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 Apr 8 comment How to deduce that $1\cdot 1 + 2\cdot 1 + 2\cdot 2 + 3\cdot 1+3\cdot 2+3\cdot 3 +…+(n\cdot n) = n(n+1)(n+2)(3n+1)/24$ Try proof by induction ? Apr 6 revised Solving $z=w/2-\sin(tw)/(2t)$ for $w$ deleted 140 characters in body Apr 4 accepted Solving $z=w/2-\sin(tw)/(2t)$ for $w$ Apr 4 reviewed Approve Solving $z=w/2-\sin(tw)/(2t)$ for $w$ Apr 4 asked Solving $z=w/2-\sin(tw)/(2t)$ for $w$ Apr 2 accepted Question on branches and $\iff$. Mar 30 comment Question on branches and $\iff$. Thank you. So if I restrict my attention to the principal branch (and I will also assume $f$ and $g$ are continuous) then $f+ig=0\iff e^{f(x)}\cos(g(x))+ie^{f(x)}\sin(g(x))=1$ ? Mar 30 revised Question on branches and $\iff$. added 68 characters in body Mar 30 revised Question on branches and $\iff$. added 8 characters in body Mar 30 asked Question on branches and $\iff$. Mar 30 revised $(\delta,\varepsilon)$ Proof of Limit added 8 characters in body Mar 30 revised $(\delta,\varepsilon)$ Proof of Limit added 523 characters in body Mar 30 revised $(\delta,\varepsilon)$ Proof of Limit added 2 characters in body Mar 30 answered $(\delta,\varepsilon)$ Proof of Limit Mar 27 comment What does $O\left(\frac{1}{\log\log T}\right)$ mean? Thanks. That's what I thought. So basically what the paper says is that as $T\to\infty$ the number of zeros outside the region is some constant multiple of $1/(\log\log T)$ ? Mar 26 revised What does $O\left(\frac{1}{\log\log T}\right)$ mean? added 16 characters in body Mar 26 asked What does $O\left(\frac{1}{\log\log T}\right)$ mean? Mar 25 comment Series with $e^{\frac{1}{n}}$ Shouldn't that be $+O(n^{-4})$ in your equality? Mar 25 comment Series with $e^{\frac{1}{n}}$ You could first try expanding $e^{1/n}$ to some order ($O(1/n^k)$). Presumably the value of $k$ will be related to the existence of $1/(2n^2)$ in your summand. Then simplify if possible, and see what happens from there. Haven't tried it so can't be 100% sure, but that's what I'd do first. Mar 24 comment Complex integration confusion Try $z=e^{i\theta}$, where $\theta\in[0,2\pi]$.