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Feb
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Oct
29
awarded  Popular Question
Oct
18
comment $\sum_{n=0}^{\infty} \sin (nx) = \cot(x/2)$?
I think it should be $$\sum_{k=1}^\infty 2\sin(k x) = \cot(\frac{x}{2})$$
Oct
18
comment Does the series $\sum{(\frac{1}{n^2} - \frac{1}{n})}$ converge or diverge?
@SyedMuhammadAsad yeah that is correct
Oct
13
answered suppose $A$ is a set where $x \in A \iff x + T \in A$ and $\mu$ denotes the lesbesque measure. prove that $\mu(A\cap[0,T]) = \mu(A\cap[a,a+T]) $
Oct
13
comment suppose $A$ is a set where $x \in A \iff x + T \in A$ and $\mu$ denotes the lesbesque measure. prove that $\mu(A\cap[0,T]) = \mu(A\cap[a,a+T]) $
Why should the set $A$ be measurable?
Oct
9
comment If a $p$ is prime number, for some $p$ ,fraction $1/p$ ,is decimal is $p-1$ period repetition, can anyone prove it?
you mean like for $p=2$ or like $p=3$ or $p=5$ ? in these cases they don't have a period repeatation or of the wrong length. What exactly is your question?
Oct
9
comment Compute the integral over these paths
@beak why? what is different there`?
Oct
9
comment Compute the integral over these paths
@baek yeah and split it up in the four paths you already gave us. The integral you get is always of the form $\int \frac{1}{t+c} \, \mathrm{d}t$ if you factor out some constants and this shouldn't be that hard
Oct
9
comment Compute the integral over these paths
@DanielFischer I assumed that it is one path $C:[0,4]\to \mathbb{C}$ so it is just the boundary of a square where one singularity is in the interior of the closed curve
Oct
9
comment Compute the integral over these paths
@beak well then just ignore that part. Later in the lecture you will see that the line integral (for holomorphic functions) is not only well defined on the set of all curves but even on the quotient where you say that two curves are equivalent if they are homotopic. Just use the definition of line integral
Oct
9
comment Question on infinite T4 topological space
Before I start thinking, is $T_4$ for you stronger than $T_2$ or incomparable?
Oct
9
answered Compute the integral over these paths
Oct
6
revised Limit of $\frac{\frac{1}{e}(1+x)^{1/x}-1+\frac{x}{2}}{x^2}$ when $x\to0$
added 559 characters in body
Oct
6
comment Inner Product for Functions
Well you should point out, that the nontrivial part is to proof that $\langle f,f\rangle=0$ iff $f=0$
Oct
6
revised Limit of $\frac{\frac{1}{e}(1+x)^{1/x}-1+\frac{x}{2}}{x^2}$ when $x\to0$
added 21 characters in body
Oct
6
revised Limit of $\frac{\frac{1}{e}(1+x)^{1/x}-1+\frac{x}{2}}{x^2}$ when $x\to0$
added 335 characters in body