above expression be equal to $phi$$$frac{tan phi +1}{tan phi-1}=sqrt{frac{1+x^2}{1-x^2}}$$$$frac{1+tan^2phi +2tan phi}{1+tan^2 phi-2tan phi}=frac{1+x^2}{1-x^2}$$ $$frac{1+tan^2phi}{2tan phi }=frac{1}{x^2}$$$$sin 2phi=x^2$$$$phi=frac{pi}{4}-frac 12...
Asked on 11/01/2021
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