Welcome to my MathJax Test Page

This page shall help demonstrate the use of the MathJax JavaScript library.

\[ \mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix} \]

Another very Interesting position I found is this: $\widehat O(\log^2N)$, also known as \(\widehat O(\log^2N)\).

\[ \prod \limits_{i=1}^{n+1}i = 1\cdot 2\cdot\dots\cdot n\cdot (n+1) \]

Here is a little bit longer text on web-typesetting mathematical formulas. Here I try to use a mathematical representation within a link: Checking the Numbers of the form \(N=2kp_1^{m_1}p_2^{m_2}\cdots p_n^{m_n}-1\) for Primality, which is in fact a very interesting text on prime numbers and one of the most cited articles in Russian mathematical journals.

\[ \Gamma(x) = \left[ x \cdot \mathrm{e}^{\gamma x} \cdot \prod_{k=1}^{\infty} \left(1+\frac{x}{k}\right) \mathrm{e}^{-x/k} \right]^{-1}, \]

\[\log\Gamma(x) = (\frac12-x)(\gamma + \log(2\pi)) + \frac12\log\frac{\pi}{\sin(\pi x)} + \frac1{\pi}\sum_{k=2}^{\infty}\frac{\log k}{k}\sin(2k\pi x),\quad 0<x<1,\]

\[G\colon\mathbb R_{>0}\to\mathbb R_{>0}, \]

\[ \begin{eqnarray} y &=& ax^2 + bx + c \\ f(x) &=& x^2 + 2xy + y^2 \\ \int\limits_0^3 x^2 dx &=& 9 \\ \iint_{-3}^0 x^\pi dx &=& 1/x \end{eqnarray} \]

\[ \begin{eqnarray} \int_a^b \left( f\left(x\right) + g\left(x\right) \right) \, \mathrm dx &=& \int_a^b f\left(x\right) \, \mathrm dx + \int_a^b g\left(x\right) \, \mathrm dx \end{eqnarray} \]

This is just a dummy paragraph.

\[ \begin{split} \left(a + b\right)^2 &= (a + b)(a + b) \\ &= a^2 + 2ab + b^2 \end{split} \]

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