Intereting Posts

Define two differents vector space structures over a field on an abelian group
A binary quadratic form: $nx^2-y^2=2$
Minkowski's inequality
On inequalities for norms of matrices
How to pass from $L^2(0,T;V')$ to $\mathcal{D}'\big(\Omega\times (0,T)\big)$?
Expected number of steps/probability in a Markov Chain?
Diffeomorphisms and Stokes' theorem
Hatcher algebraic Topology $\Delta$-complex
Is the integral closure of local domain a local ring?
Defining the determinant of linear transformations as multilinear alternating form
Is the sequence $a_{n}=\prod\limits_{i=1}^{n}\left(1+\frac{i}{n^2}\right)$ decreasing?
How do we know whether certain mathematical theorems are circular?
Upper bound for zeros of holomorphic function
Every power series expansion for an entire function converges everywhere
Is $\int_a^b f(x) dx = \int_{f(a)}^{f(b)} f^{-1}(x) dx$?

How to show the following identity holds?

$$

\displaystyle\sum_{n=1}^\infty\dfrac{2z}{z^2-n^2}=\pi\cot \pi z-\dfrac{1}{z}\qquad |z|<1

$$

- Why there is no continuous argument function on $\mathbb{C}\setminus\{0\}$?
- Rouché's Theorem for $p(z)=z^7-5z^3+12$
- Harmonic functions with zeros on two lines
- Is there an elementary way to see that there is only one complex manifold structure on $R^2$?
- All the zeroes of $p(z)$ lie inside the unit disk
- Application of Cauchy Integral

- Why is it called a series?
- Suppose $\lim \limits_{n \to ∞} a_n=L$. Prove that $\lim\limits_{n \to ∞} \frac{a_1+a_2+\cdots+a_n}{n}=L$
- Quadratic Formula in Complex Variables
- Cauchy's residue theorem with an infinite number of poles
- Closed form expressions for harmonic sums
- Proof that 1-1 analytic functions have nonzero derivative
- Is there a fast technique to tell that the poles of $\frac{1}{\sin z}$ are simple?
- Need help proving this integration
- $a_{n+1}=|a_n|-a_{n-1} \implies a_n \; \text{is periodic}$
- Compute $ \sum_{k=1}^{\infty} \text{sech}(2 k)$

I have found a link which deals with this problem: people.reed.edu/~jerry/311/cotan.pdf

- Integral $I:=\int_0^1 \frac{\log^2 x}{x^2-x+1}\mathrm dx=\frac{10\pi^3}{81 \sqrt 3}$
- Show that this polynomial is positive
- how to get $dx\; dy=r\;dr\;d\theta$
- Average order of $\mathrm{rad}(n)$
- Prove: $ \frac{1}{\sin 2x} + \frac{1}{\sin 4x } + \cdots + \frac{1 }{\sin 2^n x} = \cot x – \cot 2^n x $
- Limit calculation
- Show that the set of functions $\mathbb{N}\to\{0,1\}$ is not countable
- hatchet planimeter
- Example of Artinian module that is not Noetherian
- $\forall x,y>0, x^x+y^y \geq x^y + y^x$
- Prove that the Gaussian Integer's ring is a Euclidean domain
- Integral basis of an extension of number fields
- Fermat numbers are coprime
- multiplicative group of infinite fields
- Prove that if $F_n$ is highly abundant, then so is $n$.