pbs
Reputation
2,597
Top tag
Next privilege 3,000 Rep.
 Apr13 comment Calculate $\int_\Gamma ze^{z}dz$ where $\Gamma$ is line from point $z_1=0$ to point $z_2=\frac{\pi i}{2}$ @user227317 yes. See my answer for full details, but you got the answer! You can also use Blatter's approach too. Apr13 answered Calculate $\int_\Gamma ze^{z}dz$ where $\Gamma$ is line from point $z_1=0$ to point $z_2=\frac{\pi i}{2}$ Apr12 comment Calculate $\int_\Gamma ze^{z}dz$ where $\Gamma$ is line from point $z_1=0$ to point $z_2=\frac{\pi i}{2}$ @user227317 no, as I said use the substitution $z=it$. Also @ JessicaK's solution will also work. See also @ ChrisrianBlatter's answer. Apr12 comment Calculate $\int_\Gamma ze^{z}dz$ where $\Gamma$ is line from point $z_1=0$ to point $z_2=\frac{\pi i}{2}$ You need to parametrize the curve $\Gamma$, e.g. let $z(t)=it$ where $t\in[0,\pi/2]$. Looks like integration by parts may be helpful too. Apr11 revised Calculating the lie algebra of $SO(2,1)$ added 1 character in body Apr8 comment $F(x)+G(y)= e^{x+y}?$ Yes, the way it is written confused me for a moment. However, on expanding the middle equality now I clearly see it does equal $F(1)-F(0)$. I was looking at what you had written from a different perspective - I was trying to construct the middle equality from the first by rearranging the original equation. Sorted now I see clearly what's happing - that "old trick" of adding something and then taking it away, so yes maybe best read right to left. +1 for your answer! Apr8 comment $F(x)+G(y)= e^{x+y}?$ I could be wrong, but shouldn't the middle equality be $-G(y)+e^{1+y}-(-G(y)+e^y)$ ? Maybe it's equivalent... Apr8 revised How to deduce that $1\cdot 1 + 2\cdot 1 + 2\cdot 2 + 3\cdot 1+3\cdot 2+3\cdot 3 +…+(n\cdot n) = n(n+1)(n+2)(3n+1)/24$ edited title Apr8 revised How to deduce that $1\cdot 1 + 2\cdot 1 + 2\cdot 2 + 3\cdot 1+3\cdot 2+3\cdot 3 +…+(n\cdot n) = n(n+1)(n+2)(3n+1)/24$ added 18 characters in body Apr8 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 ? Apr6 revised Solving $z=w/2-\sin(tw)/(2t)$ for $w$ deleted 140 characters in body Apr4 accepted Solving $z=w/2-\sin(tw)/(2t)$ for $w$ Apr4 reviewed Approve Solving $z=w/2-\sin(tw)/(2t)$ for $w$ Apr4 asked Solving $z=w/2-\sin(tw)/(2t)$ for $w$ Apr2 accepted Question on branches and $\iff$. Mar30 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 $f+ig=0\iff e^{f(x)}\cos(g(x))+ie^{f(x)}\sin(g(x))=1$ ? Mar30 revised Question on branches and $\iff$. added 68 characters in body Mar30 revised Question on branches and $\iff$. added 8 characters in body Mar30 asked Question on branches and $\iff$. Mar30 revised $(\delta,\varepsilon)$ Proof of Limit added 8 characters in body