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Oct
15
asked In proving $b^n = a$, how does one choose ${n \choose k} b^k \frac{1}{m_k^{n-k}} < \frac{\delta}{n}$?
Oct
15
revised Evaluate $\int_{\partial C} \frac{dz}{(z-a)(z-b)}$ where $\partial C$ is the boundary of a rectangle ($a$ and $b$ are not on $\partial C$)
There's more than my suggested ways of looking at the points a and b. See answers.
Oct
15
comment Prove: Convergent sequences are bounded
Helpful even two years later!
Oct
15
asked Does $\sum_{n=1}^\infty \frac{(-1)^n}{n^{1+\frac{1}{n}}}$ converge?
Oct
14
accepted Evaluate $\int_{\partial C} \frac{dz}{(z-a)(z-b)}$ where $\partial C$ is the boundary of a rectangle ($a$ and $b$ are not on $\partial C$)
Oct
14
accepted Does the series $\sum_{n=1}^\infty \frac{n+1}{n^3+10n}$ converge?
Oct
14
asked Does the series $\sum_{n=1}^\infty \frac{(-1)^n}{n^{1+\frac{1}{n}}}$ converge?
Oct
13
asked Does the series $\sum_{n=1}^\infty \frac{n+1}{n^3+10n}$ converge?
Oct
13
awarded  Tumbleweed
Oct
13
asked Evaluate $\int_{\partial C} \frac{dz}{(z-a)(z-b)}$ where $\partial C$ is the boundary of a rectangle ($a$ and $b$ are not on $\partial C$)
Oct
10
accepted First four terms of the power series of $f(z) = \frac{z}{e^z-1}$?
Oct
10
accepted Prove that the square root and exponent of a function in a $\limsup$ equals the the square root and exponent of a $\limsup$ of the function?
Oct
10
asked First four terms of the power series of $f(z) = \frac{z}{e^z-1}$?
Oct
10
awarded  Yearling
Oct
10
accepted Derive branch cuts for $\log(\sqrt{1-z^2} + iz)$ as $(-\infty,-1)$ and $(1,\infty)$?
Oct
10
comment Show $f(z) = \frac{z}{e^z-1}$ is analytic in the neighborhood of the origin and find the first 4 terms in its power series representation
So, I should be able to show that $z$ is analytic and $1/(e^z-1)$ is analytic, thus their product is analytic everywhere except at $z=0$?
Oct
10
comment Show $f(z) = \frac{z}{e^z-1}$ is analytic in the neighborhood of the origin and find the first 4 terms in its power series representation
the derivative of $e^z$ is $e^z$ so it is $1$...
Oct
10
comment Show $f(z) = \frac{z}{e^z-1}$ is analytic in the neighborhood of the origin and find the first 4 terms in its power series representation
How would one show this?
Oct
10
revised Show $f(z) = \frac{z}{e^z-1}$ is analytic in the neighborhood of the origin and find the first 4 terms in its power series representation
added 160 characters in body
Oct
10
comment Show $f(z) = \frac{z}{e^z-1}$ is analytic in the neighborhood of the origin and find the first 4 terms in its power series representation
I'm not sure if that helps. Then I can get $\frac{x+iy}{e^x \cos y + i e^x \sin y - 1}$ but I'm still not able to separate out the imaginary from the real components?