Prove equation using Bessel functions: $\frac{d}{dx}[xJ_n(x)J_{n+1}(x)]=x[J_n^{2}(x)-J_{n+1}^{2}(x)]$
125061
Bessel function equation with derivation: $\frac{d}{dx} (xJ_{\alpha}(x)J_{\alpha+1}(x)) = x(J_{\alpha}^2(x)-J_{\alpha +1}^2(x))$
102334
How can you prove $\frac{n(n+1)(2n+1)}{6}+(n+1)^2= \frac{(n+1)(n+2)(2n+3)}{6}$ without much effort?
131581
Convert $\frac{d^2y}{dx^2}+x^2y=0$ to Bessel equivalent and show that its solution is $\sqrt x(AJ_{1/4}+BJ_{-1/4})$
44438
Prove : $\frac{\cos(x_1) +\cos(x_2) +\cdots+\cos(x_{10})}{\sin(x_1) +\sin(x_2) +\cdots+\sin(x_{10})} \ge 3$
71708
Proving that $\left( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} \right) \lvert f(z) \rvert^2 = 4 \lvert f'(z) \rvert^2$
17241
How to prove $ \prod_{d|n} d= n^{\frac{\tau (n)}{2}}$
80553
Show that,$\int_0^\pi \left|\frac{\sin nx}{x}\right|\mathrm{d}x \ge \frac{2}{\pi}\left(1+\frac12+\cdots+\frac{1}{n}\right)$
150642
How to prove $\sum^n_{i=1} \frac{1}{i(i+1)} = \frac{n}{n+1}$?
49806
Prove that $\frac{R/ \ker \phi}{(\ker \phi + J)/ \ker \phi} \cong \frac{S}{\phi(J)}$
131120
Proving an integral equation.
50972
Prove that $\sum_{x=1}^{n} \frac{1}{x (x+1)(x+2)} = \frac{1}{4} - \frac{1}{2 (n+1) (n+2)}$
14763
How to prove $\frac{1}{4}(\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{d}+\frac{d^2}{a})\ge \sqrt[4]{\frac{a^4+b^4+c^4+d^4}{4}}$
32823
Prove $\forall n \in \mathbb{N}: \int_{0}^{\frac{\pi}{2}} |\frac{\sin(nx)}{x}|dx \geq \frac{2}{\pi}\sum_{k=1}^{n}\frac{1}{k}$
147648
Proving $\frac{a}{a^2-a+1}+\frac{b}{b^2-b+1}+\frac{c}{c^2-c+1}+\frac{d}{d^2-d+1}\le \frac{8}{3}$ given $a+b+c+d=2$
90218
Proving $\frac{x}{y} +\frac{y}{z} + \frac{z}{x} \ge 3$ for positive $x,y,z$
145509
Prove the roots of $p(z)+z^n\bar{p}(\frac{1}{z})$ lie on the unit circle
156766
Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$