Intereting Posts

How to prove $4\times{_2F_1}(-1/4,3/4;7/4;(2-\sqrt3)/4)-{_2F_1}(3/4,3/4;7/4;(2-\sqrt3)/4)\stackrel?=\frac{3\sqrt{2+\sqrt3}}{\sqrt2}$
Showing that $a \mid b$ and $b \mid a$ if and only if $a= \pm b$.
a question about fixed-point-free automorphism
Linear optimization problem.
$|f(x)-f(y)|\geq k|x-y|$.Then $f$ is bijective and its inverse is continuous.
Count the number of topological sorts for poset (A|)?
Prob. 1, Chap. 6, in Baby Rudin: If $f(x_0)=1$ and $f(x)=0$ for all $x \neq x_0$, then $\int f\ \mathrm{d}\alpha=0$
Union of closure of sets is the closure of the union: true for finite, false for infinite unions
Prove that $\frac{a^2}{a + b} + \frac{b^2}{b + c} + \frac{c^2}{c + a} \ge \frac{3}{2}$
When does $\sum\frac{1}{(n\ln n)^a}$ converge?
Characteristic function of Normal random variable squared
Entire function with vanishing derivatives?
Normal Intersection of Parabola
Using the LRT statistic to test $H_0$ vs $H_1$
Identity for a weighted sum of sines / sines with different amplitudes

Could anyone solve this integration?

$$\int_0^L \frac{\cos(2 \pi x /\ell)}{t^2+x^2} \, dx$$

- Is $\lim_{n \rightarrow \infty} a_{n+1}/a_n=L \implies \lim_{n \rightarrow \infty} \sqrt {a_n}=L$ true? If not, is there a counter example?
- Find the limit of $(2\sin x-\sin 2x)/(x-\sin x)$ as $x\to 0$ without L'Hôpital's rule
- Finding the sum- $x+x^{2}+x^{4}+x^{8}+x^{16}\cdots$
- Prove that the integral of an even function is odd
- Inequality $\sum\limits_{1\le k\le n}\frac{\sin kx}{k}\ge 0$ (Fejer-Jackson)
- Suppose $f(0) = f(1) = 0$ and $f(x_0) = 1$. Show that there is $\rho$ with $\lvert f'(\rho) \rvert \geq 2$.

- How do I differentiate this integral?
- Can we differentiate equations without changing the solutions?
- Arithmetic-geometric mean of 3 numbers
- Why do we say the harmonic series is divergent?
- Please show $\int_0^\infty x^{2n} e^{-x^2}\mathrm dx=\frac{(2n)!}{2^{2n}n!}\frac{\sqrt{\pi}}{2}$ without gamma function?
- Proving $\left( \sum_{n=-\infty}^{\infty} e^{-\pi n^2} \right)^2= 1 + 4 \sum_{n=0}^{\infty} \frac{(-1)^n}{e^{(2n+1)\pi} - 1}$
- Determining if a quadratic polynomial is always positive
- Proving $f'(1)$ exist for $f$ satisfying $f(xy)=xf(y)+yf(x)$
- What is vector division?
- Rewrite an Integeral according to elliptic function of the second kind

- Is there a reason why the number of non-isomorphic graphs with $v=4$ is odd?
- The sup norm on $C$ is not equivalent to another one, induced by some inner product
- lower bound for the prime number function
- Sum of tangent functions where arguments are in specific arithmetic series
- Modulus of Fraction
- number of table with $1$ and $-1$
- geometric motivation for negative self-intersection
- History of the theory of equations: John Colson
- Where to go after calculus?
- Rotation invariant tensors
- Why is a general formula for Kostka numbers “unlikely” to exist?
- Combination of quadratic and arithmetic series
- Is a proposition about something which doesn't exist true or false?
- What is the universal cover of SL(2,R)?
- Inverse function of $\operatorname{li}(x)$ over $x>\mu$?