# HandWiki:HelpMathEquations

HandWiki uses MathJax for rendering equations. You can show equations as this $\displaystyle{ F_2=\frac{H_1}{H^2} }$ inline. This is programmed as:

You can show equations as this $F_2=\frac{H_1}{H^2}$ inline. This is programmed as:


You can show equations using the LaTeX syntax "dollar sign":

$F_2=\frac{H_1}{H^2}$

As you can see, it positions the equation at centre. This is programmed as:

$F_2=\frac{H_1}{H^2}$


Alternatively, you can do this formula $\displaystyle{ F_2=\frac{H_1}{H^2} }$ as:

<math inline>F_2=\frac{H_1}{H^2}[/itex]


## More examples

See more examples here (original source [1].

$E=mc^2$

$\displaystyle{ E=mc^2 }$

<nowiki>$E=mc^2$</nowiki>

$E=mc^2$

## Inequality Sign Test

$1<2$

$\displaystyle{ 1\lt 2 }$

$2>1$

$\displaystyle{ 2\gt 1 }$

$1\lt 2$

$\displaystyle{ 1\lt 2 }$

$2\gt 1$

$\displaystyle{ 2\gt 1 }$

## Inequality Sign Test 2

$a<b$

$\displaystyle{ a\lt b }$

$a < b$

$\displaystyle{ a \lt b }$

$a>b$

$\displaystyle{ a\gt b }$

$a > b$

$\displaystyle{ a \gt b }$

$\displaystyle{ f(x)=1 }$

## UTF-8 Test

$전압 = 전류 \times 저항$

$\displaystyle{ 전압 = 전류 \times 저항 }$

$저항 = \frac{전압}{전류}$

$\displaystyle{ 저항 = \frac{전압}{전류} }$

## The Lorenz Equations

\begin{align} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{align}

\displaystyle{ \begin{align} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{align} }

## The Cauchy-Schwarz Inequality

$\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$

$\displaystyle{ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) }$

## A Cross Product Formula

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

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

## The probability of getting k heads when flipping n coins is

$P(E) = {n \choose k} p^k (1-p)^{ n-k}$

$\displaystyle{ P(E) = {n \choose k} p^k (1-p)^{ n-k} }$

## An Identity of Ramanujan

$\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } }$

$\displaystyle{ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } } }$

## A Rogers-Ramanujan Identity

$1 + \frac{q^2}{(1-q)} + \frac{q^6}{(1-q)(1-q^2)} + \cdots = \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad for\,|q|<1.$

$\displaystyle{ 1 + \frac{q^2}{(1-q)} + \frac{q^6}{(1-q)(1-q^2)} + \cdots = \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad for\,|q|\lt 1. }$

## Maxwell’s Equations

\begin{align} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{align}

\displaystyle{ \begin{align} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{align} }