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1d
asked Find the first three terms of the maclaurin series of $\tanh(z)$ and its radius of convergence
2d
asked In proving “if a set is compact, then it must be closed”, why does the finite subcover behave differently than the infinite open cover?
Oct
21
asked Find the Laurent series of $f(z) = \frac{1}{z-2} + \frac{1}{z-3}$ for $2 < |z| < 3$ and for $|z| > 3$
Oct
21
asked Deduce the Bolzano-Weierstrass Theorem from the Heine-Borel Theorem
Oct
18
asked Prove if $a$ is a nonnegative real number and $n$ is a positive integer, there exists a $b \geq 0$ such that $b^n = a$
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
asked Does $\sum_{n=1}^\infty \frac{(-1)^n}{n^{1+\frac{1}{n}}}$ 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
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
asked First four terms of the power series of $f(z) = \frac{z}{e^z-1}$?
Oct
9
asked 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
Oct
8
asked Derive branch cuts for $\log(\sqrt{1-z^2} + iz)$ as $(-\infty,-1)$ and $(1,\infty)$?
Oct
7
asked How do we define the branch cuts for $\sin^{-1}z = \frac{1}{i} \log(\sqrt{1-z^2} + iz)$ as $(-\infty,-1)$ and $(1,\infty)$?
Oct
6
asked How does one define appropriate branch cuts for arcsin(z) in the complex plane?
Oct
5
asked Convergence of $\sum_{n=0}^\infty (-1)^n (e-(1+\frac{1}{n})^n)$
Oct
5
asked How do I show that $\lim_{n \to \infty} (1 + \frac{1}{n+1})^{2n} = e^2$?
Oct
4
asked Why does $ \frac{b^n-a^n}{b-a}=\sum_{k=1}^nb^{n-k}a^{k-1}$?
Oct
4
asked Does $\sum_{n=0}^\infty \left(\frac{n}{n+1}\right)^{2n}$ converge?
Oct
3
asked Assume $a_1 > 1$. Find the limit of $a_{n+1} = 2 - ( \frac{1}{a_n} + a_n )$.