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Apr
13
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.
Apr
13
answered Calculate $\int_\Gamma ze^{z}dz$ where $\Gamma$ is line from point $z_1=0$ to point $z_2=\frac{\pi i}{2}$
Apr
12
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.
Apr
12
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.
Apr
11
revised Calculating the lie algebra of $SO(2,1)$
added 1 character in body
Apr
8
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!
Apr
8
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...
Apr
8
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
Apr
8
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
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